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Bluman a.g. elementary statistics a step by step approach


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statistics book for MBA

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  • 1. This page intentionally left blank
  • 2. Important Formulas Chapter 3 Data Description ᎐ Mean for individual data: X ϭ ᎐ Mean for grouped data: X ϭ Chapter 5 Discrete Probability Distributions ͚X n ͚ f • Xm n ͙ ͚Θ X Ϫ X Ι 2 nϪ1 ͙ nΘ ͚X 2Ι Ϫ Θ͚XΙ 2 nΘn Ϫ 1Ι (Shortcut formula) sϭ or Standard deviation for grouped data: sϭ ͙ 2 nΘ͚ f • X m Ι Ϫ Θ ͚ f • Xm Ι 2 nΘn Ϫ 1Ι Range rule of thumb: s Ϸ s2 ϭ ͚[X 2 и P(X)] Ϫ m2 s ϭ ͙͚[X 2 • PΘXΙ ] Ϫ m2 Standard deviation for a sample: sϭ Mean for a probability distribution: m ϭ ͚[X и P(X)] Variance and standard deviation for a probability distribution: range 4 n! • pX • q nϪX Ϫ XΙ !X! Mean for binomial distribution: m ϭ n и p Variance and standard deviation for the binomial distribution: s2 ϭ n и p и q s ϭ ͙n • p • q Multinomial probability: n! X X X PΘXΙ ϭ • p X 1 • p2 2 • p3 3 • • • pk k X1!X2!X3! . . . Xk! 1 Binomial probability: PΘXΙ ϭ Θn Poisson probability: P(X; l) ϭ Chapter 4 Probability and Counting Rules Addition rule 1 (mutually exclusive events): P(A or B) ϭ P(A) ϩ P(B) Addition rule 2 (events not mutually exclusive): P(A or B) ϭ P(A) ϩ P(B) Ϫ P(A and B) Multiplication rule 1 (independent events): P(A and B) ϭ P(A) и P(B) Multiplication rule 2 (dependent events): P(A and B) ϭ P(A) и P(B ͉ A) Conditional probability: PΘB Խ AΙ ϭ Expectation: E(X) ϭ ͚[X и P(X)] PΘ A and BΙ PΘ AΙ ᎐ Complementary events: P(E ) ϭ 1 Ϫ P(E) Fundamental counting rule: Total number of outcomes of a sequence when each event has a different number of possibilities: k 1 и k 2 и k 3 и и и k n Permutation rule: Number of permutations of n objects n! taking r at a time is n Pr ϭ Θn Ϫ rΙ ! Combination rule: Number of combinations of r objects n! selected from n objects is n Cr ϭ Θ n Ϫ r Ι !r! X ϭ 0, 1, 2, . . . e Ϫ ␭␭X where X! Hypergeometric probability: PΘXΙ ϭ a CX • bCnϪX aϩbCn Chapter 6 The Normal Distribution Standard score z ϭ ᎐ XϪ␮ ␴ zϭ or XϪX s Mean of sample means: mX ϭ m ␴ ͙n ᎐ XϪ␮ Central limit theorem formula: z ϭ ␴ ր͙n Standard error of the mean: sX ϭ Chapter 7 Confidence Intervals and Sample Size z confidence interval for means: ᎐ X Ϫ z ␣ր2 ␴ ␴ Θ ͙n Ι Ͻ ␮ Ͻ X ϩ z ր Θ ͙n Ι ᎐ ␣ 2 t confidence interval for means: ᎐ X Ϫ t ␣ր2 s s Θ ͙n Ι Ͻ ␮ Ͻ X ϩ t ր Θ ͙n Ι ᎐ ␣ 2 z␣ր2 • ␴ E maximum error of estimate Sample size for means: n ϭ Θ Ι 2 where E is the Confidence interval for a proportion: p Ϫ Θz ␣ ր 2Ι ˆ ͙ pq ˆˆ Ͻ p Ͻ p ϩ Θz ␣ ր 2Ι ˆ n ͙ pq ˆˆ n
  • 3. ˆˆ Sample size for a proportion: n ϭ p q z␣ 2 Θ Eր Ι 2 Formula for the confidence interval for difference of two means (small independent samples, variance unequal): X and qϭ1Ϫp ˆ ˆ n Confidence interval for variance: pϭ ˆ where Θn ᎐ Θ X1 ͙ ᎐ Ϫ X2Ι Ϫ t ␣ ր 2 Θ n Ϫ 1 Ι s2 Ϫ 1Ι s2 Ͻ ␴2 Ͻ 2 ␹ right ␹2 left ᎐ ͙ Ϫ 1Ι s2 Ͻ␴Ͻ ␹2 right ͙ Θn ᎐ tϭ ᎐ XϪ␮ for any value n. If n Ͻ 30, ␴ ր͙n population must be normally distributed. sD ϭ (d.f. ϭ n Ϫ 1) Θn Ϫ 1Ι s 2 ␴2 ᎐ ᎐ Ϫ X2Ι Ϫ z␣ր2 ͙ ␴2 ␴2 1 ϩ 2 Ͻ ␮1 Ϫ ␮ 2 n1 n2 ᎐ ᎐ ᎐ ᎐ Ϫ X2 Ι Ϫ Θ␮1 Ϫ ␮ 2Ι ͙ ͙ __ pq Θ n1 ϩ n1 Ι 1 _ pϭ 2 X1 ϩ X2 n1 ϩ n2 _ _ qϭ1Ϫp p1 ϭ ˆ X1 n1 p2 ϭ ˆ X2 n2 s2 s2 1 ϩ 2 n1 n2 (d.f. ϭ the smaller of n 1 Ϫ 1 or n2 Ϫ 1) Θ p1 ˆ Ϫ p2Ι Ϫ z␣ր2 ˆ ͙ ˆ ˆ p1 q1 p2 q2 ˆ ˆ ϩ Ͻ p1 Ϫ p2 n1 n2 Ͻ Θ p1 Ϫ p2Ι ϩ z␣ ր 2 ˆ ˆ ͙ ␴2 ␴2 1 ϩ 2 n1 n2 t test for comparing two means (independent samples, variances not equal): Θ X1 Ϫ p2Ι Ϫ Θ p1 Ϫ p2Ι ˆ Formula for the confidence interval for the difference of two proportions: Ͻ ΘX1 Ϫ X2Ι ϩ z ␣ ր 2 tϭ Θ p1 ˆ where Ϫ Θ ␮1 Ϫ ␮ 2 Ι ␴2 ␴2 1 ϩ 2 n1 n2 Formula for the confidence interval for difference of two means (large samples): Θ X1 ϭ n Ϫ 1Ι z test for comparing two proportions: z test for comparing two means (independent samples): ͙ Θ d.f. and SD S ᎐ Ͻ ␮D Ͻ D ϩ t␣ր2 D ͙n ͙n (d.f. ϭ n Ϫ 1) zϭ Chapter 9 Testing the Difference Between Two Means, Two Proportions, and Two Variances Ϫ n͚D 2 Ϫ Θ͚DΙ 2 nΘn Ϫ 1Ι ͚D n ᎐ Dϭ ᎐ (d.f. ϭ n Ϫ 1) zϭ ͙ where D Ϫ t␣ր2 pϪp ˆ ͙pqրn Chi-square test for a single variance: ␹ 2 ϭ ᎐ X2 Ι D Ϫ ␮D sD ր͙n Formula for confidence interval for the mean of the difference for dependent samples: ᎐ ᎐ Θ X1 s2 s2 1 ϩ 2 n1 n2 t test for comparing two means for dependent samples: z test: z ϭ z test for proportions: z ϭ ͙ (d.f. ϭ smaller of n1 Ϫ 1 and n2 Ϫ 1) Ϫ 1Ι s2 ␹2 left Chapter 8 Hypothesis Testing XϪ␮ t test: t ϭ sր͙n ᎐ Ͻ ΘX1 Ϫ X2Ι ϩ t ␣ ր 2 Confidence interval for standard deviation: Θn s2 s2 1 ϩ 2 Ͻ ␮1 Ϫ ␮ 2 n1 n2 ͙ p1 q1 p2 q2 ˆ ˆ ˆ ˆ ϩ n1 n2 s2 1 where s 2 is the 1 s2 2 larger variance and d.f.N. ϭ n1 Ϫ 1, d.f.D. ϭ n2 Ϫ 1 F test for comparing two variances: F ϭ
  • 4. Chapter 10 Correlation and Regression Chapter 11 Other Chi-Square Tests Correlation coefficient: Chi-square test for goodness-of-fit: rϭ nΘ͚xyΙ Ϫ Θ ͚xΙΘ͚yΙ t test for correlation coefficient: t ϭ r (d.f. ϭ n Ϫ 2) ͙ nϪ2 1 Ϫ r2 The regression line equation: yЈ ϭ a ϩ bx Ϫ EΙ 2 E [d.f. ϭ (rows Ϫ 1)(col. Ϫ 1)] Ϫ Θ͚xΙΘ͚xyΙ nΘ͚x2Ι Ϫ Θ͚xΙ 2 nΘ͚xyΙ Ϫ Θ͚xΙΘ͚yΙ nΘ ͚x 2Ι Ϫ Θ͚xΙ 2 bϭ Coefficient of determination: r 2 ϭ ͙ explained variation total variation ANOVA test: F ϭ d.f.N. ϭ k Ϫ 1 d.f.D. ϭ N Ϫ k ͚y2 Ϫ a ͚y Ϫ b ͚xy nϪ2 ͙ ͚niΘXi Ϫ XGM Ι 2 kϪ1 2 sW ϭ ᎐ 1 nΘ x Ϫ X Ι 2 1ϩ ϩ n n ͚x 2 Ϫ Θ ͚xΙ 2 Ͻ y Ͻ yЈ ϩ t␣ ր 2s est ͙ ᎐ 1 nΘ x Ϫ XΙ 2 1ϩ ϩ n n ͚x2 Ϫ Θ͚xΙ 2 (d.f. ϭ n Ϫ 2) Formula for the multiple correlation coefficient: Rϭ ͙ 2 2 r yx 1 ϩ r yx 2 Ϫ 2ryx 1 • ryx 2 • rx 1x2 1 Ϫ r 21 x 2 x Formula for the F test for the multiple correlation coefficient: Fϭ Θ1 Ϫ R 2րk ր Ϫ k Ϫ 1Ι R 2Ι Θn ͚Θni Ϫ 1Ι s2 i ͚Θni Ϫ 1Ι Scheffé test: FS ϭ Θ1 ΄ Ϫ R2 ΙΘn Ϫ 1Ι nϪkϪ1 Xi Ϫ Xj 2 ͙sW րn Formulas for two-way ANOVA: SSA aϪ1 SSB MSB ϭ bϪ1 MSA ϭ MSW ϭ ΅ and Tukey test: q ϭ (d.f.N. ϭ n Ϫ k and d.f.D. ϭ n Ϫ k Ϫ 1) R2 ϭ 1 Ϫ adj Ϫ Xj Ι 2 րni ϩ 1րnjΙ ΘXi 2 sW Θ1 FЈ ϭ (k Ϫ 1)(C.V.) MSAϫB ϭ Formula for the adjusted R2: 2 sB ͚X where XGM ϭ 2 sW N where N ϭ n1 ϩ n2 ϩ и и и ϩ nk where k ϭ number of groups 2 sB ϭ Prediction interval for y: yЈ Ϫ t␣ ր 2 sest ΘO Chapter 12 Analysis of Variance Standard error of estimate: sest ϭ ΘO Chi-square test for independence and homogeneity of proportions: x2 ϭ a Θ ͚y ΙΘ ͚x2 Ι aϭ where Ϫ EΙ 2 E (d.f. ϭ no. of categories Ϫ 1) x2 ϭ a ͙[nΘ͚x2 Ι Ϫ Θ͚xΙ 2][nΘ ͚y2Ι Ϫ Θ ͚yΙ 2] Θa SSAϫB Ϫ 1ΙΘb Ϫ 1Ι SSW abΘ n Ϫ 1Ι MSA MSW MSB FB ϭ MSW FA ϭ FAϫB ϭ MSAϫB MSW
  • 5. Chapter 13 Nonparametric Statistics ϩ 0.5Ι Ϫ Θnր2Ι z test value in the sign test: z ϭ ͙n ր 2 where n ϭ sample size (greater than or equal to 26) X ϭ smaller number of ϩ or Ϫ signs Kruskal-Wallis test: ΘX Wilcoxon rank sum test: z ϭ R Ϫ mR sR where ␮R ϭ n1Θn1 ϩ n2 ϩ 1Ι 2 ͙ n 1 n 2Θn1 ϩ n 2 ϩ 1Ι 12 R ϭ sum of the ranks for the smaller sample size (n1) n1 ϭ smaller of the sample sizes n2 ϭ larger of the sample sizes n1 Ն 10 and n2 Ն 10 ␴R ϭ Wilcoxon signed-rank test: z ϭ where A ws Ϫ nΘn ϩ 1Ι 4 nΘn ϩ 1ΙΘ2n ϩ 1Ι 24 Hϭ R2 R2 12 R2 1 ϩ 2 ϩ • • • ϩ k Ϫ 3ΘN ϩ 1Ι NΘN ϩ 1Ι n1 n2 nk Θ Ι where R1 ϭ sum of the ranks of sample 1 n1 ϭ size of sample 1 R2 ϭ sum of the ranks of sample 2 n2 ϭ size of sample 2 и и и Rk ϭ sum of the ranks of sample k nk ϭ size of sample k N ϭ n1 ϩ n2 ϩ и и и ϩ nk k ϭ number of samples Spearman rank correlation coefficient: rS ϭ 1 Ϫ 6 ͚d 2 nΘn2 Ϫ 1Ι where d ϭ difference in the ranks n ϭ number of data pairs n ϭ number of pairs where the difference is not 0 ws ϭ smaller sum in absolute value of the signed ranks Procedure Table Solving Hypothesis-Testing Problems (Traditional Method) State the hypotheses and identify the claim. Step 2 Find the critical value(s) from the appropriate table in Appendix C. Step 3 Compute the test value. Step 4 Make the decision to reject or not reject the null hypothesis. Step 5 Summarize the results. Procedure Table Solving Hypothesis-Testing Problems (P-value Method) Step 1 State the hypotheses and identify the claim. Step 2 Compute the test value. Step 3 Find the P-value. Step 4 Make the decision. Step 5 Summarize the results. ISBN-13: 978–0–07–743861–6 ISBN-10: 0–07–743861–2 Step 1
  • 6. Table E The Standard Normal Distribution Cumulative Standard Normal Distribution z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 Ϫ3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 Ϫ3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003 Ϫ3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005 Ϫ3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 Ϫ3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 Ϫ2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 Ϫ2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 Ϫ2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026 Ϫ2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036 Ϫ2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 Ϫ2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064 Ϫ2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 Ϫ2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 Ϫ2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 Ϫ2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 Ϫ1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 Ϫ1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 Ϫ1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 Ϫ1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 Ϫ1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559 Ϫ1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681 Ϫ1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823 Ϫ1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985 Ϫ1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 Ϫ1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379 Ϫ0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 Ϫ0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 Ϫ0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 Ϫ0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 Ϫ0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 Ϫ0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 Ϫ0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 Ϫ0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859 Ϫ0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247 Ϫ0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641 For z values less than Ϫ3.49, use 0.0001. Area z 0
  • 7. Table E (continued ) Cumulative Standard Normal Distribution z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359 0.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714 .5753 0.2 .5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .6141 0.3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517 0.4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879 0.5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224 0.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 0.7 .7580 .7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852 0.8 .7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .8133 0.9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389 1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621 1.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830 1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015 1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177 1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319 1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441 1.6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545 1.7 .9554 .9564 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .9633 1.8 .9641 .9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 .9706 1.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767 2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817 2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857 2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890 2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9913 .9916 2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936 2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952 2.6 .9953 .9955 .9956 .9957 .9959 .9960 .9961 .9962 .9963 .9964 2.7 .9965 .9966 .9967 .9968 .9969 .9970 .9971 .9972 .9973 .9974 2.8 .9974 .9975 .9976 .9977 .9977 .9978 .9979 .9979 .9980 .9981 2.9 .9981 .9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986 .9986 3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990 3.1 .9990 .9991 .9991 .9991 .9992 .9992 .9992 .9992 .9993 .9993 3.2 .9993 .9993 .9994 .9994 .9994 .9994 .9994 .9995 .9995 .9995 3.3 .9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996 .9997 3.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9998 For z values greater than 3.49, use 0.9999. Area 0 z
  • 8. Table F The t Distribution Confidence intervals 90% 95% 98% 99% One tail, A d.f. 80% 0.10 0.05 0.025 0.01 0.005 Two tails, A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 45 50 55 60 65 70 75 80 90 100 500 1000 (z) ϱ 0.20 0.10 0.05 0.02 0.01 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.309 1.307 1.306 1.304 1.303 1.301 1.299 1.297 1.296 1.295 1.294 1.293 1.292 1.291 1.290 1.283 1.282 1.282a 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.694 1.691 1.688 1.686 1.684 1.679 1.676 1.673 1.671 1.669 1.667 1.665 1.664 1.662 1.660 1.648 1.646 1.645b 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.037 2.032 2.028 2.024 2.021 2.014 2.009 2.004 2.000 1.997 1.994 1.992 1.990 1.987 1.984 1.965 1.962 1.960 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.449 2.441 2.434 2.429 2.423 2.412 2.403 2.396 2.390 2.385 2.381 2.377 2.374 2.368 2.364 2.334 2.330 2.326c 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.738 2.728 2.719 2.712 2.704 2.690 2.678 2.668 2.660 2.654 2.648 2.643 2.639 2.632 2.626 2.586 2.581 2.576d a This value has been rounded to 1.28 in the textbook. This value has been rounded to 1.65 in the textbook. c This value has been rounded to 2.33 in the textbook. d This value has been rounded to 2.58 in the textbook. One tail Two tails b Source: Adapted from W. H. Beyer, Handbook of Tables for Probability and Statistics, 2nd ed., CRC Press, Boca Raton, Fla., 1986. Reprinted with permission. Area ␣ t Area ␣ 2 Ϫt Area ␣ 2 ϩt
  • 9. Table G The Chi-Square Distribution A Degrees of freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 50 60 70 80 90 100 — 0.010 0.072 0.207 0.412 0.676 0.989 1.344 1.735 2.156 2.603 3.074 3.565 4.075 4.601 5.142 5.697 6.265 6.844 7.434 8.034 8.643 9.262 9.886 10.520 11.160 11.808 12.461 13.121 13.787 20.707 27.991 35.534 43.275 51.172 59.196 67.328 — 0.020 0.115 0.297 0.554 0.872 1.239 1.646 2.088 2.558 3.053 3.571 4.107 4.660 5.229 5.812 6.408 7.015 7.633 8.260 8.897 9.542 10.196 10.856 11.524 12.198 12.879 13.565 14.257 14.954 22.164 29.707 37.485 45.442 53.540 61.754 70.065 0.001 0.051 0.216 0.484 0.831 1.237 1.690 2.180 2.700 3.247 3.816 4.404 5.009 5.629 6.262 6.908 7.564 8.231 8.907 9.591 10.283 10.982 11.689 12.401 13.120 13.844 14.573 15.308 16.047 16.791 24.433 32.357 40.482 48.758 57.153 65.647 74.222 0.004 0.103 0.352 0.711 1.145 1.635 2.167 2.733 3.325 3.940 4.575 5.226 5.892 6.571 7.261 7.962 8.672 9.390 10.117 10.851 11.591 12.338 13.091 13.848 14.611 15.379 16.151 16.928 17.708 18.493 26.509 34.764 43.188 51.739 60.391 69.126 77.929 0.016 0.211 0.584 1.064 1.610 2.204 2.833 3.490 4.168 4.865 5.578 6.304 7.042 7.790 8.547 9.312 10.085 10.865 11.651 12.443 13.240 14.042 14.848 15.659 16.473 17.292 18.114 18.939 19.768 20.599 29.051 37.689 46.459 55.329 64.278 73.291 82.358 2.706 4.605 6.251 7.779 9.236 10.645 12.017 13.362 14.684 15.987 17.275 18.549 19.812 21.064 22.307 23.542 24.769 25.989 27.204 28.412 29.615 30.813 32.007 33.196 34.382 35.563 36.741 37.916 39.087 40.256 51.805 63.167 74.397 85.527 96.578 107.565 118.498 3.841 5.991 7.815 9.488 11.071 12.592 14.067 15.507 16.919 18.307 19.675 21.026 22.362 23.685 24.996 26.296 27.587 28.869 30.144 31.410 32.671 33.924 35.172 36.415 37.652 38.885 40.113 41.337 42.557 43.773 55.758 67.505 79.082 90.531 101.879 113.145 124.342 5.024 7.378 9.348 11.143 12.833 14.449 16.013 17.535 19.023 20.483 21.920 23.337 24.736 26.119 27.488 28.845 30.191 31.526 32.852 34.170 35.479 36.781 38.076 39.364 40.646 41.923 43.194 44.461 45.722 46.979 59.342 71.420 83.298 95.023 106.629 118.136 129.561 6.635 9.210 11.345 13.277 15.086 16.812 18.475 20.090 21.666 23.209 24.725 26.217 27.688 29.141 30.578 32.000 33.409 34.805 36.191 37.566 38.932 40.289 41.638 42.980 44.314 45.642 46.963 48.278 49.588 50.892 63.691 76.154 88.379 100.425 112.329 124.116 135.807 7.879 10.597 12.838 14.860 16.750 18.548 20.278 21.955 23.589 25.188 26.757 28.299 29.819 31.319 32.801 34.267 35.718 37.156 38.582 39.997 41.401 42.796 44.181 45.559 46.928 48.290 49.645 50.993 52.336 53.672 66.766 79.490 91.952 104.215 116.321 128.299 140.169 Source: Owen, Handbook of Statistical Tables, Table A–4 “Chi-Square Distribution Table,” © 1962 by Addison-Wesley Publishing Company, Inc. Copyright renewal © 1990. Reproduced by permission of Pearson Education, Inc. Area ␣ ␹2
  • 10. blu38582_IFC.qxd 9/13/10 Table E 7:09 PM Page 1 The Standard Normal Distribution Cumulative Standard Normal Distribution z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 Ϫ3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 Ϫ3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003 Ϫ3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005 Ϫ3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 Ϫ3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 Ϫ2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 Ϫ2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 Ϫ2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026 Ϫ2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036 Ϫ2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 Ϫ2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064 Ϫ2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 Ϫ2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 Ϫ2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 Ϫ2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 Ϫ1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 Ϫ1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 Ϫ1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 Ϫ1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 Ϫ1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559 Ϫ1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681 Ϫ1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823 Ϫ1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985 Ϫ1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 Ϫ1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379 Ϫ0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 Ϫ0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 Ϫ0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 Ϫ0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 Ϫ0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 Ϫ0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 Ϫ0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 Ϫ0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859 Ϫ0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247 Ϫ0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641 For z values less than Ϫ3.49, use 0.0001. Area z 0
  • 11. blu38582_IFC.qxd 9/13/10 Table E 7:09 PM Page 2 (continued ) Cumulative Standard Normal Distribution z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359 0.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714 .5753 0.2 .5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .6141 0.3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517 0.4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879 0.5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224 0.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 0.7 .7580 .7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852 0.8 .7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .8133 0.9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389 1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621 1.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830 1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015 1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177 1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319 1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441 1.6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545 1.7 .9554 .9564 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .9633 1.8 .9641 .9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 .9706 1.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767 2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817 2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857 2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890 2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9913 .9916 2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936 2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952 2.6 .9953 .9955 .9956 .9957 .9959 .9960 .9961 .9962 .9963 .9964 2.7 .9965 .9966 .9967 .9968 .9969 .9970 .9971 .9972 .9973 .9974 2.8 .9974 .9975 .9976 .9977 .9977 .9978 .9979 .9979 .9980 .9981 2.9 .9981 .9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986 .9986 3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990 3.1 .9990 .9991 .9991 .9991 .9992 .9992 .9992 .9992 .9993 .9993 3.2 .9993 .9993 .9994 .9994 .9994 .9994 .9994 .9995 .9995 .9995 3.3 .9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996 .9997 3.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9998 For z values greater than 3.49, use 0.9999. Area 0 z
  • 12. blu38582_fm_i-xxviii.qxd 9/29/10 2:43 PM Page i E I G H T H E D I T I O N Elementary Statistics A Step by Step Approach Allan G. Bluman Professor Emeritus Community College of Allegheny County TM
  • 13. blu38582_fm_i-xxviii.qxd 9/29/10 2:43 PM Page ii TM ELEMENTARY STATISTICS: A STEP BY STEP APPROACH, EIGHTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Previous editions © 2009, 2007, and 2004. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 QDB/QDB 1 0 9 8 7 6 5 4 3 2 1 ISBN 978–0–07–338610–2 MHID 0–07–338610–3 ISBN 978–0–07–743858–6 (Annotated Instructor’s Edition) MHID 0–07–743858–2 Vice President, Editor-in-Chief: Marty Lange Vice President, EDP: Kimberly Meriwether David Senior Director of Development: Kristine Tibbetts Editorial Director: Stewart K. Mattson Sponsoring Editor: John R. Osgood Developmental Editor: Adam Fischer Marketing Manager: Kevin M. Ernzen Senior Project Manager: Vicki Krug Senior Buyer: Sandy Ludovissy Designer: Tara McDermott Cover Designer: Ellen Pettengell Cover Image: © Ric Ergenbright/CORBIS Senior Photo Research Coordinator: Lori Hancock Compositor: MPS Limited, a Macmillan Company Typeface: 10.5/12 Times Roman Printer: Quad/Graphics All credits appearing on page or at the end of the book are considered to be an extension of the copyright page. Library of Congress Cataloging-in-Publication Data Bluman, Allan G. Elementary statistics : a step by step approach / Allan Bluman. — 8th ed. p. cm. Includes bibliographical references and index. ISBN 978–0–07–338610–2 — ISBN 0–07–338610–3 (hard copy : alk. paper) 1. Statistics—Textbooks. I. Title. QA276.12.B59 2012 519.5—dc22 2010031466
  • 14. blu38582_fm_i-xxviii.qxd 10/7/10 7:38 AM Page iii About the Author Allan G. Bluman Allan G. Bluman is a professor emeritus at the Community College of Allegheny County, South Campus, near Pittsburgh, Pennsylvania. He has taught mathematics and statistics for over 35 years. He received an Apple for the Teacher award in recognition of his bringing excellence to the learning environment at South Campus. He has also taught statistics for Penn State University at the Greater Allegheny (McKeesport) Campus and at the Monroeville Center. He received his master’s and doctor’s degrees from the University of Pittsburgh. He is also author of Elementary Statistics: A Brief Version and co-author of Math in Our World. In addition, he is the author of four mathematics books in the McGraw-Hill DeMystified Series. They are Pre-Algebra, Math Word Problems, Business Math, and Probability. He is married and has two sons and a granddaughter. Dedication: To Betty Bluman, Earl McPeek, and Dr. G. Bradley Seager, Jr. iii
  • 15. blu38582_fm_i-xxviii.qxd 9/29/10 2:43 PM Page iv statistics Hosted by ALEKS Corp. Connect Statistics Hosted by ALEKS Corporation is an exciting, new assignment and assessment platform combining the strengths of McGraw-Hill Higher Education and ALEKS Corporation. Connect Statistics Hosted by ALEKS is the first platform on the market to combine an artificially-intelligent, diagnostic assessment with an intuitive ehomework platform designed to meet your needs. Connect Statistics Hosted by ALEKS Corporation is the culmination of a one-of-a-kind market development process involving math full-time and adjunct statistics faculty at every step of the process. This process enables us to provide you with a solution that best meets your needs. Connect Statistics Hosted by ALEKS Corporation is built by statistics educators for statistics educators! 1 Your students want a well-organized homepage where key information is easily viewable. Modern Student Homepage ▶ This homepage provides a dashboard for students to immediately view their assignments, grades, and announcements for their course. (Assignments include HW, quizzes, and tests.) ▶ Students can access their assignments through the course Calendar to stay up-to-date and organized for their class. Modern, intuitive, and simple interface. 2 You want a way to identify the strengths and weaknesses of your class at the beginning of the term rather than after the first exam. Integrated ALEKS® Assessment ▶ This artificially-intelligent (AI), diagnostic assessment identifies precisely what a student knows and is ready to learn next. ▶ Detailed assessment reports provide instructors with specific information about where students are struggling most. ▶ This AI-driven assessment is t the only one of its kind in an online homework platform. Recommended to be used as the first assignment in any course. ALEKS is a registered trademark of ALEKS Corporation. Bluman_Connect_Math.indd 2 29/09/10 10:12 AM Bluman_C
  • 16. 0 10:12 AM blu38582_fm_i-xxviii.qxd 9/29/10 2:44 PM Page v Built by Statistics Educators for Statistics Educators 3 Y Your students want an assignment page that is easy to use and includes l lots of extra help resources. Efficient Assignment Navigation ▶ Students have access to immediate feedback and help while working through assignments. ▶ Students have direct access ess to a media-rich eBook for easy r referencing. ▶ Students can view detailed, ed, step-by-step solutions written by instructors who teach the course, providing a unique solution on to each and every exercise. e 4 Students can easily monitor and track their progress on a given assignment. Y You want a more intuitive and efficient assignment creation process b because of your busy schedule. Assignment Creation Process ▶ Instructors can select textbookspecific questions organized by chapter, section, and objective. ▶ Drag-and-drop functionality makes creating an assignment quick and easy. ▶ Instructors can preview their assignments for efficient editing. TM Bluman_Connect_Math.indd 3 29/09/10 10:12 AM
  • 17. blu38582_fm_i-xxviii.qxd 9/29/10 2:44 PM Page vi statistics Hosted by ALEKS Corp. 5 Your students want an interactive eBook with rich functionality integrated into the product. statistics Hosted by ALEKS Corp. Integrated Media-Rich eBook ▶ A Web-optimized eBook is seamlessly integrated within ConnectPlus Statistics Hosted by ALEKS Corp for ease of use. ▶ Students can access videos, images, and other media in context within each chapter or subject area to enhance their learning experience. ▶ Students can highlight, take notes, or even access shared instructor highlights/notes to learn the course material. ▶ The integrated eBook provides students with a cost-saving alternative to traditional textbooks. 6 You want a flexible gradebook that is easy to use. Flexible Instructor Gradebook ▶ Based on instructor feedback, Connect Statistics Hosted by ALEKS Corp’s straightforward design creates an intuitive, visually pleasing grade management environment. ▶ Assignment types are color-coded for easy viewing. ▶ The gradebook allows instructors the flexibility to import and export additional grades. Instructors have the ability to drop grades as well as assign extra credit. Bluman_Connect_Math.indd 4 29/09/10 10:12 AM Bluman_C
  • 18. 0 10:12 AM blu38582_fm_i-xxviii.qxd 9/29/10 2:44 PM Page vii Built by Statistics Educators for Statistics Educators 7 Y You want algorithmic content that was developed by math faculty to e ensure the content is pedagogically sound and accurate. Digital Content Development Story The development of McGraw-Hill’s Connect Statistics Hosted by ALEKS Corp. content involved collaboration between McGraw-Hill, experienced instructors, and ALEKS, a company known for its high-quality digital content. The result of this process, outlined below, is accurate content created with your students in mind. It is available in a simple-to-use interface with all the functionality tools needed to manage your course. 1. McGraw-Hill selected experienced instructors to work as Digital Contributors. 2. The Digital Contributors selected the textbook exercises to be included in the algorithmic content to ensure appropriate coverage of the textbook content. 3. The Digital Contributors created detailed, stepped-out solutions for use in the Guided Solution and Show Me features. 4. The Digital Contributors provided detailed instructions for authoring the algorithm specific to each exercise to maintain the original intent and integrity of each unique exercise. 5. Each algorithm was reviewed by the Contributor, went through a detailed quality control process by ALEKS Corporation, and was copyedited prior to being posted live. Connect Statistics Hosted by ALEKS Corp. Built by Statistics Educators for Statistics Educators Lead Digital Contributors Tim Chappell Metropolitan Community College, Penn Valley Digital Contributors Al Bluman, Community College of Allegheny County John Coburn, St. Louis Community College, Florissant Valley Vanessa Coffelt, Blinn College Donna Gerken, Miami-Dade College Kimberly Graham J.D. Herdlick, St. Louis Community College, Meramec Jeremy Coffelt Blinn College Nancy Ikeda Fullerton College Vickie Flanders, Baton Rouge Community College Nic LaHue, Metropolitan Community College, Penn Valley Nicole Lloyd, Lansing Community College Jackie Miller, The Ohio State University Anne Marie Mosher, St. Louis Community College, Florissant Valley Reva Narasimhan, Kean University David Ray, University of Tennessee, Martin Amy Naughten Kristin Stoley, Blinn College Stephen Toner, Victor Valley College Paul Vroman, St. Louis Community College, Florissant Valley Michelle Whitmer, Lansing Community College TM Bluman_Connect_Math.indd 5 29/09/10 10:12 AM
  • 19. blu38582_fm_i-xxviii.qxd 9/29/10 2:44 PM Page viii Contents Preface xii CHAPTE R 2–2 The Histogram 51 1 The Frequency Polygon 53 The Ogive 54 The Nature of Probability and Statistics 1 Relative Frequency Graphs 56 Distribution Shapes 59 Introduction 2 1–1 1–2 1–3 Descriptive and Inferential Statistics 3 Variables and Types of Data 6 Data Collection and Sampling Techniques 9 2–3 Observational and Experimental Studies 13 Uses and Misuses of Statistics 16 Suspect Samples 17 Ambiguous Averages 17 Changing the Subject 17 Detached Statistics 18 Implied Connections 18 Misleading Graphs 18 Faulty Survey Questions 18 1–6 Pareto Charts 70 The Time Series Graph 71 The Pie Graph 73 Misleading Graphs 76 Stem and Leaf Plots 80 Summary 94 CHAPTE R Introduction 104 3–1 Frequency Distributions and Graphs 35 Measures of Central Tendency 105 The Mean 106 The Median 109 The Mode 111 The Midrange 114 Summary 25 2 3 Data Description 103 Computers and Calculators 19 CHAPTE R Other Types of Graphs 68 Bar Graphs 69 Random Sampling 10 Systematic Sampling 11 Stratified Sampling 12 Cluster Sampling 12 Other Sampling Methods 12 1–4 1–5 Histograms, Frequency Polygons, and Ogives 51 The Weighted Mean 115 Distribution Shapes 117 3–2 Measures of Variation 123 Range 124 Population Variance and Standard Deviation 125 Introduction 36 2–1 Sample Variance and Standard Deviation 128 Organizing Data 37 Variance and Standard Deviation for Grouped Data 129 Categorical Frequency Distributions 38 Grouped Frequency Distributions 39 Coefficient of Variation 132 All examples and exercises in this textbook (unless cited) are hypothetical and are presented to enable students to achieve a basic understanding of the statistical concepts explained. These examples and exercises should not be used in lieu of medical, psychological, or other professional advice. Neither the author nor the publisher shall be held responsible for any misuse of the information presented in this textbook. viii
  • 20. blu38582_fm_i-xxviii.qxd 9/29/10 2:44 PM Page ix Contents Range Rule of Thumb 133 Chebyshev’s Theorem 134 The Empirical (Normal) Rule 136 3–3 Measures of Position 142 Standard Scores 142 Percentiles 143 Quartiles and Deciles 149 Outliers 151 3–4 Mean 259 Variance and Standard Deviation 262 Expectation 264 5–3 5–4 The Binomial Distribution 270 Other Types of Distributions (Optional) 283 The Multinomial Distribution 283 The Poisson Distribution 284 The Hypergeometric Distribution 286 Summary 292 Exploratory Data Analysis 162 The Five-Number Summary and Boxplots 162 Summary 171 CHAPTE R CHAPTE R 4 Probability and Counting Rules 181 The Normal Distribution 299 Introduction 300 6–1 Introduction 182 4–1 4–2 4–3 The Addition Rules for Probability 199 The Multiplication Rules and Conditional Probability 211 The Multiplication Rules 211 Conditional Probability 216 Probabilities for “At Least” 218 4–4 4–5 6–2 6–3 CHAPTE R 6–4 CHAPTE R 5–2 Probability Distributions 253 Mean, Variance, Standard Deviation, and Expectation 259 7 Confidence Intervals and Sample Size 355 Introduction 356 7–1 Confidence Intervals for the Mean When s Is Known 357 Confidence Intervals 358 Sample Size 363 7–2 Introduction 252 5–1 The Normal Approximation to the Binomial Distribution 340 Summary 347 5 Discrete Probability Distributions 251 The Central Limit Theorem 331 Distribution of Sample Means 331 Finite Population Correction Factor (Optional) 337 Probability and Counting Rules 237 Summary 242 Applications of the Normal Distribution 316 Finding Data Values Given Specific Probabilities 319 Determining Normality 322 Counting Rules 224 The Fundamental Counting Rule 224 Factorial Notation 227 Permutations 227 Combinations 229 Normal Distributions 302 The Standard Normal Distribution 304 Finding Areas Under the Standard Normal Distribution Curve 305 A Normal Distribution Curve as a Probability Distribution Curve 307 Sample Spaces and Probability 183 Basic Concepts 183 Classical Probability 186 Complementary Events 189 Empirical Probability 191 Law of Large Numbers 193 Subjective Probability 194 Probability and Risk Taking 194 6 7–3 Confidence Intervals for the Mean When s Is Unknown 370 Confidence Intervals and Sample Size for Proportions 377 Confidence Intervals 378 Sample Size for Proportions 379 ix
  • 21. blu38582_fm_i-xxviii.qxd 9/29/10 2:44 PM Page x Contents x 7–4 Confidence Intervals for Variances and Standard Deviations 385 Summary 392 CHAPTE R 8 Hypothesis Testing 399 Introduction 400 8–1 8–2 Steps in Hypothesis Testing—Traditional Method 401 z Test for a Mean 413 P-Value Method for Hypothesis Testing 418 8–3 8–4 8–5 8–6 t Test for a Mean 427 z Test for a Proportion 437 x2 Test for a Variance or Standard Deviation 445 Additional Topics Regarding Hypothesis Testing 457 Confidence Intervals and Hypothesis Testing 457 10–2 Regression 551 Line of Best Fit 551 Determination of the Regression Line Equation 552 10–3 Coefficient of Determination and Standard Error of the Estimate 565 Types of Variation for the Regression Model 565 Residual Plots 568 Coefficient of Determination 569 Standard Error of the Estimate 570 Prediction Interval 572 10–4 Multiple Regression (Optional) 575 The Multiple Regression Equation 577 Testing the Significance of R 579 Adjusted R 2 579 Summary 584 Type II Error and the Power of a Test 459 Summary 462 CHAPTE R 9 Testing the Difference Between Two Means, Two Proportions, and Two Variances 471 Introduction 472 9–1 9–2 9–3 9–4 9–5 Testing the Difference Between Two Means: Using the z Test 473 Testing the Difference Between Two Means of Independent Samples: Using the t Test 484 Testing the Difference Between Two Means: Dependent Samples 492 Testing the Difference Between Proportions 504 Testing the Difference Between Two Variances 513 Summary 524 Hypothesis-Testing Summary 1 532 CHAPTE R 10 Correlation and Regression 533 Introduction 534 10–1 Scatter Plots and Correlation 535 Correlation 538 CHAPTE R 11 Other Chi-Square Tests 591 Introduction 592 11–1 Test for Goodness of Fit 593 Test of Normality (Optional) 598 11–2 Tests Using Contingency Tables 606 Test for Independence 606 Test for Homogeneity of Proportions 611 Summary 621 CHAPTE R 12 Analysis of Variance 629 Introduction 630 12–1 One-Way Analysis of Variance 631 12–2 The Scheffé Test and the Tukey Test 642 Scheffé Test 642 Tukey Test 644 12–3 Two-Way Analysis of Variance 647 Summary 661 Hypothesis-Testing Summary 2 669
  • 22. blu38582_fm_i-xxviii.qxd 9/29/10 2:44 PM Page xi Contents xi APPENDIX A Algebra Review 753 APPENDIX B–1 Writing the Research Report 759 APPENDIX B–2 Bayes’ Theorem 761 APPENDIX B–3 Alternate Approach to the Standard Normal Distribution 765 The Wilcoxon Rank Sum Test 683 The Wilcoxon Signed-Rank Test 688 The Kruskal-Wallis Test 693 The Spearman Rank Correlation Coefficient and the Runs Test 700 APPENDIX C Tables 769 APPENDIX D Data Bank 799 Rank Correlation Coefficient 700 APPENDIX E Glossary 807 APPENDIX F Bibliography 815 APPENDIX G Photo Credits 817 APPENDIX H Selected Answers SA–1 Instructor’s Edition replaces Appendix H with all answers and additional material for instructors. CHAPTE R 13 Nonparametric Statistics 671 Introduction 672 13–1 Advantages and Disadvantages of Nonparametric Methods 673 Advantages 673 Disadvantages 673 Ranking 673 13–2 The Sign Test 675 Single-Sample Sign Test 675 Paired-Sample Sign Test 677 13–3 13–4 13–5 13–6 The Runs Test 702 Summary 710 Hypothesis-Testing Summary 3 716 CHAPTE R 14 Sampling and Simulation 719 Introduction 720 14–1 Common Sampling Techniques 721 Random Sampling 721 Systematic Sampling 725 Stratified Sampling 726 Cluster Sampling 728 Other Types of Sampling Techniques 729 14–2 Surveys and Questionnaire Design 736 14–3 Simulation Techniques and the Monte Carlo Method 739 The Monte Carlo Method 739 Summary 745 Index I–1
  • 23. blu38582_fm_i-xxviii.qxd 9/29/10 2:44 PM Page xii Preface Approach Elementary Statistics: A Step by Step Approach was written as an aid in the beginning statistics course to students whose mathematical background is limited to basic algebra. The book follows a nontheoretical approach without formal proofs, explaining concepts intuitively and supporting them with abundant examples. The applications span a broad range of topics certain to appeal to the interests of students of diverse backgrounds and include problems in business, sports, health, architecture, education, entertainment, political science, psychology, history, criminal justice, the environment, transportation, physical sciences, demographics, eating habits, and travel and leisure. About This Book While a number of important changes have been made in the eighth edition, the learning system remains untouched and provides students with a useful framework in which to learn and apply concepts. Some of the retained features include the following: • Over 1800 exercises are located at the end of major sections within each chapter. • Hypothesis-Testing Summaries are found at the end of Chapter 9 (z, t, x2, and F tests for testing means, proportions, and variances), Chapter 12 (correlation, chi-square, and ANOVA), and Chapter 13 (nonparametric tests) to show students the different types of hypotheses and the types of tests to use. • A Data Bank listing various attributes (educational level, cholesterol level, gender, etc.) for 100 people and several additional data sets using real data are included and referenced in various exercises and projects throughout the book. • An updated reference card containing the formulas and the z, t, x2, and PPMC tables is included with this textbook. • End-of-chapter Summaries, Important Terms, and Important Formulas give students a concise summary of the chapter topics and provide a good source for quiz or test preparation. • Review Exercises are found at the end of each chapter. • Special sections called Data Analysis require students to work with a data set to perform various statistical tests or procedures and then summarize the results. The data are included in the Data Bank in Appendix D and can be downloaded from the book’s website at • Chapter Quizzes, found at the end of each chapter, include multiple-choice, true/false, and completion questions along with exercises to test students’ knowledge and comprehension of chapter content. • The Appendixes provide students with an essential algebra review, an outline for report writing, Bayes’ theorem, extensive reference tables, a glossary, and answers to all quiz questions, all odd-numbered exercises, selected even-numbered exercises, and an alternate method for using the standard normal distribution. • The Applying the Concepts feature is included in all sections and gives students an opportunity to think about the new concepts and apply them to hypothetical examples and scenarios similar to those found in newspapers, magazines, and radio and television news programs. xii
  • 24. blu38582_fm_i-xxviii.qxd 9/29/10 2:44 PM Page xiii Preface Changes in the Eighth Edition xiii Overall • Added over 30 new Examples and 250 new Exercises throughout the book. • Chapter summaries were revised into bulleted paragraphs representing each section from the chapter. • New Historical Notes and Interesting facts have been added throughout the book. Chapter 1 Updated and added new Speaking of Statistics. Revised the definition of nominal level of measurement. Chapter 6 Revised presentation for finding areas under the standard normal distribution curve. New figures created to clarify explanations for steps in the Central Limit Theorem. Chapter 7 Changed section 7.1 to Confidence Intervals for the Mean When s is Known. Maximum error of the estimate has been updated to the margin of error. Updated the Formula for the Confidence Interval of the Mean for a Specific a to include when s is Known. Added assumptions for Finding a Confidence Interval for a Mean When s is Known. Revised the explanation for rounding up when determining sample size. Added assumptions for Finding a Confidence Interval for a Mean when s is Unknown. Added assumptions for Finding a Confidence Interval for a Population Proportion. Added assumptions for Finding a Confidence Interval for a Variance or Standard Deviation. Chapter 8 Added assumptions for the z Test for a Mean When s Is Known. Added assumptions for the t Test for a Mean When s Is Unknown. Added assumptions for Testing a Proportion. Chapter 9 Revised the assumptions for the z Test to Determine the Difference Between Two Means. Added that it will be assumed that variances are not equal when using a t test to test the difference between means when the two samples are independent and when the samples are taken from two normally or approximately normally distributed populations. Added assumptions for the t Test for Two Independent Means When s1 and s2 Are Unknown. Added assumptions for the t Test for Two Means When the Samples Are Dependent. Added assumptions for the z Test for Two Proportions. Revised the assumptions for Testing the Difference Between Two Variables. Chapter 10 Added assumptions for the Correlation Coefficient. Residuals, are now covered in full with figures illustrating different examples of Residual Plots.
  • 25. blu38582_fm_i-xxviii.qxd xiv 9/29/10 2:44 PM Page xiv Preface Acknowledgments It is important to acknowledge the many people whose contributions have gone into the Eighth Edition of Elementary Statistics. Very special thanks are due to Jackie Miller of The Ohio State University for her provision of the Index of Applications, her exhaustive accuracy check of the page proofs, and her general availability and advice concerning all matters statistical. The Technology Step by Step sections were provided by Gerry Moultine of Northwood University (MINITAB), John Thomas of College of Lake County (Excel), and Michael Keller of St. Johns River Community College (TI-83 Plus and TI-84 Plus). I would also like to thank Diane P. Cope for providing the new exercises; Kelly Jackson for writing the new Data Projects; and Sally Robinson for error checking, adding technology-accurate answers to the answer appendix, and writing the Solutions Manuals. Finally, at McGraw-Hill Higher Education, thanks to John Osgood, Sponsoring Editor; Adam Fischer, Developmental Editor; Kevin Ernzen, Marketing Manager; Vicki Krug, Project Manager; and Sandra Schnee, Senior Media Project Manager. Allan G. Bluman Special thanks for their advice and recommendations for revisions found in the Eighth Edition go to Rosalie Abraham, Florida State College, South Campus James Ball, Indiana State University Luis Beltran, Miami Dade College Abraham Biggs, Broward College Melissa Bingham, University of Wisconsin–Lacrosse Don Brown, Macon State College Richard Carney, Camden County College Joe Castillo, Broward College James Cook, Belmont University Rosemary Danaher, Sacred Heart University Gregory Davis, University of Wisconsin–Green Bay Hemangini Deshmukh, Mercy Hurst College Abdulaziz Elfessi, University of Wisconsin–Lacrosse Nancy Eschen, Florida State College, South Campus Elaine Fitt, Bucks County Community College David Gurney, Southeastern Louisiana University John Todd Hammond, Truman State University Willard Hannon, Las Positas College James Helmreich, Marist College Dr. James Hodge, Mountain State University Kelly Jackson, Camden County College Rose Jenkins, Midlands Technical College June Jones, Macon State College Grazyna Kamburowska, State University College–Oneonta Jong Sung Kim, Portland State University Janna Liberant, Rockland Community College Scott McClintock, West Chester University of Pennsylvania James Meyer, University of Wisconsin–Green Bay David Milazzo, Niagara County Community College–Sanborn Tommy Minton, Seminole Community College Jason Molitierno, Sacred Heart University Barry Monk, Macon State College Carla Monticelli, Camden County College Lyn Noble, Florida State College, South Campus Jeanne Osborne, Middlesex County College Ronald Persky, Christopher Newport University Blanche Presley, Macon State College William Radulovich, Florida State College, South Campus Azar Raiszadeh, Chattanooga State College Kandethody Ramachandran, Hillsborough Community College–Brandon Dave Reineke, University of Wisconsin–Lacrosse Vicki Schell, Pensacola Junior College James Seibert, Regis University Lee Seltzer, Florida State College, South Campus Christine Tirella, Niagara County Community College–Sanborn Christina Vertullo, Marist College Jen-Ting Wang, State University College–Oneonta Xubo Wang, Macon State College Yajni Warnapala, Roger Williams University Robert White, Allan Hancock College Bridget Young, Suffolk County Community College Bashar Zogheib, Nova Southeastern College
  • 26. blu38582_fm_i-xxviii.qxd 9/29/10 2:45 PM Page xv Guided Tour: Features and Supplements Each chapter begins with an outline and a list of learning objectives. The objectives are repeated at the beginning of each section to help students focus on the concepts presented within that section. C H A P T E 592 Outline After completing this chapter, you should be able to Introduction 1 for terval ence in e or stanconfid c find a ngle varian to and 8 bout a si mple pters 7 sa “If a sa h the in Cha hypothesi ch as a s used ns, su lected wit e o tion on wa and to test c ti ibutio se c trodu are distribu eviation y distr h color be independen In nc freque he hi squ l ac d rd d Over 300 examples with detailed solutions serve as models to help students solve problems on their own. Examples are solved by using a step by step explanation, and illustrations provide a clear display of results for students. Find probabilities for a normally distributed variable by transforming it into a standard normal variable. 5 ., D on. ges, Jr rmissi : J. Hod with pe Source 229. Used 8– pp. 22 Identify the properties of a normal distribution. 4 tics Statis day To Identify distributions as symmetric or skewed. 2 3 s are nciple his pri ty of peas e s, and enetic grow a vari s that had g udied time to ea 84), st results ding p 22–18 d his spare crossbree ed that the some eredity el (18 l use o c lved s and H, Gregor Mend cs. Menderiments invon seeds. He nthtiyellow seeds, green c Statisti rian monk odern geneti any expe kled gree had smoo had wrinkledmed to st m m me wrin ffspring e see ption An Au ndation for ne of his and so at had ch typ eo e fou nastery. O with peas th some of th ellow seeds, tages of ea n the assum d his th dy rcen t is, e mo ow seeds sed o n crossbre Tha rinkle ts, the pe theory ba at th yell larity. n had w e the smooth d with regu eds, some l experime ulated his results. H theory e e rm se ra e if his in this occurr ooth green , after seve . Mendel fo predict th s to se to e d had sm Furthermore ly the sam s and tried generation. tical result is explaine re te t it seeds. approxima cessive tra ver the nex ith the theo test, which w o ), w-Hill remain inant and re 556 seeds tual results chi-square is chapter. McGra ” c York: of dom d examined pared the a d a “simple e end of th s (New atistic at th use s an com n to St pea , he ductio isited y, he l Intro Finall To do this oday—Rev pirica An Em ics T orrect. at Lab, eld, St was c See Statist rutchfi d R. C ter. , an chap . Krech 6 The Normal Distribution Objectives Tests quare Chi-S Other er 11 Chapt R Find specific data values for given percentages, using the standard normal distribution. 6–1 Normal Distributions 6–2 Applications of the Normal Distribution Find the area under the standard normal distribution, given various z values. 6–3 The Central Limit Theorem 6–4 The Normal Approximation to the Binomial Distribution Summary The outline and learning objectives are followed by a feature titled Statistics Today, in which a real-life problem shows students the relevance of the material in the chapter. This problem is subsequently solved near the end of the chapter by using the statistical techniques presented in the chapter. 38 Chapter 2 Freque ncy Distrib utions and Graphs Two typ frequency es of frequen cy structing distribution and distributions tha the grou these dis t are mo ped tributions st are show frequency distri often used are the Categor n now. bution. Th ical Freq e proced categorical ures for The categ uency conDistrib or utions gories, su ical frequency distribut ch as nomi ion is us religious nal- or or ed for da affiliatio dinal-lev ta that ca n, or major el Exampl n be place field of stu data. For example e 2–1 d in sp , da dy would Distribut use categ ta such as politica ecific cateorical fre ion of Bl quency dis l affiliation, ood Type Twentytributions s five arm . y inductee data set is s were giv en a blo od test to A determine B their blo B O od type. AB O The O B B AB B B O A A O O O AB O A AB Construct O B a frequen A cy distri bution fo Solutio r the data. n Since the data are A, B, O, ca and AB. tegorical, discre These typ te classe The pr s can be es used given ne ocedure for cons will be used as xt. the classe . There are four tructing a frequen s for the blood typ Step 1 cy distri es: bution fo distribution. Make a tab r categor le as show ical data n. is A B Class Tally C Frequenc A D y Percent B O AB Step 2 Tally the data and Step 3 place the Count the results in tallies an column B. Step 4 d pla ce the res Find the ults in co percenta lumn C. ge of value s in each f l % xv
  • 27. 9/29/10 2:45 PM Page xvi re al change s a perso is not enough ev n’s chole idence to sterol lev support the claim el. The steps that for this t test are su mmarize d in the Procedur Proced e Table. ure Tabl e Exercises 8–2 State the hypotheses and identify the claim. Find the critical value(s). Compute the test value. Make the decision. Summarize the results. Use diagrams to show the critical region (or regions), and use the traditional method of hypothesis testing unless otherwise specified. 1. Warming and Ice Melt The average depth of the Hudson Bay is 305 feet. Climatologists were interested in seeing if the effects of warming and ice melt were affecting the water level. Fifty-five measurements over a period of weeks yielded a sample mean of 306.2 feet. The population variance is known to be 3.57. Can it be concluded at the 0.05 level of significance that the average depth has increased? Is there evidence of what caused this to happen? Source: World Almanac and Book of Facts 2010. 2. Credit Card Debt It has been reported that the average credit card debt for college seniors at the college book store for a specific college is $3262. The student senate at a large university feels that their seniors have a debt much less than this, so it conducts a study of 50 randomly selected seniors and finds that the average debt is $2995, and the population standard deviation is $1100. With a ϭ 0.05, is the student senate correct? 3. Revenue of Large Businesses Aresearcher estimates that the average revenue of the largest businesses in the United States is greater than $24 billion. A sample of 50 companies is selected, and the revenues (in billions of dollars) are shown. At a ϭ 0.05, is there enough evidence to support the researcher’s claim? Assume s ϭ 28.7. 178 122 91 44 35 61 30 29 41 31 24 25 24 22 56 28 16 38 30 16 25 23 21 46 28 16 36 19 15 18 17 20 20 20 19 15 19 15 14 17 17 32 27 15 25 19 19 15 22 20 Testing th Step 1 Step 2 Step 3 e Between Samples X1 A X2 D‫؍‬X 1 ؊ X B 2 D 2 ‫( ؍‬X 1 ؊ X )2 2 ͚D ϭ b. Find the differ ences an 2 ͚D ϭ d place the DϭX Ϫ results in 1 X2 column A. c. Find the mean of the dif ferences. D ϭ ͚D n d. Squa re the dif ferences and place D 2 ϭ (X the result s in colum 1 Ϫ X )2 2 n B. Comp e. Find lete the tab the stand ard devia le. tion of the difference sD ϭ n ͚D 2 Ϫ Θ͚D 2 s. Ι A nΘn Ϫ 1Ι f. Find the test value . t ϭ D Ϫ mD sD ր 2n with d.f. ϭnϪ1 Make the decision . Summari ze the res ults Unusual Stat Source: New York Times Almanac. 4. Moviegoers The average “moviegoer” sees 8.5 movies a year. A moviegoer is defined as a person who sees at least one movie in a theater in a 12-month period. A random sample of 40 moviegoers from a large university revealed that the average number of movies seen per person was 9.6. The population standard deviation is 3.2 movies. At the 0.05 level of significance, can it be concluded that this represents a difference from the national average? About 4% of America ns spen d at least one night in jail ea ch year. Source: MPAA Study. 5. Nonparental Care According to the Digest of Educational Statistics, a certain group of preschool children under the age of one year each spends an average of 30.9 hours per week in nonparental care. A study of state university center-based programs indicated that a random sample of 32 infants spent an average of 32.1 hours per week in their care. The standard deviation of the population is 3.6 hours. At a ϭ 0.01 is there sufficient evidence to conclude that the sample mean differs from the national mean? Step 4 Step 5 Numerous Procedure Tables summarize processes for students’ quick reference. All use the step by step method. Source: 8–24 Numerous examples and exercises use real data. The icon shown here indicates that the data set for the exercise is available in a variety of file formats on the text’s website and Data CD. Section 14–1 Common Sampling Techniques e Differenc Means for State the Dependen hypotheses t and identi Find the fy the cla critical va im. lue(s). Compute the test va lue. a. Make a table, as shown. … a. b. c. d. e. Figure 2–2 Histogr am Example for 2–4 Section 2–2 His tograms, Frequency Polygons , and Og ives Recor y 18 d High Tem peratures 15 Historical Note Frequency For Exercises 1 through 13, perform each of the following steps. … blu38582_fm_i-xxviii.qxd 12 9 Graphs originate d when an 6 cient astronome rs drew 3 the position of the sta rs in the heav 0 ens. Roma n surveyors 99.5° also used 104.5° coordina 109.5° tes to loc 114.5° ate landmark 119.5° s on the Temperatu 124.5° Step 2 ir x maps. re (°F) 129.5° Represen 134.5° t the frequ The deve Step 3 ency on lopment Using the the y axis of statis tical and the cla Figure 2– frequencies as the can be tra graphs ss bounda 2. heights, ced to ries on the draw verti William As the x axis. Playfair cal bars 109.5–114 histogram show for each (1748–1 s, class. Se 819), an clusterin .5, followed by 13 the class with the e enginee g around r and dra greatest for 114.5 it. fter number –119.5. Th who used of data va e graph als graphs to lues (1 present o has on econom e peak wi 8) is The Freq ic data pic th the da uency torially. ta Poly Anoth 725 Speaking of Statistics Should We Be Afraid of Lightning? The National Weather Service collects various types of data about the weather. For example, each year in the United States about 400 million lightning strikes occur. On average, 400 people are struck by lightning, and 85% of those struck are men. About 100 of these people die. The cause of most of these deaths is not burns, even though temperatures as high as 54,000°F are reached, but heart attacks. The lightning strike short-circuits the body’s autonomic nervous system, causing the heart to stop beating. In some instances, the heart will restart on its own. In other cases, the heart victim will need emergency resuscitation. The most dangerous places to be during a thunderstorm are open fields, golf courses, under trees, and near water, such as a lake or swimming pool. It’s best to be inside a building during a thunderstorm although there’s no guarantee that the building won’t be struck by lightning. Are these statistics descriptive or inferential? Why do you think more men are struck by lightning than women? Should you be afraid of lightning? er way to Exampl e 2–5 gon represen t the same data set The frequ is by using a frequen points plo ency polygon cy polyg is on. represen tted for the frequ a graph that dis ted by the en pla heights cies at the midp ys the data by of the po us oints of the class ing lines that co ints. es. The nn Example frequencie ect 2–5 show s are s the procedur e for cons tructing Record a frequen High Te cy polyg mperatu on. Using the res frequency distributio n given in Solutio Example n 2–4 c Historical Notes, Unusual Stats, and Interesting Facts, located in the margins, make statistics come alive for the reader. The Speaking of Statistics sections invite students to think about poll results and other statistics-related news stories in another connection between statistics and the real world. Rules and definitions are set off for easy referencing by the student. 418 Chapter 8 Hypothesis Testing Again, remember that nothing is being proved true or false. The statistician is only stating that there is or is not enough evidence to say that a claim is probably true or false. As noted previously, the only way to prove something would be to use the entire population under study, and usually this cannot be done, especially when the population is large. P-Value Method for Hypothesis Testing Statisticians usually test hypotheses at the common a levels of 0.05 or 0.01 and sometimes at 0.10. Recall that the choice of the level depends on the seriousness of the type I error. Besides listing an a value, many computer statistical packages give a P-value for hypothesis tests. The P-value (or probability value) is the probability of getting a sample statistic (such as the mean) or a more extreme sample statistic in the direction of the alternative hypothesis when the null hypothesis is true. I xvi th d th P l i th t l d th t d d l di t ib ti 53
  • 28. blu38582_fm_i-xxviii.qxd 9/29/10 2:46 PM Page xvii Critical Thinking sections at the end of each chapter challenge students to apply what they have learned to new situations. The problems presented are designed to deepen conceptual understanding and/or to extend topical coverage. At the end of appropriate sections, Technology Step by Step boxes show students how to use MINITAB, the TI-83 Plus and TI-84 Plus graphing calculators, and Excel to solve the types of problems covered in the section. Instructions are presented in numbered steps, usually in the context of examples—including examples from the main part of the section. Numerous computer or calculator screens are displayed, showing intermediate steps as well as the final answer. 248 Chapter 4 Probability and Counting Rules Critical Thinking Challenges 1. Con Man Game Consider this problem: A con man has 3 coins. One coin has been specially made and has a head on each side. A second coin has been specially made, and on each side it has a tail. Finally, a third coin has a head and a tail on it. All coins are of the same denomination. The con man places the 3 coins in his pocket, selects one, and shows you one side. It is heads. He is willing to bet you even money that it is the two-headed coin. His reasoning is that it can’t be the two-tailed coin since a head is showing; therefore, there is a 50-50 chance of it being the two-headed coin. Would you take the bet? (Hint: See Exercise 1 in Data Projects.) 2. de Méré Dice Game Chevalier de Méré won money when he bet unsuspecting patrons that in 4 rolls of 1 die, he could get at least one 6; but he lost money when he bet that in 24 rolls of 2 dice, he could get at least a double 6. Using the probability rules, find the probability of each event and explain why he won the majority of the time on the first game but lost the majority of the time when playing the second game. (Hint: Find the probabilities of losing each game and subtract from 1.) 3. Classical Birthday Problem How many people do you MINITAB Step by Step In a study to determine a person’s yearly income 10 years after high school, it was found that the two biggest predictors are number of math courses taken and number of hours worked per week during a person’s senior year of high school. The multiple regression equation generated from a sample of 20 individuals is yЈ ϭ 6000 ϩ 4540x1 ϩ 1290x2 6. 7. 8. 9. 10. What is the dependent variable? What are the independent variables? What are the multiple regression assumptions? Explain what 4540 and 1290 in the equation tell us. What is the predicted income if a person took 8 math classes and worked 20 hours per week during her or his senior year in high school? What does a multiple correlation coefficient of 0.77 mean? Compute R2. Compute the adjusted R2. Would the equation be considered a good predictor of income? What are your conclusions about the relationship among courses taken, hours worked, and yearly income? See page 590 for the answers. Data Projects 1. Business and Finance Use 30 stocks classified as the Dow Jones industrials as the sample. Note the amount each stock has gained or lost in the last quarter. Compute the mean and standard deviation for the data set. Compute the 95% confidence interval for the mean and the 95% confidence interval for the standard deviation. Compute the percentage of stocks that had a gain in the last quarter. Find a 95% confidence interval for the percentage of stocks with a gain. 2. Sports and Leisure Use the top home run hitter from each major league baseball team as the data set. Find the mean and the standard deviation for the number of home runs hit by the top hitter on each team. Find a 95% confidence interval for the mean number of home runs hit. 3. Technology Use the data collected in data project 3 of Chapter 2 regarding song lengths. Select a specific genre, and compute the percentage of songs in the sample that are of that genre. Create a 95% confidence interval for the true percentage. Use the entire music library, and find the population percentage of the library with that genre. Does the population percentage fall within the confidence interval? P(at least 2 people have the same birthday) Pk ϭ 1 Ϫ 365 k 365 Using your calculator, complete the table and verify that for at least a 50% chance of 2 people having the same birthday, 23 or more people will be needed. Number of people Probability that at least 2 have the same birthday Determining Normality There are several ways in which statisticians test a data set for normality. Four are shown here. Inspect the histogram for shape. 1. Enter the data in the first column of a new worksheet. Name the column Inventory. 2. Use Stat>Basic Statistics>Graphical Summary presented in Section 3–3 to create the histogram. Is it symmetric? Is there a single peak? Check for Outliers Let x1 represent the number of mathematics courses taken and x2 represent hours worked. The correlation between income and mathematics courses is 0.63. The correlation between income and hours worked is 0.84, and the correlation between mathematics courses and hours worked is 0.31. Use this information to answer the following questions. 1. 2. 3. 4. 5. 1 Ϫ 0.992 ϭ 0.008 Hence, for k people, the formula is Construct a Histogram 5 29 34 44 45 63 68 74 74 81 88 91 97 98 113 118 151 158 More Math Means More Money 365 364 363 365P3 • • ϭ ϭ 0.992 365 365 365 365 3 Hence, the probability that at least 2 of the 3 people will have the same birthday will be Technology Step by Step Data Applying the Concepts 10–4 For example, suppose there were 3 people in the room. The probability that each had a different birthday would be 4. Health and Wellness Use your class as the sample. Have each student take her or his temperature on a healthy day. Compute the mean and standard deviation for the sample. Create a 95% confidence interval for the mean temperature. Does the confidence interval obtained support the long-held belief that the average body temperature is 98.6ЊF? 5. Politics and Economics Select five political polls and note the margin of error, sample size, and percent favoring the candidate for each. For each poll, determine the level of confidence that must have been used to obtain the margin of error given, knowing the percent favoring the candidate and number of participants. Is there a pattern that emerges? 6. Your Class Have each student compute his or her body mass index (BMI) (703 times weight in pounds, divided by the quantity height in inches squared). Find the mean and standard deviation for the data set. Compute a 95% confidence interval for the mean BMI of a student. A BMI score over 30 is considered obese. Does the confidence interval indicate that the mean for BMI could be in the obese range? Inspect the boxplot for outliers. There are no outliers in this graph. Furthermore, the box is in the middle of the range, and the median is in the middle of the box. Most likely this is not a skewed distribution either. Calculate The Pearson Coefficient of Skewness The measure of skewness in the graphical summary is not the same as the Pearson coefficient. Use the calculator and the formula. PC ϭ 3ΘX Ϫ medianΙ s 3. Select Calc>Calculator, then type PC in the text box for Store result in:. 4. Enter the expression: 3*(MEAN(C1)؊MEDI(C1))/(STDEV(C1)). Make sure you get all the parentheses in the right place! 5. Click [OK]. The result, 0.148318, will be stored in the first row of C2 named PC. Since it is smaller than ϩ1, the distribution is not skewed. Construct a Normal Probability Plot 6. Select Graph>Probability Plot, then Single and click [OK]. 7. Double-click C1 Inventory to select the data to be graphed. 8 Cli k [Di ib i ] d k h N li l d Cli k [OK] Applying the Concepts are exercises found at the end of each section to reinforce the concepts explained in the section. They give the student an opportunity to think about the concepts and apply them to hypothetical examples similar to real-life ones found in newspapers, magazines, and professional journals. Most contain open-ended questions—questions that require interpretation and may have more than one correct answer. These exercises can also be used as classroom discussion topics for instructors who like to use this type of teaching technique. Data Projects, which appear at the end of each chapter, further challenge students’ understanding and application of the material presented in the chapter. Many of these require the student to gather, analyze, and report on real data. xvii
  • 29. blu38582_fm_i-xxviii.qxd xviii 9/29/10 8:30 PM Page xviii Guided Tour: Features and Supplements Multimedia Supplements Connect— McGraw-Hill’s Connect is a complete online homework system for mathematics and statistics. Instructors can assign textbook-specific content from over 40 McGraw-Hill titles as well as customize the level of feedback students receive, including the ability to have students show their work for any given exercise. Assignable content includes an array of videos and other multimedia tools along with algorithmic exercises, providing study tools for students with many different learning styles. Within Connect, a diagnostic assessment tool powered by ALEKS™ is available to measure student preparedness and provide detailed reporting and personalized remediation. Connect also helps ensure consistent assignment delivery across several sections through a course administration function and makes sharing courses with other instructors easy. For more information, visit the book’s website ( or contact your local McGraw-Hill sales representative ( ALEKS— ALEKS (Assessment and LEarning in Knowledge Spaces) is a dynamic online learning system for mathematics education, available over the Web 24/7. ALEKS assesses students, accurately determines their knowledge, and then guides them to the material that they are most ready to learn. With a variety of reports, Textbook Integration Plus, quizzes, and homework assignment capabilities, ALEKS offers flexibility and ease of use for instructors. • ALEKS uses artificial intelligence to determine exactly what each student knows and is ready to learn. ALEKS remediates student gaps and provides highly efficient learning and improved learning outcomes. • ALEKS is a comprehensive curriculum that aligns with syllabi or specified textbooks. When it is used in conjunction with McGraw-Hill texts, students also receive links to text-specific videos, multimedia tutorials, and textbook pages. • Textbook Integration Plus allows ALEKS to be automatically aligned with syllabi or specified McGraw-Hill textbooks with instructor-chosen dates, chapter goals, homework, and quizzes. • ALEKS with AI-2 gives instructors increased control over the scope and sequence of student learning. Students using ALEKS demonstrate a steadily increasing mastery of the content of the course. • ALEKS offers a dynamic classroom management system that enables instructors to monitor and direct student progress toward mastery of course objectives. ALEKS Prep for Statistics ALEKS Prep for Statistics can be used during the beginning of the course to prepare students for future success and to increase retention and pass rates. Backed by two decades of National Science Foundation–funded research, ALEKS interacts with students much as a human tutor, with the ability to precisely assess a student’s preparedness and provide instruction on the topics the student is ready to learn. ALEKS Prep for Statistics • Assists students in mastering core concepts that should have been learned prior to entering the present course. • Frees up lecture time for instructors, allowing more time to focus on current course material and not review material. • Provides up to six weeks of remediation and intelligent tutorial help to fill in students’ individual knowledge gaps.
  • 30. blu38582_fm_i-xxviii.qxd 9/29/10 2:46 PM Page xix Guided Tour: Features and Supplements xix TEGRITY— Tegrity Campus is a service that makes class time available all the time by automatically capturing every lecture in a searchable format for students to review when they study and complete assignments. With a simple one-click start and stop process, you capture all computer screens and corresponding audio. Students replay any part of any class with easy-to-use browser-based viewing on a PC or Mac. Educators know that the more students can see, hear, and experience class resources, the better they learn. With Tegrity Campus, students quickly recall key moments by using Tegrity Campus’s unique search feature. This search helps students efficiently find what they need, when they need it across an entire semester of class recordings. Help turn all your students’ study time into learning moments immediately supported by your lecture. To learn more about Tegrity watch a 2 minute Flash demo at Electronic Textbook CourseSmart is a new way for faculty to find and review eTextbooks. It’s also a great option for students who are interested in accessing their course materials digitally and saving money. CourseSmart offers thousands of the most commonly adopted textbooks across hundreds of courses from a wide variety of higher education publishers. It is the only place for faculty to review and compare the full text of a textbook online, providing immediate access without the environmental impact of requesting a print exam copy. At CourseSmart, students can save up to 50% off the cost of a print book, reduce the impact on the environment, and gain access to powerful Web tools for learning including full text search, notes and highlighting, and e-mail tools for sharing notes between classmates. MegaStat® MegaStat® is a statistical add-in for Microsoft Excel, handcrafted by J. B. Orris of Butler University. When MegaStat is installed it appears as a menu item on the Excel menu bar and allows you to perform statistical analysis on data in an Excel workbook. ELEMENTARY STATISTICS: A BRIEF VERSION requires the use of this MegaStat add-in for Excel only for those Excel Technology Step by Step operations in the text that Excel would otherwise not have been able to perform. The MegaStat plug-in can be found at Computerized Test Bank (CTB) Online (instructors only) The computerized test bank contains a variety of questions, including true/false, multiplechoice, short-answer, and short problems requiring analysis and written answers. The testing material is coded by type of question and level of difficulty. The Brownstone Diploma® system enables you to efficiently select, add, and organize questions, such as by type of question or by level of difficulty. It also allows for printing tests along with answer keys as well as editing the original questions, and it is available for Windows and Macintosh systems. Printable tests and a print version of the test bank can also be found on the website. Lecture Videos Lecture videos introduce concepts, definitions, theorems, formulas, and problem-solving procedures to help students better comprehend the topic at hand. These videos are closedcaptioned for the hearing-impaired, are subtitled in Spanish, and meet the Americans with Disabilities Act Standards for Accessible Design. They can be found online at
  • 31. blu38582_fm_i-xxviii.qxd xx 9/29/10 2:46 PM Page xx Guided Tour: Features and Supplements Exercise Videos In these videos the instructor works through selected exercises, following the solution methodology employed in the text. Also included are tutorials for using the TI-83 Plus and TI-84 Plus calculators, Excel, and MINITAB, presented in an engaging format for students. These videos are closed-captioned for the hearing-impaired, are subtitled in Spanish, and meet the Americans with Disabilities Act Standards for Accessible Design. They can be found online at MINITAB Student Release 14 The student version of MINITAB statistical software is available with copies of the text. Ask your McGraw-Hill representative for details. SPSS Student Version for Windows A student version of SPSS statistical software is available with copies of this text. Consult your McGraw-Hill representative for details. Print Supplements Annotated Instructor’s Edition (instructors only) The Annotated Instructor’s Edition contains answers to all exercises and tests. The answers to most questions are printed in red next to each problem. Answers not appearing on the page can be found in the Answer Appendix at the end of the book. Instructor’s Solutions Manual (instructors only) By Sally Robinson of South Plains College, this manual includes worked-out solutions to all the exercises in the text and answers to all quiz questions. This manual can be found online at Student’s Solutions Manual By Sally Robinson of South Plains College, this manual contains detailed solutions to all odd-numbered text problems and answers to all quiz questions. MINITAB 14 Manual This manual provides the student with how-to information on data and file management, conducting various statistical analyses, and creating presentation-style graphics while following each text chapter. TI-83 Plus and TI-84 Plus Graphing Calculator Manual This friendly, practical manual teaches students to learn about statistics and solve problems by using these calculators while following each text chapter. Excel Manual This workbook, specially designed to accompany the text, provides additional practice in applying the chapter concepts while using Excel.
  • 32. blu38582_fm_i-xxviii.qxd 9/29/10 2:46 PM Page xxi Index of Applications CHAPTE R 1 The Nature of Probability and Statistics Education and Testing Attendance and Grades, 5 Piano Lessons Improve Math Ability, 31 Environmental Sciences, the Earth, and Space Statistics and the New Planet, 5 Medicine, Clinical Studies, and Experiments Beneficial Bacteria, 28 Caffeine and Health, 28 Smoking and Criminal Behavior, 31 The Worst Day for Weight Loss, 11 Psychology and Human Behavior Anger and Snap Judgments, 31 Hostile Children Fight Unemployment, 31 Public Health and Nutrition Are We Improving Our Diet?, 2, 29 Chewing Tobacco, 16 Sports, Exercise, and Fitness ACL Tears in Collegiate Soccer Players, 31 Surveys and Culture American Culture and Drug Abuse, 13 Transportation Safe Travel, 9 World’s Busiest Airports, 31 CHAPTE R 2 Frequency Distributions and Graphs Buildings and Structures Selling Real Estate, 60 Stories in Tall Buildings, 83 Stories in the World’s Tallest Buildings, 46 Successful Space Launches, 86 The Great Lakes, 100 Outpatient Cardiograms, 80 Quality of Health Care, 62 Business, Management, and Work Bank Failures, 96 Career Changes, 96 Job Aptitude Test, 96 Workers Switch Jobs, 85 Food and Dining Cost of Milk, 87 Sales of Coffee, 85 Super Bowl Snack Foods, 73 Worldwide Sales of Fast Foods, 84 Public Health and Nutrition Calories in Salad Dressings, 86 Cereal Calories, 62 Grams per Food Servings, 46 Protein Grams in Fast Food, 62 Demographics and Population Characteristics Boom in Number of Births, 87 Characteristics of the Population 65 and Over, 85 Counties, Divisions, or Parishes for 50 States, 61 Distribution of Blood Types, 38 Homeless People, 70 How People Get Their News, 95 Wealthy People, 37 Government, Taxes, Politics, Public Policy, and Voting How Much Paper Money Is in Circulation Today?, 81 Presidential Vetoes, 47 State Gasoline Tax, 47 Education and Testing College Spending for First-Year Students, 69 Do Students Need Summer Development?, 61 GRE Scores at Top-Ranked Engineering Schools, 47 Instruction Time, 85 Making the Grade, 62 Math and Reading Achievement Scores, 86 Number of College Faculty, 61 Percentage Completing 4 Years of College, 95 Public Libraries, 96 Teacher Strikes, 100 Entertainment Unclaimed Expired Prizes, 47 Environmental Sciences, the Earth, and Space Air Quality, 96 Air Quality Standards, 61 Average Global Temperatures, 85 Carbon Dioxide Concentrations, 85 Cost of Utilities, 61 Number of Hurricanes, 84 Record High Temperatures, 41 Recycled Trash, 98 History Ages of Declaration of Independence Signers, 47 Ages of Presidents at Inauguration, 45, 86 Ages of Vice Presidents at the Time of Their Death, 96 JFK Assassination, 48 Law and Order: Criminal Justice Car Thefts in a Large City, 82 Identity Fraud, 36, 97 Identity Thefts, 99 Murders in Selected Cities, 98 Workplace Homicides, 72 Manufacturing and Product Development Meat Production, 86 Marketing, Sales, and Consumer Behavior Items Purchased at a Convenience Store, 98 Music Sales, 86 Public Debt, 96 Water Usage, 99 Medicine, Clinical Studies, and Experiments BUN Count, 95 How Quick Are Dogs?, 61 How Quick Are Older Dogs?, 62 Leading Cause of Death, 83 Needless Deaths of Children, 99 Sports, Exercise, and Fitness Ball Sales, 95 Calories Burned While Exercising, 84 Miles Run per Week, 57 NFL Franchise Values, 95 NFL Payrolls, 47 NFL Salaries, 61 Salaries of College Coaches, 47 Weights of the NBA’s Top 50 Players, 46 Technology Cell Phone Usage, 74 Trust in Internet Information, 46 The Sciences Nobel Prizes in Physiology or Medicine, 87 Twenty Days of Plant Growth, 86 Transportation Activities While Driving, 96 Airline Passengers, 47 Colors of Automobiles, 85 MPGs for SUVs, 43 Railroad Crossing Accidents, 61 Safety Record of U.S. Airlines, 85 Top 10 Airlines, 86 Travel and Leisure Museum Visitors, 96, 99 Reasons We Travel, 85 Roller Coaster Mania, 84 CHAPTER 3 Data Description Buildings and Structures Prices of Homes, 135, 140 Sizes of Malls, 177 Stories in the Tallest Buildings, 138 xxi
  • 33. blu38582_fm_i-xxviii.qxd xxii 9/29/10 2:46 PM Page xxii Index of Applications Suspension Bridges, 139 Water-Line Breaks, 114 Business, Management, and Work Average Earnings of Workers, 174 Average Weekly Earnings, 154 Commissions Earned, 120 Costs to Train Employees, 174 Days Off per Year, 106 Employee Salaries, 125 Employee Years of Service, 177 Executive Bonuses, 119 Foreign Workers, 119 Hourly Compensation for Production Workers, 119 Hours Worked, 175 Labor Charges, 174 Missing Work, 139 New Worth of Corporations, 120 Salaries of Personnel, 113 The Noisy Workplace, 166 Top-Paid CEOs, 119 Travel Allowances, 135 Years of Service of Employees, 174 Demographics and Population Characteristics Ages of Accountants, 139 Ages of Consumers, 140 Ages of the Top 50 Wealthiest People, 109 Ages of U.S. Residents, 179 Best Friends of Students, 177 Net Worth of Wealthy People, 173 Percentage of College-Educated Population over 25, 120 Percentage of Foreign-Born People in the U.S., 120 Populations of Selected Cities, 119 Economics and Investment Branches of Large Banks, 112 Investment Earnings, 174 Education and Testing Achievement Test Scores, 154 College and University Debt, 154 College Room and Board Costs, 154 Enrollments for Selected Independent Religiously Controlled 4-Year Colleges, 120 Errors on a Typing Test, 176 Exam Grades, 175 Exam Scores, 177 Expenditures per Pupil for Selected States, 118 Final Grade, 121 Grade Point Average, 115, 118 SAT Scores, 173, 178 Starting Teachers’ Salaries, 138 Teacher Salaries, 118, 153 Teacher Strikes, 167 Test Scores, 142, 147, 155, 177 Textbooks in Professors’ Offices, 174 Work Hours for College Faculty, 140 Entertainment Earnings of Nonliving Celebrities, 118 FM Radio Stations, 139 Households with Four Television Networks, 174 Top Movie Sites, 175 Environmental Sciences, the Earth, and Space Ages of Astronaut Candidates, 138 Earthquake Strengths, 119 Farm Sizes, 140 Garbage Collection, 119 High Temperatures, 118 Hurricane Damage, 155 Inches of Rain, 177 Licensed Nuclear Reactors, 112 Number of Meteorites Found, 163 Number of Tornadoes, 168 Observers in the Frogwatch Program, 118 Precipitation and High Temperatures, 138 Rise in Tides, 173 Shark Attacks, 173 Size of Dams, 167 Size of U.S. States, 138 Solid Waste Production, 140 Tornadoes in 2005, 167 Tornadoes in the United States, 110 Unhealthful Smog Days, 168 Food and Dining Citrus Fruit Consumption, 140 Diet Cola Preference, 121 Specialty Coffee Shops, 120 Government, Taxes, Politics, Public Policy, and Voting Age of Senators, 153 Cigarette Taxes, 137 History Years of Service of Supreme Court Members, 174 Law and Order: Criminal Justice Murders in Cities, 139 Murder Rates, 139 Police Calls in Schools, 137 Manufacturing and Product Development Battery Lives, 139, 173 Comparison of Outdoor Paint, 123 Copier Service Calls, 120 Shipment Times, 177 Word Processor Repairs, 139 Marketing, Sales, and Consumer Behavior Average Cost of Smoking, 178 Average Cost of Weddings, 178 Brands of Toothpaste Carried, 177 Cost per Load of Laundry Detergents, 138 Delivery Charges, 174 European Auto Sales, 129 Magazines in Bookstores, 174 Magazines Purchased, 111 Newspapers for Sale, 177 Sales of Automobiles, 132 Medicine, Clinical Studies, and Experiments Asthma Cases, 111 Blood Pressure, 137 Determining Dosages, 153 Hospital Emergency Waiting Times, 139 Hospital Infections, 107 Serum Cholesterol Levels, 140 Systolic Blood Pressure, 146 Psychology and Human Behavior Reaction Times, 139 Trials to Learn a Maze, 140 Public Health and Nutrition Fat Grams, 121 Sodium Content of Cheese, 164 Sports, Exercise, and Fitness Baseball Team Batting Averages, 138 Earned Run Average and Number of Games Pitched, 167 Football Playoff Statistics, 138 Innings Pitched, 167 Miles Run Per Week, 107 NFL Salaries, 174 NFL Signing Bonuses, 111 Technology Time Spent Online, 140 Transportation Airplane Speeds, 154 Automobile Fuel Efficiency, 119, 139 Commuter Times, 175 Cost of Car Rentals, 174 Cost of Helicopters, 121 Driver’s License Exam Scores, 153 Fuel Capacity, 173 Gas Prices for Rental Cars, 177 How Long Are You Delayed by Road Congestion?, 104, 175 Miles per Gallon, 176 Passenger Vehicle Deaths, 138 Times Spent in Rush-Hour Traffic, 138 Travel and Leisure Airport Parking, 118 Area Boat Registrations, 113 Hotel Rooms, 110 National Park Vehicle Pass Costs, 110 Pages in Women’s Fitness Magazines, 133 Vacation Days, 153 Visitors Who Travel to Foreign Countries, 167 CHAPTER 4 Probability and Counting Rules Buildings and Structures Building a New Home, 207 Business, Management, and Work Distribution of CEO Ages, 198 Research and Development Employees, 201 Working Women and Computer Use, 221 Demographics and Population Characteristics Blood Types and Rh Factors, 222 Distribution of Blood Types, 192 Human Blood Types, 196 Male Color Blindness, 213 Marital Status of Women, 223 Residence of People, 190 War Veterans, 244 Young Adult Residences, 205 Education and Testing College Courses, 222 College Debt, 197 College Degrees Awarded, 204 College Enrollment, 224 Computers in Elementary Schools, 197 Doctoral Assistantships, 223 Education Level and Smoking, 244 Full-Time College Enrollment, 223 Gender of College Students, 196 High School Grades of First-Year College Students, 224 Online Course Selection, 243 Reading to Children, 223 Required First-Year College Courses, 198 Student Financial Aid, 221 Entertainment Cable Television, 221 Craps Game, 197 Family and Children’s Computer Games, 223 Movie Releases, 244 Online Electronic Games, 223 Poker Hands, 235 Selecting a Movie, 204
  • 34. blu38582_fm_i-xxviii.qxd 9/29/10 2:46 PM Page xxiii Index of Applications The Mathematics of Gambling, 240 Video and Computer Games, 220 Yahtzee, 245 Environmental Sciences, the Earth, and Space Corn Products, 206 Endangered Species, 205 Plant Selection, 241 Sources of Energy Uses in the United States, 197 Threatened Species of Reptiles, 233 Food and Dining Family Dinner Combinations, 198 Pizzas and Salads, 222 Purchasing a Pizza, 207 Government, Taxes, Politics, Public Policy, and Voting Congressional Committee Memberships, 241 Federal Government Revenue, 197 Large Monetary Bills in Circulation, 197 Senate Partisanship, 241 Territories and Colonies, 245 Law and Order: Criminal Justice Guilty or Innocent?, 220 Prison Populations, 221, 222 University Crime, 214 Manufacturing and Product Development Defective Items, 222 Defective Transistors, 238 Marketing, Sales, and Consumer Behavior Coffee Shop Selection, 200 Commercials, 224 Customer Purchases, 223 Door-to-Door Sales, 206 Gift Baskets, 222 Magazine Sales, 238 Shopping Mall Promotion, 196 Medicine, Clinical Studies, and Experiments Chronic Sinusitis, 244 Effectiveness of a Vaccine, 244 Hospital Stays for Maternity Patients, 193 Medical Patients, 206 Medical Tests on Emergency Patients, 206 Medication Effectiveness, 223 Multiple Births, 205 Which Pain Reliever Is Best?, 203 Psychology and Human Behavior Would You Bet Your Life?, 182, 245 Sports, Exercise, and Fitness Exercise, 220 Health Club Membership, 244 Leisure Time Exercise, 223 MLS Players, 221 Olympic Medals, 222 Sports Participation, 205 Surveys and Culture Student Survey, 205 Survey on Stress, 212 Survey on Women in the Military, 217 Technology Computer Ownership, 223 DVD Players, 244 Garage Door Openers, 232 Software Selection, 243 Text Messages via Cell Phones, 221 Transportation Automobile Insurance, 221 Automobile Sales, 221 Driving While Intoxicated, 202 Fatal Accidents, 223 Gasoline Mileage for Autos and Trucks, 197 Licensed Drivers in the United States, 205 On-Time Airplane Arrivals, 223 Rural Speed Limits, 197 Seat Belt Use, 221 Types of Vehicles, 224 Travel and Leisure Borrowing Books, 243 Country Club Activities, 222 Tourist Destinations, 204 Travel Survey, 192 CHAPTER 5 Discrete Probability Distributions Business, Management, and Work Job Elimination, 278 Labor Force Couples, 277 Demographics and Population Characteristics Left-Handed People, 286 Likelihood of Twins, 276 Unmarried Women, 294 Economics and Investment Bond Investment, 265 Education and Testing College Education and Business World Success, 277 Dropping College Courses, 257 High School Dropouts, 277 People Who Have Some College Education, 278 Students Using the Math Lab, 267 Entertainment Chuck-a-Luck, 296 Lottery Numbers, 296 Lottery Prizes, 268 Number of Televisions per Household, 267 On Hold for Talk Radio, 263 Roulette, 268 Environmental Sciences, the Earth, and Space Household Wood Burning, 294 Radiation Exposure, 266 Food and Dining Coffee Shop Customers, 283 M&M Color Distribution, 290 Pizza Deliveries, 267 Pizza for Breakfast, 294 Unsanitary Restaurants, 276 Government, Taxes, Politics, Public Policy, and Voting Accuracy Count of Votes, 294 Federal Government Employee E-mail Use, 278 Poverty and the Federal Government, 278 Social Security Recipients, 278 History Rockets and Targets, 289 Law and Order: Criminal Justice Emergency Calls, 293 Firearm Sales, 290 Study of Robberies, 290 U.S. Police Chiefs and the Death Penalty, 294 Manufacturing and Product Development Defective Calculators, 291 Defective Compressor Tanks, 288 Defective Computer Keyboards, 291 Defective DVDs, 267 Defective Electronics, 291 Marketing, Sales, and Consumer Behavior Cellular Phone Sales, 267 Commercials During Children’s TV Programs, 267 Company Mailings, 291 Credit Cards, 293 Internet Purchases, 278 Mail Ordering, 291 Number of Credit Cards, 267 Suit Sales, 267 Telephone Soliciting, 291 Tie Purchases, 293 Medicine, Clinical Studies, and Experiments Flu Shots, 294 Pooling Blood Samples, 252, 295 xxiii Psychology and Human Behavior The Gambler’s Fallacy, 269 Sports, Exercise, and Fitness Baseball World Series, 255 Surveys and Culture Survey on Answering Machine Ownership, 278 Survey on Bathing Pets, 278 Survey on Concern for Criminals, 277 Survey on Doctor Visits, 272 Survey on Employment, 273 Survey on Fear of Being Home Alone at Night, 274 Survey of High School Seniors, 278 Survey on Internet Awareness, 278 Technology Computer Literacy Test, 294 Internet Access via Cell Phone, 294 The Sciences Mendel’s Theory, 290 Transportation Alternate Sources of Fuel, 278 Arrivals at an Airport, 293 Driving to Work Alone, 277 Driving While Intoxicated, 274 Emissions Inspection Failures, 291 Traffic Accidents, 267 Truck Inspection Violations, 290 Travel and Leisure Destination Weddings, 278 Lost Luggage in Airlines, 294 Number of Trips of Five Nights or More, 261 Outdoor Regatta, 293 Watching Fireworks, 278 CHAPTER 6 The Normal Distribution Buildings and Structures New Home Prices, 326 New Home Sizes, 326 Business, Management, and Work Multiple-Job Holders, 349 Retirement Income, 349 Salaries for Actuaries, 348 Weekly Income of Private Industry Information Workers, 340 Unemployment, 351 Demographics and Population Characteristics Ages of Proofreaders, 340
  • 35. blu38582_fm_i-xxviii.qxd xxiv 9/29/10 2:46 PM Page xxiv Index of Applications Amount of Laundry Washed Each Year, 339 Life Expectancies, 340 Per Capita Income of Delaware Residents, 339 Population of College Cities, 347 Residences of U.S. Citizens, 347 U.S. Population, 349 Economics and Investment Itemized Charitable Contributions, 326 Monthly Mortgage Payments, 325 Education and Testing College Costs, 338 Doctoral Student Salaries, 325 Elementary School Teachers, 347 Enrollment in Personal Finance Course, 349 Exam Scores, 327 Female Americans Who Have Completed 4 Years of College, 346 GMAT Scores, 351 High School Competency Test, 326 Private Four-Year College Enrollment, 349 Professors’ Salaries, 325 Reading Improvement Program, 326 Salary of Full-Time Male Professors, 326 SAT Scores, 325, 327, 339 School Enrollment, 346 Smart People, 324 Teachers’ Salaries, 325 Teachers’ Salaries in Connecticut, 339 Teachers’ Salaries in North Dakota, 339 Years to Complete a Graduate Program, 351 Entertainment Admission Charge for Movies, 325 Box Office Revenues, 328 Drive-in Movies, 327 Hours That Children Watch Television, 334 Slot Machines, 349 Environmental Sciences, the Earth, and Space Amount of Rain in a City, 351 Annual Precipitation, 339 Average Precipitation, 349 Glass Garbage Generation, 338 Heights of Active Volcanoes, 349 Lake Temperatures, 326 Monthly Newspaper Recycling, 317 Newborn Elephant Weights, 326 Water Use, 339 Food and Dining Bottled Drinking Water, 327 Coffee Consumption, 319 Confectionary Products, 349 Meat Consumption, 336 Waiting to Be Seated, 326 Government, Taxes, Politics, Public Policy, and Voting Cigarette Taxes, 327 Medicare Hospital Insurance, 339 Voter Preference, 346 Law and Order: Criminal Justice Police Academy Acceptance Exams, 327 Police Academy Qualifications, 320 Population in U.S. Jails, 325 Manufacturing and Product Development Breaking Strength of Steel Cable, 340 Portable CD Player Lifetimes, 349 Repair Cost for Microwave Ovens, 351 Wristwatch Lifetimes, 327 Marketing, Sales, and Consumer Behavior Credit Card Debt, 325 Mail Order Sales, 346 Product Marketing, 327 Summer Spending, 317 Medicine, Clinical Studies, and Experiments Lengths of Hospital Stays, 326 Normal Ranges for Vital Statistics, 300, 350 Per Capita Spending on Health Care, 348 Serum Cholesterol Levels, 339 Systolic Blood Pressure, 321, 340 Public Health and Nutrition Calories in Fast-Food Sandwiches, 351 Chocolate Bar Calories, 325 Cholesterol Content, 340 Sodium in Frozen Food, 339 Youth Smoking, 346 Sports, Exercise, and Fitness Batting Averages, 344 Mountain Climbing Safety, 346 Number of Baseball Games Played, 323 Number of Runs Made, 328 Surveys and Culture Sleep Survey, 351 Technology Cell Phone Lifetimes, 339 Computer Ownership, 351 Cost of iPod Repair, 349 Cost of Personal Computers, 326 Household Computers, 346 Household Online Connection, 351 Monthly Spending for Paging and Messaging Services, 349 Technology Inventories, 322 Telephone Answering Devices, 347 National Accounting Examination, 367 Number of Faculty, 366 Private Schools, 382 Students per Teacher in U.S. Public Schools, 374 Students Who Major in Business, 383 Transportation Ages of Amtrak Passenger Cars, 326 Commute Time to Work, 325 Commuter Train Passengers, 348 Fuel Efficiency for U.S. Light Vehicles, 339 Miles Driven Annually, 325 Passengers on a Bus, 351 Price of Gasoline, 325 Reading While Driving, 343 Used Car Prices, 326 Vehicle Ages, 335 Entertainment Direct Satellite Television, 383 Lengths of Children’s Animated Films, 394 Playing Video Games, 366 Television Viewing, 366 Would You Change the Channel?, 356, 395 Travel and Leisure Number of Branches of the 50 Top Libraries, 311 Widowed Bowlers, 343 CHAPTER 7 Confidence Intervals and Sample Size Buildings and Structures Home Fires Started by Candles, 372 Business, Management, and Work Dog Bites to Postal Workers, 394 Number of Jobs, 366 Work Interruptions, 382 Workers’ Distractions, 366 Demographics and Population Characteristics Ages of Insurance Representatives, 396 Unmarried Americans, 383 Widows, 383 Economics and Investment Credit Union Assets, 362 Financial Well-being, 383 Stock Prices, 391 Education and Testing Actuary Exams, 366 Adult Education, 394 Age of College Students, 391 Child Care Programs, 394 Cost of Textbooks, 396 Covering College Costs, 379 Day Care Tuition, 367 Educational Television, 382 Freshmen’s GPA, 366 High School Graduates Who Take the SAT, 382 Hours Spent Studying, 396 Environmental Sciences, the Earth, and Space Elements and Isotopes, 394 Depth of a River, 364 Length of Growing Seasons, 367 Number of Farms, 366 Thunderstorm Speeds, 374 Travel to Outer Space, 382 Unhealthy Days in Cities, 375 Food and Dining Cost of Pizzas, 367 Fruit Consumption, 382 Sport Drink Decision, 373 Government, Taxes, Politics, Public Policy, and Voting Regular Voters in America, 382 State Gasoline Taxes, 374 Women Representatives in State Legislature, 374 History Ages of Presidents at Time of Death, 390 Law and Order: Criminal Justice Burglaries, 396 Gun Control, 383 Workplace Homicides, 374 Manufacturing and Product Development Baseball Diameters, 394 Calculator Battery Lifetimes, 391 How Many Kleenexes Should Be in a Box?, 365 Lifetimes of Snowmobiles, 394 Lifetimes of Wristwatches, 390 MPG for Lawn Mowers, 394 Nicotine Content, 389 Marketing, Sales, and Consumer Behavior Convenience Store Shoppers, 367 Costs for a 30-Second Spot on Cable Television, 375 Credit Card Use by College Students, 385 Days It Takes to Sell an Aveo, 360
  • 36. blu38582_fm_i-xxviii.qxd 9/29/10 2:46 PM Page xxv Index of Applications Medicine, Clinical Studies, and Experiments Birth Weights of Infants, 367 Contracting Influenza, 381 Cost of Knee Replacement Surgery, 391 Doctor Visit Costs, 396 Emergency Room Accidents, 394, 396 Hospital Noise Levels, 367, 375 Patients Treated in Hospital Emergency Rooms, 396 Waiting Times in Emergency Rooms, 360 Home Prices in Pennsylvania, 423 Monthly Home Rent, 464 Water Consumption, 435 Wind Speed, 420 Business, Management, and Work Copy Machine Use, 423 Hourly Wage, 424 Number of Jobs, 435 Revenue of Large Businesses, 422 Salaries for Actuaries, 464 Sick Days, 424 Union Membership, 464 Weekly Earnings for Leisure and Hospitality Workers, 461 Working at Home, 461 Food and Dining Chewing Gum Use, 467 Peanut Production in Virginia, 423 Soft Drink Consumption, 423 Public Health and Nutrition Carbohydrates in Yogurt, 390 Carbon Monoxide Deaths, 390 Diet Habits, 383 Health Insurance Coverage for Children, 394 Obesity, 383 Skipping Lunch, 396 Demographics and Population Characteristics Ages of Professional Women, 466 Average Family Size, 435 First-Time Marriages, 467 Foreign Languages Spoken in Homes, 443 Heights of 1-Year-Olds, 423 Heights of Models, 467 Home Ownership, 442 Sports, Exercise, and Fitness Cost of Ski Lift Tickets, 389 Dance Company Students, 374 Football Player Heart Rates, 375 Surveys and Culture Belief in Haunted Places, 382 Does Success Bring Happiness?, 381 Fighting U.S. Hunger, 383 Grooming Times for Men and Women, 375 Political Survey, 396 Survey on Politics, 383 Technology Digital Camera Prices, 374 Home Computers, 380 Social Networking Sites, 374 Television Set Ownership, 396 Visits to Networking Sites, 374 Transportation Automobile Pollution, 396 Chicago Commuters, 374 Commuting Times in New York, 367 Distance Traveled to Work, 374 Money Spent on Road Repairs, 396 Truck Safety Check, 396 Weights of Minivans, 396 Travel and Leisure Overseas Travel, 383 Religious Books, 379 Vacation Days, 394 Vacations, 382 CHAPTER 8 Hypothesis Testing Buildings and Structures Heights of Tall Buildings, 434 Home Closing Costs, 466 Economics and Investment Stocks and Mutual Fund Ownership, 442 Education and Testing College Room and Board Costs, 454 Cost of College Tuition, 419 Debt of College Graduates, 464 Doctoral Students’ Salaries, 443 Exam Grades, 454 Improvement on the SAT, 400, 465 Nonparental Care, 422 Student Expenditures, 423 Substitute Teachers’ Salaries, 430 Teaching Assistants’ Stipends, 435 Undergraduate Enrollment, 442 Variation of Test Scores, 448 Entertainment Cost of Making a Movie, 435 Movie Admission Prices, 465 Moviegoers, 422, 442 Television Set Ownership, 443 Television Viewing by Teens, 435 Times of Videos, 465 Environmental Sciences, the Earth, and Space Farm Sizes, 424 Heights of Volcanoes, 454 High Temperatures in January, 453 High Temperatures in the United States, 463 Natural Gas Heat, 443 Park Acreages, 434 Pollution By-products, 467 Tornado Deaths, 454 Use of Disposable Cups, 423 Warming and Ice Melt, 422 Government, Taxes, Politics, Public Policy, and Voting Ages of U.S. Senators, 423 Family and Medical Leave Act, 439 Free School Lunches, 464 IRS Audits, 461 Replacing $1 Bills with $1 Coins, 440 Salaries of Government Employees, 423 Law and Order: Criminal Justice Ages of Robbery Victims, 467 Car Thefts, 421 Federal Prison Populations, 464 Speeding Tickets, 424 Stolen Aircraft, 454 Manufacturing and Product Development Breaking Strength of Cable, 424 Manufactured Machine Parts, 454 Nicotine Content of Cigarettes, 450 Soda Bottle Content, 454 Strength of Wrapping Cord, 467 Sugar Production, 457 Weights on Men’s Soccer Shoes, 464 Marketing, Sales, and Consumer Behavior Consumer Protection Agency Complaints, 460 Cost of Men’s Athletic Shoes, 415 Credit Card Debt, 422 Medicine, Clinical Studies, and Experiments Can Sunshine Relieve Pain?, 433 Doctor Visits, 435 Female Physicians, 442 Hospital Infections, 429 How Much Nicotine Is in Those Cigarettes?, 433 Outpatient Surgery, 449 Time Until Indigestion Relief, 464 Public Health and Nutrition After-School Snacks, 442 Alcohol and Tobacco Use by High School Students, 465 Calories in Pancake Syrup, 453 Carbohydrates in Fast Foods, 454 Chocolate Chip Cookie Calories, 435 xxv Eggs and Your Health, 412 High-Potassium Foods, 454 Overweight Children, 442 People Who Are Trying to Avoid Trans Fats, 438 Quitting Smoking, 441 Youth Smoking, 443 Sports, Exercise, and Fitness Burning Calories by Playing Tennis, 424 Canoe Trip Times, 461 Exercise and Reading Time Spent by Men, 434 Exercise to Reduce Stress, 442 Football Injuries, 443 Games Played by NBA Scoring Leaders, 465 Joggers’ Oxygen Uptake, 432 Walking with a Pedometer, 414 Surveys and Culture Breakfast Survey, 467 Caffeinated Beverage Survey, 467 Survey on Vitamin Usage, 467 Veterinary Expenses of Cat Owners, 434 Technology Cell Phone Bills, 435 Cell Phone Call Lengths, 434 Internet Visits, 435 Portable Radio Ownership, 464 Radio Ownership, 467 Transferring Phone Calls, 454 The Sciences Hog Weights, 458 Plant Leaf Lengths, 465 Seed Germination Times, 467 Whooping Crane Eggs, 464 Transportation Car Inspection Times, 452 Commute Time to Work, 434 Days on Dealers’ Lots, 414 Experience of Taxi Drivers, 467 First-Class Airline Passengers, 443 Fuel Consumption, 465 Interstate Speeds, 454 One-Way Airfares, 461 Operating Costs of an Automobile, 423 Stopping Distances, 423 Testing Gas Mileage Claims, 453 Tire Inflation, 465 Transmission Service, 424 Travel Time to Work, 464 Travel and Leisure Borrowing Library Books, 443 Hotel Rooms, 467 Newspaper Reading Times, 461 Pages in Romance Novels, 467 Traveling Overseas, 442
  • 37. blu38582_fm_i-xxviii.qxd xxvi 9/29/10 2:46 PM Page xxvi Index of Applications CHAPTER 9 Testing the Difference Between Two Means, Two Proportions, and Two Variances Buildings and Structures Ages of Homes, 489 Apartment Rental Fees, 527 Heights of Tall Buildings, 521 Heights of World Famous Cathedrals, 526 Home Prices, 480 Sale Prices for Houses, 482 Business, Management, and Work Animal Bites of Postal Workers, 510 Too Long on the Telephone, 487 Demographics and Population Characteristics Ages of Gamblers, 488 Ages of Hospital Patients, 520 County Size in Indiana and Iowa, 521 Family Incomes, 528 Heights of 9-Year-Olds, 480 Male Head of Household, 528 Married People, 510 Per Capita Income, 480 Population and Area, 520 Salaries of Chemists, 528 Senior Workers, 511 Economics and Investment Bank Deposits, 493 Daily Stock Prices, 521 Education and Testing ACT Scores, 480 Ages of College Students, 481 Average Earnings for College Graduates, 482, 525 College Education, 511 Cyber School Enrollment, 488 Elementary School Teachers’ Salaries, 521 Exam Scores at Private and Public Schools, 482 Factory Worker Literacy Rates, 528 High School Graduation Rates, 510 Improving Study Habits, 500 Lay Teachers in Religious Schools, 526 Lecture versus Computer-Assisted Instruction, 510 Literacy Scores, 481 Mathematical Skills, 528 Medical School Enrollments, 489 Out-of-State Tuitions, 489 Reducing Errors in Grammar, 501 Retention Test Scores, 500 Teachers’ Salaries, 480, 488, 525 Tuition Costs for Medical School, 521 Undergraduate Financial Aid, 510 Women Science Majors, 480 Entertainment Hours Spent Watching Television, 488 Environmental Sciences, the Earth, and Space Air Quality, 500 Average Temperatures, 525 Farm Sizes, 485 High and Low Temperatures, 526 Lengths of Major U.S. Rivers, 479 Winter Temperatures, 520 Food and Dining Prices of Low-Calorie Foods, 528 Soft Drinks in School, 525 Government, Taxes, Politics, Public Policy, and Voting Money Spent on Road Repair, 528 Monthly Social Security Benefits, 480 Partisan Support of Salary Increase Bill, 511 Tax-Exempt Properties, 487 Manufacturing and Product Development Automobile Part Production, 526 Battery Voltage, 481 Weights of Running Shoes, 488 Weights of Vacuum Cleaners, 488 Marketing, Sales, and Consumer Behavior Credit Card Debt, 481 Paint Prices, 526 Medicine, Clinical Studies, and Experiments Can Video Games Save Lives?, 499 Hospital Stays for Maternity Patients, 489 Is More Expensive Better?, 508 Length of Hospital Stays, 480 Noise Levels in Hospitals, 488, 520, 526 Obstacle Course Times, 501 Only the Timid Die Young, 529 Overweight Dogs, 501 Pulse Rates of Identical Twins, 501 Sleeping Brain, Not at Rest, 529 Vaccination Rates in Nursing Homes, 472, 505, 526 Waiting Time to See a Doctor, 517 Psychology and Human Behavior Bullying, 511 Problem-Solving Ability, 481 Self-Esteem Scores, 481 Smoking and Education, 509 Public Health and Nutrition Calories in Ice Cream, 520 Carbohydrates in Candy, 488, 521 Cholesterol Levels, 496, 527 Heart Rates of Smokers, 516 Hypertension, 511 Sports, Exercise, and Fitness College Sports Offerings, 476 Heights of Basketball Players, 528 Hockey’s Highest Scorers, 489 Home Runs, 478 NFL Salaries, 488 PGA Golf Scores, 501 Surveys and Culture Adopted Pets, 526 Desire to Be Rich, 510 Dog Ownership, 510 Sleep Report, 501 Smoking Survey, 511 Survey on Inevitability of War, 511 Technology Communication Times, 525 The Sciences Egg Production, 528 Wolf Pack Pups, 520 Transportation Automatic Transmissions, 519 Commuting Times, 480 Seat Belt Use, 510 Texting While Driving, 507 Travel and Leisure Airline On-Time Arrivals, 511 Airport Passengers, 518 Bestseller Books, 487 Driving for Pleasure, 525 Hotel Room Cost, 475 Jet Ski Accidents, 528 Leisure Time, 510 Museum Attendance, 520 CHAPTER 10 Correlation and Regression Buildings and Structures Tall Buildings, 550, 559 Business, Management, and Work Typing Speed and Word Processing, 586 Demographics and Population Characteristics Age and Cavities, 588 Age and Net Worth, 560 Age and Wealth, 538 Age, GPA, and Income, 581 Father’s and Son’s Weights, 560 Education and Testing Absences and Final Grades, 537, 560 Alumni Contributions, 549 Aspects of Students’ Academic Behavior, 581 Elementary and Secondary School, 586 Faculty and Students, 550, 559 Home Smart Home, 576 More Math Means More Money, 580 School Districts and Secondary Schools, 549, 559 State Board Scores, 578 Entertainment Commercial Movie Releases, 549, 558 Television Viewers, 560 Environmental Sciences, the Earth, and Space Average Temperature and Precipitation, 550, 559 Coal Production, 560 Do Dust Storms Affect Respiratory Health?, 534, 587 Farm Acreage, 560 Forest Fires and Acres Burned, 549, 559 Precipitation and Snow/Sleet, 550, 559 Food and Dining Special Occasion Cakes, 581 Government, Taxes, Politics, Public Policy, and Voting Gas Tax and Fuel Use, 549, 558 State Debt and Per Capita Tax, 549, 559 Manufacturing and Product Development Assembly Line Work, 581 Copy Machine Maintenance Costs, 570 Marketing, Sales, and Consumer Behavior Product Sales, 588 Medicine, Clinical Studies, and Experiments Coffee Not Disease Culprit, 548 Emergency Calls and Temperature, 550, 559 Fireworks and Injuries, 559 Hospital Beds, 550, 559 Medical Specialties and Gender, 586 Prescription Drug Prices, 588 Public Health and Nutrition Age, Cholesterol, and Sodium, 581 Fat and Cholesterol, 588 Fat Calories and Fat Grams, 559 Fat Grams and Secondary Schools, 550 Protein and Diastolic Blood Pressure, 586
  • 38. blu38582_fm_i-xxviii.qxd 9/29/10 2:46 PM Page xxvii Index of Applications Sports, Exercise, and Fitness NHL Assists and Total Points, 550, 559 Touchdowns and QB Ratings, 586 Triples and Home Runs, 549, 559 The Sciences Egg Production, 549, 559 Transportation Age and Driving Accidents, 586 Car Rental Companies, 536 Stopping Distances, 547, 558 Travel and Leisure Passengers and Airline Fares, 585 CHAPTER 11 Other Chi-Square Tests Business, Management, and Work Displaced Workers, 622 Employment of High School Females, 623 Employment Satisfaction, 625 Job Loss Reasons, 624 Mothers Working Outside the Home, 616 Retired Senior Executives Return to Work, 596 Work Force Distribution, 616 Demographics and Population Characteristics Education Level and Health Insurance, 602 Ethnicity and Movie Admissions, 614 Health Insurance Coverage, 623 Population and Age, 615 Women in the Military, 614 Economics and Investment Pension Investments, 622 Education and Testing Ages of Head Start Program Students, 602 Assessment of Mathematics Students, 602 Foreign Language Speaking Dorms, 616 Home-Schooled Student Activities, 601 Student Majors at Colleges, 615 Volunteer Practices of Students, 616 Entertainment Record CDs Sold, 615 Television Viewing, 624 Environmental Sciences, the Earth, and Space Tornadoes, 623 Food and Dining Consumption of Takeout Foods, 624 Favorite Ice Cream Flavor, 625 Fruit Soda Flavor Preference, 594 Genetically Modified Food, 601 Grocery Lists, 617 M&M’s Color Distribution, 626 Skittles Color Distribution, 600 Types of Pizza Purchased, 625 The Sciences Endangered or Threatened Species, 614 Government, Taxes, Politics, Public Policy, and Voting Composition of State Legislatures, 615 Congressional Representatives, 615 Tax Credit Refunds, 625 Travel and Leisure Recreational Reading and Gender, 615 Thanksgiving Travel, 617 Law and Order: Criminal Justice Firearm Deaths, 597 Gun Sale Denials, 622 Marketing, Sales, and Consumer Behavior Music Sales, 601 Payment Preference, 602 Pennant Colors Purchased, 625 Weekend Furniture Sales, 615 Medicine, Clinical Studies, and Experiments Cardiovascular Procedures, 624 Effectiveness of a New Drug, 615 Fathers in the Delivery Room, 616 Hospitals and Infections, 608 Mendel’s Peas, 592, 623 Organ Transplantation, 615 Paying for Prescriptions, 602 Risk of Injury, 623 Psychology and Human Behavior Alcohol and Gender, 610 Combating Midday Drowsiness, 601 Does Color Affect Your Appetite?, 618 Money and Happiness, 611 Sports, Exercise, and Fitness Choice of Exercise Equipment, 615 Injuries on Monkey Bars, 617 Medal Counts for the Olympics, 615 Youth Physical Fitness, 616 Surveys and Culture Participation in a Market Research Survey, 616 Technology Internet Users, 602 Satellite Dishes in Restricted Areas, 613 Transportation On-Time Performance by Airlines, 601 Tire Labeling, 622 Travel Accident Fatalities, 622 Truck Colors, 602 Ways to Get to Work, 625 CHAPTER 12 Analysis of Variance Buildings and Structures Home Building Times, 657 Lengths of Suspension Bridges, 638 Lengths of Various Types of Bridges, 663 Business, Management, and Work Weekly Unemployment Benefits, 647 Demographics and Population Characteristics Ages of Late-Night TV Talk Show Viewers, 665 Education and Testing Alumni Gift Solicitation, 666 Annual Child Care Costs, 639 Average Debt of College Graduates, 640 Expenditures per Pupil, 638, 647 Review Preparation for Statistics, 664 Environmental Sciences, the Earth, and Space Air Pollution, 666 Number of Farms, 639 Number of State Parks, 663 Temperatures in January, 663 Government, Taxes, Politics, Public Policy, and Voting Voters in Presidential Elections, 665 Law and Order: Criminal Justice Eyewitness Testimony, 630, 664 School Incidents Involving Police Calls, 664 Manufacturing and Product Development Durability of Paint, 657 Environmentally Friendly Air Freshener, 657 Types of Outdoor Paint, 657 Weights of Digital Cameras, 646 xxvii Marketing, Sales, and Consumer Behavior Age and Sales, 658 Automobile Sales Techniques, 655 Microwave Oven Prices, 639 Prices of Body Soap, 666 Medicine, Clinical Studies, and Experiments Diets and Exercise Programs, 666 Effects of Different Types of Diets, 664 Lowering Blood Pressure, 632 Tricking Knee Pain, 644 Psychology and Human Behavior Adult Children of Alcoholics, 667 Colors That Make You Smarter, 636, 645 Public Health and Nutrition Calories in Fast-Food Sandwiches, 639 Fiber Content of Foods, 646 Grams of Fat per Serving of Pizza, 663 Healthy Eating, 638 Iron Content of Foods and Drinks, 663 Sodium Content of Foods, 637 Sports, Exercise, and Fitness Basketball Scores for College Teams, 640 Weight Gain of Athletes, 638 Technology Cell Phone Bills, 639 The Sciences Increasing Plant Growth, 656 Transportation Employees at Toll Road Interchanges, 634 Gasoline Consumption, 650 Hybrid Vehicles, 637 CHAPTER 13 Nonparametric Statistics Buildings and Structures Home Prices, 714 Business, Management, and Work Employee Absences, 708 Increasing Supervisory Skills, 681 Job Offers for Chemical Engineers, 697 Weekly Earnings of Women, 680 Demographics and Population Characteristics Age of Foreign-Born Residents, 677 Ages of City Residents, 712
  • 39. blu38582_fm_i-xxviii.qxd xxviii 9/29/10 2:46 PM Page xxviii Index of Applications Ages of Drug Program Participants, 705 Ages When Married, 680 Family Income, 681 Gender of Train Passengers, 704 Economics and Investment Bank Branches and Deposits, 700 Natural Gas Costs, 680 Education and Testing Cyber School Enrollment, 680, 707 Exam Scores, 681, 713 Expenditures for Pupils, 697 Funding and Enrollment for Head Start Students, 715 Homework Exercises and Exam Scores, 713 Hours Worked by Student Employees, 712 Legal Costs for School Districts, 693 Mathematics Achievement Test Scores, 707 Mathematics Literacy Scores, 697 Medical School Enrollments, 687 Number of Faculty for Proprietary Schools, 681 Student Grade Point Averages, 714 Students’ Opinions on Lengthening the School Year, 681 Technology Proficiency Test, 686 Textbook Costs, 714 Entertainment Concert Seating, 708 Daily Lottery Numbers, 708 Motion Picture Releases and Gross Revenue, 707 State Lottery Numbers, 715 Television Viewers, 681, 713 Environmental Sciences, the Earth, and Space Clean Air, 679 Deaths Due to Severe Weather, 681 Heights of Waterfalls, 696 Tall Trees, 706 Food and Dining Cola Orders, 708 Lunch Costs, 712 Snow Cone Sales, 675 Government, Taxes, Politics, Public Policy, and Voting Property Assessments, 692 Tolls for Bridge, 715 Unemployment Benefits, 697 Law and Order: Criminal Justice Lengths of Prison Sentences, 686 Motor Vehicle Thefts and Burglaries, 707 Number of Crimes per Week, 698 Shoplifting Incidents, 688 Manufacturing and Product Development Breaking Strengths of Ropes, 712 Fill Rates of Bottles, 672, 713 Lifetime of Batteries, 714 Lifetime of Truck Tires, 712 Lifetimes of Handheld Video Games, 687 Output of Motors, 715 Routine Maintenance and Defective Parts, 682 Marketing, Sales, and Consumer Behavior Book Publishing, 707 Grocery Store Repricing, 712 Lawnmower Costs, 697 Printer Costs, 698 Medicine, Clinical Studies, and Experiments Diet Medication and Weight, 681 Drug Prices, 692, 693, 708, 715 Drug Side Effects, 674 Ear Infections in Swimmers, 677 Effects of a Pill on Appetite, 681 Hospitals and Nursing Homes, 707 Hospital Infections, 694 Medication and Reaction Times, 715 Pain Medication, 692 Speed of Pain Relievers, 687 Weight Loss Through Diet, 692 Public Health and Nutrition Amounts of Caffeine in Beverages, 698 Calories and Cholesterol in Fast-Food Sandwiches, 707 Calories in Cereals, 697 School Lunch, 686 Sodium Content of Fast-Food Sandwiches, 715 Sports, Exercise, and Fitness Game Attendance, 680 Hunting Accidents, 687 Olympic Medals, 715 Skiing Conditions, 708 Times to Complete an Obstacle Course, 684 Winning Baseball Games, 687 The Sciences Maximum Speeds of Animals, 698 Weights of Turkeys, 714 Transportation Fuel Efficiency of Automobiles, 712 Gasoline Costs, 707 Stopping Distances of Automobiles, 687 Subway and Commuter Rail Passengers, 707 Travel and Leisure Beach Temperatures for July, 713 CHAPTER 14 Sampling and Simulation Demographics and Population Characteristics Foreign-Born Residents, 745 Population and Areas of U.S. Cities, 731 Stay-at-Home Parents, 745 Education and Testing Is That Your Final Answer?, 729 Entertainment The Monty Hall Problem, 720, 749 Environmental Sciences, the Earth, and Space Rainfall in U.S. Cities, 732 Record High Temperatures, 732 Should We Be Afraid of Lightning?, 725 Wind Speed of Hurricanes, 746, 747 Wind Speeds, 732 Food and Dining Smoking Bans and Profits, 738 Government, Taxes, Politics, Public Policy, and Voting Composition of State Legislatures, 747 Electoral Votes, 732, 733 Law and Order: Criminal Justice State Governors on Capital Punishment, 723 Medicine, Clinical Studies, and Experiments Snoring, 741 Public Health and Nutrition The White or Wheat Bread Debate, 730 Sports, Exercise, and Fitness Basketball Foul Shots, 745 Clay Pigeon Shooting, 745 Playing Basketball, 745 Technology Television Set Ownership, 745
  • 40. blu38582_ch01_001-034.qxd 8/18/10 10:12 Page 1 C H A P T E R 1 The Nature of Probability and Statistics Objectives Outline After completing this chapter, you should be able to 1 2 3 4 Demonstrate knowledge of statistical terms. Differentiate between the two branches of statistics. Identify types of data. Identify the measurement level for each variable. 5 Identify the four basic sampling techniques. 6 Explain the difference between an observational and an experimental study. 7 Explain how statistics can be used and misused. 8 Introduction 1–1 Descriptive and Inferential Statistics 1–2 Variables and Types of Data 1–3 Data Collection and Sampling Techniques 1–4 Observational and Experimental Studies 1–5 Uses and Misuses of Statistics 1–6 Computers and Calculators Explain the importance of computers and calculators in statistics. Summary 1–1
  • 41. blu38582_ch01_001-034.qxd 2 8/18/10 10:12 Page 2 Chapter 1 The Nature of Probability and Statistics Are We Improving Our Diet? Statistics Today It has been determined that diets rich in fruits and vegetables are associated with a lower risk of chronic diseases such as cancer. Nutritionists recommend that Americans consume five or more servings of fruits and vegetables each day. Several researchers from the Division of Nutrition, the National Center for Chronic Disease Control and Prevention, the National Cancer Institute, and the National Institutes of Health decided to use statistical procedures to see how much progress is being made toward this goal. The procedures they used and the results of the study will be explained in this chapter. See Statistics Today—Revisited at the end of this chapter. Introduction You may be familiar with probability and statistics through radio, television, newspapers, and magazines. For example, you may have read statements like the following found in newspapers. Unusual Stats Of people in the United States, 14% said that they feel happiest in June, and 14% said that they feel happiest in December. • Nearly one in seven U.S. families are struggling with bills from medical expenses even though they have health insurance. (Source: Psychology Today.) • Eating 10 grams of fiber a day reduces the risk of heart attack by 14%. (Source: Archives of Internal Medicine, Reader’s Digest.) • Thirty minutes of exercise two or three times each week can raise HDLs by 10% to 15%. (Source: Prevention.) • In 2008, the average credit card debt for college students was $3173. (Source: • About 15% of men in the United States are left-handed and 9% of women are lefthanded. (Source: Scripps Survey Research Center.) • The median age of people who watch the Tonight Show with Jay Leno is 48.1. (Source: Nielsen Media Research.) Statistics is used in almost all fields of human endeavor. In sports, for example, a statistician may keep records of the number of yards a running back gains during a football 1–2
  • 42. blu38582_ch01_001-034.qxd 8/18/10 10:12 Page 3 Section 1–1 Descriptive and Inferential Statistics Interesting Fact Every day in the United States about 120 golfers claim that they made a hole-in-one. Historical Note A Scottish landowner and president of the Board of Agriculture, Sir John Sinclair introduced the word statistics into the English language in the 1798 publication of his book on a statistical account of Scotland. The word statistics is derived from the Latin word status, which is loosely defined as a statesman. 3 game, or the number of hits a baseball player gets in a season. In other areas, such as public health, an administrator might be concerned with the number of residents who contract a new strain of flu virus during a certain year. In education, a researcher might want to know if new methods of teaching are better than old ones. These are only a few examples of how statistics can be used in various occupations. Furthermore, statistics is used to analyze the results of surveys and as a tool in scientific research to make decisions based on controlled experiments. Other uses of statistics include operations research, quality control, estimation, and prediction. Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data. Students study statistics for several reasons: 1. Like professional people, you must be able to read and understand the various statistical studies performed in your fields. To have this understanding, you must be knowledgeable about the vocabulary, symbols, concepts, and statistical procedures used in these studies. 2. You may be called on to conduct research in your field, since statistical procedures are basic to research. To accomplish this, you must be able to design experiments; collect, organize, analyze, and summarize data; and possibly make reliable predictions or forecasts for future use. You must also be able to communicate the results of the study in your own words. 3. You can also use the knowledge gained from studying statistics to become better consumers and citizens. For example, you can make intelligent decisions about what products to purchase based on consumer studies, about government spending based on utilization studies, and so on. These reasons can be considered some of the goals for studying statistics. It is the purpose of this chapter to introduce the goals for studying statistics by answering questions such as the following: What are the branches of statistics? What are data? How are samples selected? 1–1 Objective 1 Demonstrate knowledge of statistical terms. Descriptive and Inferential Statistics To gain knowledge about seemingly haphazard situations, statisticians collect information for variables, which describe the situation. A variable is a characteristic or attribute that can assume different values. Data are the values (measurements or observations) that the variables can assume. Variables whose values are determined by chance are called random variables. Suppose that an insurance company studies its records over the past several years and determines that, on average, 3 out of every 100 automobiles the company insured were involved in accidents during a 1-year period. Although there is no way to predict the specific automobiles that will be involved in an accident (random occurrence), the company can adjust its rates accordingly, since the company knows the general pattern over the long run. (That is, on average, 3% of the insured automobiles will be involved in an accident each year.) A collection of data values forms a data set. Each value in the data set is called a data value or a datum. 1–3
  • 43. blu38582_ch01_001-034.qxd 4 8/26/10 Page 4 Chapter 1 The Nature of Probability and Statistics Objective 2 Differentiate between the two branches of statistics. Historical Note The origin of descriptive statistics can be traced to data collection methods used in censuses taken by the Babylonians and Egyptians between 4500 and 3000 B.C. In addition, the Roman Emperor Augustus (27 B.C.—A.D. 17) conducted surveys on births and deaths of the citizens of the empire, as well as the number of livestock each owned and the crops each citizen harvested yearly. Historical Note Inferential statistics originated in the 1600s, when John Graunt published his book on population growth, Natural and Political Observations Made upon the Bills of Mortality. About the same time, another mathematician/ astronomer, Edmund Halley, published the first complete mortality tables. (Insurance companies use mortality tables to determine life insurance rates.) 1–4 9:18 AM Data can be used in different ways. The body of knowledge called statistics is sometimes divided into two main areas, depending on how data are used. The two areas are 1. Descriptive statistics 2. Inferential statistics Descriptive statistics consists of the collection, organization, summarization, and presentation of data. In descriptive statistics the statistician tries to describe a situation. Consider the national census conducted by the U.S. government every 10 years. Results of this census give you the average age, income, and other characteristics of the U.S. population. To obtain this information, the Census Bureau must have some means to collect relevant data. Once data are collected, the bureau must organize and summarize them. Finally, the bureau needs a means of presenting the data in some meaningful form, such as charts, graphs, or tables. The second area of statistics is called inferential statistics. Inferential statistics consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions. Here, the statistician tries to make inferences from samples to populations. Inferential statistics uses probability, i.e., the chance of an event occurring. You may be familiar with the concepts of probability through various forms of gambling. If you play cards, dice, bingo, or lotteries, you win or lose according to the laws of probability. Probability theory is also used in the insurance industry and other areas. It is important to distinguish between a sample and a population. A population consists of all subjects (human or otherwise) that are being studied. Most of the time, due to the expense, time, size of population, medical concerns, etc., it is not possible to use the entire population for a statistical study; therefore, researchers use samples. A sample is a group of subjects selected from a population. If the subjects of a sample are properly selected, most of the time they should possess the same or similar characteristics as the subjects in the population. The techniques used to properly select a sample will be explained in Section 1–3. An area of inferential statistics called hypothesis testing is a decision-making process for evaluating claims about a population, based on information obtained from samples. For example, a researcher may wish to know if a new drug will reduce the number of heart attacks in men over 70 years of age. For this study, two groups of men over 70 would be selected. One group would be given the drug, and the other would be given a placebo (a substance with no medical benefits or harm). Later, the number of heart attacks occurring in each group of men would be counted, a statistical test would be run, and a decision would be made about the effectiveness of the drug. Statisticians also use statistics to determine relationships among variables. For example, relationships were the focus of the most noted study in the 20th century, “Smoking and Health,” published by the Surgeon General of the United States in 1964. He stated that after reviewing and evaluating the data, his group found a definite relationship between smoking and lung cancer. He did not say that cigarette smoking actually causes lung cancer, but that there is a relationship between smoking and lung cancer. This conclusion was based on a study done in 1958 by Hammond and Horn. In this study, 187,783 men were observed over a period of 45 months. The death rate from
  • 44. blu38582_ch01_001-034.qxd 8/18/10 10:12 Page 5 Section 1–1 Descriptive and Inferential Statistics 5 Speaking of Statistics Statistics and the New Planet In the summer of 2005, astronomers announced the discovery of a new planet in our solar system. Astronomers have dubbed it Xena. They also discovered that it has a moon that is larger than Pluto.1 Xena is about 9 billion miles from the Sun. (Some sources say 10 billion.) Its diameter is about 4200 miles. Its surface temperature has been estimated at Ϫ400ЊF, and it takes 560 years to circle the Sun. How does Xena compare to the other planets? Let’s look at the statistics. Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto1 Diameter (miles) Distance from the Sun (millions of miles) Orbital period (days) Mean temperature (؇F) Number of moons 3,032 7,521 7,926 4,222 88,846 74,897 31,763 30,775 1,485 36 67.2 93 141.6 483.8 890.8 1,784.8 2,793.1 3,647.2 88 224.7 365.2 687 4,331 10,747 30,589 59,800 90,588 333 867 59 Ϫ85 Ϫ166 Ϫ220 Ϫ320 Ϫ330 Ϫ375 0 0 1 2 63 47 27 13 1 Source: NASA. 1 Some astronomers no longer consider Pluto a planet. With these statistics, we can make some comparisons. For example, Xena is about the size of the planet Mars, but it is over 21 times the size of Pluto. (Compare the volumes.) It takes about twice as long to circle the Sun as Pluto. What other comparisons can you make? Unusual Stat Twenty-nine percent of Americans want their boss’s job. lung cancer in this group of volunteers was 10 times as great for smokers as for nonsmokers. Finally, by studying past and present data and conditions, statisticians try to make predictions based on this information. For example, a car dealer may look at past sales records for a specific month to decide what types of automobiles and how many of each type to order for that month next year. Applying the Concepts 1–1 Attendance and Grades Read the following on attendance and grades, and answer the questions. A study conducted at Manatee Community College revealed that students who attended class 95 to 100% of the time usually received an A in the class. Students who attended class 1–5
  • 45. blu38582_ch01_001-034.qxd 6 8/18/10 10:12 Page 6 Chapter 1 The Nature of Probability and Statistics Unusual Stat Only one-third of crimes committed are reported to the police. 80 to 90% of the time usually received a B or C in the class. Students who attended class less than 80% of the time usually received a D or an F or eventually withdrew from the class. Based on this information, attendance and grades are related. The more you attend class, the more likely it is you will receive a higher grade. If you improve your attendance, your grades will probably improve. Many factors affect your grade in a course. One factor that you have considerable control over is attendance. You can increase your opportunities for learning by attending class more often. 1. 2. 3. 4. 5. 6. What are the variables under study? What are the data in the study? Are descriptive, inferential, or both types of statistics used? What is the population under study? Was a sample collected? If so, from where? From the information given, comment on the relationship between the variables. See page 33 for the answers. 1–2 Objective 3 Identify types of data. Variables and Types of Data As stated in Section 1–1, statisticians gain information about a particular situation by collecting data for random variables. This section will explore in greater detail the nature of variables and types of data. Variables can be classified as qualitative or quantitative. Qualitative variables are variables that can be placed into distinct categories, according to some characteristic or attribute. For example, if subjects are classified according to gender (male or female), then the variable gender is qualitative. Other examples of qualitative variables are religious preference and geographic locations. Quantitative variables are numerical and can be ordered or ranked. For example, the variable age is numerical, and people can be ranked in order according to the value of their ages. Other examples of quantitative variables are heights, weights, and body temperatures. Quantitative variables can be further classified into two groups: discrete and continuous. Discrete variables can be assigned values such as 0, 1, 2, 3 and are said to be countable. Examples of discrete variables are the number of children in a family, the number of students in a classroom, and the number of calls received by a switchboard operator each day for a month. Discrete variables assume values that can be counted. Continuous variables, by comparison, can assume an infinite number of values in an interval between any two specific values. Temperature, for example, is a continuous variable, since the variable can assume an infinite number of values between any two given temperatures. Continuous variables can assume an infinite number of values between any two specific values. They are obtained by measuring. They often include fractions and decimals. The classification of variables can be summarized as follows: Data Qualitative Quantitative Discrete 1–6 Continuous
  • 46. blu38582_ch01_001-034.qxd 8/18/10 10:12 Page 7 Section 1–2 Variables and Types of Data Unusual Stat Fifty-two percent of Americans live within 50 miles of a coastal shoreline. 7 Since continuous data must be measured, answers must be rounded because of the limits of the measuring device. Usually, answers are rounded to the nearest given unit. For example, heights might be rounded to the nearest inch, weights to the nearest ounce, etc. Hence, a recorded height of 73 inches could mean any measure from 72.5 inches up to but not including 73.5 inches. Thus, the boundary of this measure is given as 72.5–73.5 inches. Boundaries are written for convenience as 72.5–73.5 but are understood to mean all values up to but not including 73.5. Actual data values of 73.5 would be rounded to 74 and would be included in a class with boundaries of 73.5 up to but not including 74.5, written as 73.5–74.5. As another example, if a recorded weight is 86 pounds, the exact boundaries are 85.5 up to but not including 86.5, written as 85.5–86.5 pounds. Table 1–1 helps to clarify this concept. The boundaries of a continuous variable are given in one additional decimal place and always end with the digit 5. Table 1–1 Recorded Values and Boundaries Variable 4 Identify the measurement level for each variable. Boundaries Length Temperature Time Mass Objective Recorded value 15 centimeters (cm) 86 degrees Fahrenheit (ºF) 0.43 second (sec) 1.6 grams (g) 14.5–15.5 cm 85.5–86.5ЊF 0.425–0.435 sec 1.55–1.65 g In addition to being classified as qualitative or quantitative, variables can be classified by how they are categorized, counted, or measured. For example, can the data be organized into specific categories, such as area of residence (rural, suburban, or urban)? Can the data values be ranked, such as first place, second place, etc.? Or are the values obtained from measurement, such as heights, IQs, or temperature? This type of classification—i.e., how variables are categorized, counted, or measured—uses measurement scales, and four common types of scales are used: nominal, ordinal, interval, and ratio. The first level of measurement is called the nominal level of measurement. A sample of college instructors classified according to subject taught (e.g., English, history, psychology, or mathematics) is an example of nominal-level measurement. Classifying survey subjects as male or female is another example of nominal-level measurement. No ranking or order can be placed on the data. Classifying residents according to zip codes is also an example of the nominal level of measurement. Even though numbers are assigned as zip codes, there is no meaningful order or ranking. Other examples of nominal-level data are political party (Democratic, Republican, Independent, etc.), religion (Christianity, Judaism, Islam, etc.), and marital status (single, married, divorced, widowed, separated). The nominal level of measurement classifies data into mutually exclusive (nonoverlapping) categories in which no order or ranking can be imposed on the data. The next level of measurement is called the ordinal level. Data measured at this level can be placed into categories, and these categories can be ordered, or ranked. For example, from student evaluations, guest speakers might be ranked as superior, average, or poor. Floats in a homecoming parade might be ranked as first place, second place, etc. Note that precise measurement of differences in the ordinal level of measurement does not exist. For instance, when people are classified according to their build (small, medium, or large), a large variation exists among the individuals in each class. 1–7
  • 47. blu38582_ch01_001-034.qxd 8 8/26/10 Page 8 Chapter 1 The Nature of Probability and Statistics Unusual Stat Sixty-three percent of us say we would rather hear the bad news first. Historical Note When data were first analyzed statistically by Karl Pearson and Francis Galton, almost all were continuous data. In 1899, Pearson began to analyze discrete data. Pearson found that some data, such as eye color, could not be measured, so he termed such data nominal data. Ordinal data were introduced by a German numerologist Frederich Mohs in 1822 when he introduced a hardness scale for minerals. For example, the hardest stone is the diamond, which he assigned a hardness value of 1500. Quartz was assigned a hardness value of 100. This does not mean that a diamond is 15 times harder than quartz. It only means that a diamond is harder than quartz. In 1947, a psychologist named Stanley Smith Stevens made a further division of continuous data into two categories, namely, interval and ratio. 1–8 9:18 AM Other examples of ordinal data are letter grades (A, B, C, D, F). The ordinal level of measurement classifies data into categories that can be ranked; however, precise differences between the ranks do not exist. The third level of measurement is called the interval level. This level differs from the ordinal level in that precise differences do exist between units. For example, many standardized psychological tests yield values measured on an interval scale. IQ is an example of such a variable. There is a meaningful difference of 1 point between an IQ of 109 and an IQ of 110. Temperature is another example of interval measurement, since there is a meaningful difference of 1ЊF between each unit, such as 72 and 73ЊF. One property is lacking in the interval scale: There is no true zero. For example, IQ tests do not measure people who have no intelligence. For temperature, 0ЊF does not mean no heat at all. The interval level of measurement ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero. The final level of measurement is called the ratio level. Examples of ratio scales are those used to measure height, weight, area, and number of phone calls received. Ratio scales have differences between units (1 inch, 1 pound, etc.) and a true zero. In addition, the ratio scale contains a true ratio between values. For example, if one person can lift 200 pounds and another can lift 100 pounds, then the ratio between them is 2 to 1. Put another way, the first person can lift twice as much as the second person. The ratio level of measurement possesses all the characteristics of interval measurement, and there exists a true zero. In addition, true ratios exist when the same variable is measured on two different members of the population. There is not complete agreement among statisticians about the classification of data into one of the four categories. For example, some researchers classify IQ data as ratio data rather than interval. Also, data can be altered so that they fit into a different category. For instance, if the incomes of all professors of a college are classified into the three categories of low, average, and high, then a ratio variable becomes an ordinal variable. Table 1–2 gives some examples of each type of data. Table 1–2 Examples of Measurement Scales Nominal-level data Ordinal-level data Interval-level data Ratio-level data Zip code Gender (male, female) Eye color (blue, brown, green, hazel) Political affiliation Religious affiliation Major field (mathematics, computers, etc.) Nationality Grade (A, B, C, D, F) Judging (first place, second place, etc.) Rating scale (poor, good, excellent) Ranking of tennis players SAT score IQ Temperature Height Weight Time Salary Age
  • 48. blu38582_ch01_001-034.qxd 8/18/10 10:13 Page 9 Section 1–3 Data Collection and Sampling Techniques 9 Applying the Concepts 1–2 Safe Travel Read the following information about the transportation industry and answer the questions. Transportation Safety The chart shows the number of job-related injuries for each of the transportation industries for 1998. Industry Number of injuries Railroad Intercity bus Subway Trucking Airline 4520 5100 6850 7144 9950 1. 2. 3. 4. 5. What are the variables under study? Categorize each variable as quantitative or qualitative. Categorize each quantitative variable as discrete or continuous. Identify the level of measurement for each variable. The railroad is shown as the safest transportation industry. Does that mean railroads have fewer accidents than the other industries? Explain. 6. What factors other than safety influence a person’s choice of transportation? 7. From the information given, comment on the relationship between the variables. See page 33 for the answers. 1–3 Objective 5 Identify the four basic sampling techniques. Data Collection and Sampling Techniques In research, statisticians use data in many different ways. As stated previously, data can be used to describe situations or events. For example, a manufacturer might want to know something about the consumers who will be purchasing his product so he can plan an effective marketing strategy. In another situation, the management of a company might survey its employees to assess their needs in order to negotiate a new contract with the employees’ union. Data can be used to determine whether the educational goals of a school district are being met. Finally, trends in various areas, such as the stock market, can be analyzed, enabling prospective buyers to make more intelligent decisions concerning what stocks to purchase. These examples illustrate a few situations where collecting data will help people make better decisions on courses of action. Data can be collected in a variety of ways. One of the most common methods is through the use of surveys. Surveys can be done by using a variety of methods. Three of the most common methods are the telephone survey, the mailed questionnaire, and the personal interview. Telephone surveys have an advantage over personal interview surveys in that they are less costly. Also, people may be more candid in their opinions since there is no faceto-face contact. A major drawback to the telephone survey is that some people in the population will not have phones or will not answer when the calls are made; hence, not all people have a chance of being surveyed. Also, many people now have unlisted numbers and cell phones, so they cannot be surveyed. Finally, even the tone of the voice of the interviewer might influence the response of the person who is being interviewed. Mailed questionnaire surveys can be used to cover a wider geographic area than telephone surveys or personal interviews since mailed questionnaire surveys are less expensive to conduct. Also, respondents can remain anonymous if they desire. Disadvantages 1–9
  • 49. blu38582_ch01_001-034.qxd 10 8/18/10 10:13 Page 10 Chapter 1 The Nature of Probability and Statistics Historical Note A pioneer in census taking was PierreSimon de Laplace. In 1780, he developed the Laplace method of estimating the population of a country. The principle behind his method was to take a census of a few selected communities and to determine the ratio of the population to the number of births in these communities. (Good birth records were kept.) This ratio would be used to multiply the number of births in the entire country to estimate the number of citizens in the country. Historical Note The first census in the United States was conducted in 1790. Its purpose was to insure proper Congressional representation. of mailed questionnaire surveys include a low number of responses and inappropriate answers to questions. Another drawback is that some people may have difficulty reading or understanding the questions. Personal interview surveys have the advantage of obtaining in-depth responses to questions from the person being interviewed. One disadvantage is that interviewers must be trained in asking questions and recording responses, which makes the personal interview survey more costly than the other two survey methods. Another disadvantage is that the interviewer may be biased in his or her selection of respondents. Data can also be collected in other ways, such as surveying records or direct observation of situations. As stated in Section 1–1, researchers use samples to collect data and information about a particular variable from a large population. Using samples saves time and money and in some cases enables the researcher to get more detailed information about a particular subject. Samples cannot be selected in haphazard ways because the information obtained might be biased. For example, interviewing people on a street corner during the day would not include responses from people working in offices at that time or from people attending school; hence, not all subjects in a particular population would have a chance of being selected. To obtain samples that are unbiased—i.e., that give each subject in the population an equally likely chance of being selected—statisticians use four basic methods of sampling: random, systematic, stratified, and cluster sampling. Random Sampling Random samples are selected by using chance methods or random numbers. One such method is to number each subject in the population. Then place numbered cards in a bowl, mix them thoroughly, and select as many cards as needed. The subjects whose numbers are selected constitute the sample. Since it is difficult to mix the cards 1–10
  • 50. blu38582_ch01_001-034.qxd 8/18/10 10:13 Page 11 Section 1–3 Data Collection and Sampling Techniques 11 Speaking of Statistics The Worst Day for Weight Loss Many overweight people have difficulty losing weight. Prevention magazine reported that researchers from Washington University of Medicine studied the diets of 48 adult weight loss participants. They used food diaries, exercise monitors, and weigh-ins. They found that the participants ate an average of 236 more calories on Saturdays than they did on the other weekdays. This would amount to a weight gain of 9 pounds per year. So if you are watching your diet, be careful on Saturdays. Are the statistics reported in this study descriptive or inferential in nature? What type of variables are used here? thoroughly, there is a chance of obtaining a biased sample. For this reason, statisticians use another method of obtaining numbers. They generate random numbers with a computer or calculator. Before the invention of computers, random numbers were obtained from tables. Some two-digit random numbers are shown in Table 1–3. To select a random sample of, say, 15 subjects out of 85 subjects, it is necessary to number each subject from 01 to 85. Then select a starting number by closing your eyes and placing your finger on a number in the table. (Although this may sound somewhat unusual, it enables us to find a starting number at random.) In this case suppose your finger landed on the number 12 in the second column. (It is the sixth number down from the top.) Then proceed downward until you have selected 15 different numbers between 01 and 85. When you reach the bottom of the column, go to the top of the next column. If you select a number greater than 85 or the number 00 or a duplicate number, just omit it. In our example, we will use the subjects numbered 12, 27, 75, 62, 57, 13, 31, 06, 16, 49, 46, 71, 53, 41, and 02. A more detailed procedure for selecting a random sample using a table of random numbers is given in Chapter 14, using Table D in Appendix C. Systematic Sampling Researchers obtain systematic samples by numbering each subject of the population and then selecting every kth subject. For example, suppose there were 2000 subjects in the population and a sample of 50 subjects were needed. Since 2000 Ϭ 50 ϭ 40, then k ϭ 40, and every 40th subject would be selected; however, the first subject (numbered between 1 and 40) would be selected at random. Suppose subject 12 were the first subject selected; then the sample would consist of the subjects whose numbers were 12, 52, 92, etc., until 50 subjects were obtained. When using systematic sampling, you must be careful about how the subjects in the population are numbered. If subjects were arranged in a manner 1–11
  • 51. blu38582_ch01_001-034.qxd 12 8/18/10 10:13 Page 12 Chapter 1 The Nature of Probability and Statistics Random Numbers Table 1–3 79 26 18 19 14 29 01 55 84 62 66 48 94 00 46 77 81 40 41 52 13 82 57 12 27 75 95 62 57 13 31 06 16 49 96 46 71 53 41 02 44 18 92 65 95 21 28 69 73 53 44 85 43 15 93 13 30 69 30 50 67 68 96 37 69 97 19 98 27 95 27 73 60 43 56 34 93 06 93 65 62 82 13 29 75 01 80 62 39 23 35 50 20 27 76 33 31 73 30 62 99 01 76 55 15 93 53 75 04 92 37 77 32 15 97 07 91 19 74 75 33 08 28 25 85 96 67 09 74 34 13 79 55 95 64 44 31 58 18 38 01 39 61 68 96 87 49 24 55 50 29 66 74 08 58 05 05 49 64 63 12 13 04 21 56 93 29 28 21 43 83 64 19 40 53 42 27 74 90 99 79 83 45 16 49 50 64 43 47 34 47 40 04 10 89 54 67 49 10 75 46 77 30 45 27 92 89 50 66 18 51 44 03 82 96 64 86 17 83 00 77 45 29 16 71 11 89 29 41 38 27 85 02 11 such as wife, husband, wife, husband, and every 40th subject were selected, the sample would consist of all husbands. Numbering is not always necessary. For example, a researcher may select every tenth item from an assembly line to test for defects. Stratified Sampling Researchers obtain stratified samples by dividing the population into groups (called strata) according to some characteristic that is important to the study, then sampling from each group. Samples within the strata should be randomly selected. For example, suppose the president of a two-year college wants to learn how students feel about a certain issue. Furthermore, the president wishes to see if the opinions of the first-year students differ from those of the second-year students. The president will randomly select students from each group to use in the sample. Historical Note In 1936, the Literary Digest, on the basis of a biased sample of its subscribers, predicted that Alf Landon would defeat Franklin D. Roosevelt in the upcoming presidential election. Roosevelt won by a landslide. The magazine ceased publication the following year. 1–12 Cluster Sampling Researchers also use cluster samples. Here the population is divided into groups called clusters by some means such as geographic area or schools in a large school district, etc. Then the researcher randomly selects some of these clusters and uses all members of the selected clusters as the subjects of the samples. Suppose a researcher wishes to survey apartment dwellers in a large city. If there are 10 apartment buildings in the city, the researcher can select at random 2 buildings from the 10 and interview all the residents of these buildings. Cluster sampling is used when the population is large or when it involves subjects residing in a large geographic area. For example, if one wanted to do a study involving the patients in the hospitals in New York City, it would be very costly and time-consuming to try to obtain a random sample of patients since they would be spread over a large area. Instead, a few hospitals could be selected at random, and the patients in these hospitals would be interviewed in a cluster. The four basic sampling methods are summarized in Table 1–4. Other Sampling Methods In addition to the four basic sampling methods, researchers use other methods to obtain samples. One such method is called a convenience sample. Here a researcher uses
  • 52. blu38582_ch01_001-034.qxd 8/18/10 10:13 Page 13 Section 1–4 Observational and Experimental Studies Table 1–4 Random Systematic Stratified Cluster Interesting Facts Older Americans are less likely to sacrifice happiness for a higherpaying job. According to one survey, 38% of those aged 18–29 said they would choose more money over happiness, while only 3% of those over 65 would. 13 Summary of Sampling Methods Subjects are selected by random numbers. Subjects are selected by using every kth number after the first subject is randomly selected from 1 through k. Subjects are selected by dividing up the population into groups (strata), and subjects are randomly selected within groups. Subjects are selected by using an intact group that is representative of the population. subjects that are convenient. For example, the researcher may interview subjects entering a local mall to determine the nature of their visit or perhaps what stores they will be patronizing. This sample is probably not representative of the general customers for several reasons. For one thing, it was probably taken at a specific time of day, so not all customers entering the mall have an equal chance of being selected since they were not there when the survey was being conducted. But convenience samples can be representative of the population. If the researcher investigates the characteristics of the population and determines that the sample is representative, then it can be used. Other sampling techniques, such as sequential sampling, double sampling, and multistage sampling, are explained in Chapter 14, along with a more detailed explanation of the four basic sampling techniques. Applying the Concepts 1–3 American Culture and Drug Abuse Assume you are a member of the Family Research Council and have become increasingly concerned about the drug use by professional sports players. You set up a plan and conduct a survey on how people believe the American culture (television, movies, magazines, and popular music) influences illegal drug use. Your survey consists of 2250 adults and adolescents from around the country. A consumer group petitions you for more information about your survey. Answer the following questi