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# Business Research Methods, 9th ed.Chapter 21

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William G. Zikmund, Barry J. Babin, Jon C. Carr, Mitch Griffin

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### Business Research Methods, 9th ed.Chapter 21

1. 1. Business Research Methods William G. Zikmund Chapter 21: Univariate Statistics
2. 2. Univariate Statistics • Test of statistical significance • Hypothesis testing one variable at a time
3. 3. Hypothesis • Unproven proposition • Supposition that tentatively explains certain facts or phenomena • Assumption about nature of the world
4. 4. Hypothesis • An unproven proposition or supposition that tentatively explains certain facts or phenomena – Null hypothesis – Alternative hypothesis
5. 5. Null Hypothesis • Statement about the status quo • No difference
6. 6. Alternative Hypothesis • Statement that indicates the opposite of the null hypothesis
7. 7. Significance Level • Critical probability in choosing between the null hypothesis and the alternative hypothesis
8. 8. Significance Level • Critical Probability • Confidence Level • Alpha • Probability Level selected is typically .05 or .01 • Too low to warrant support for the null hypothesis
9. 9. 0.3: oH The null hypothesis that the mean is equal to 3.0:
10. 10. 0.3:1 H The alternative hypothesis that the mean does not equal to 3.0:
11. 11. A Sampling Distribution 3.0 x
12. 12. 3.0 x a.025 a.025 A Sampling Distribution
13. 13. LOWER LIMIT UPPER LIMIT 3.0 A Sampling Distribution
14. 14. Critical values of  Critical value - upper limit n S ZZSX  or         225 5.1 96.10.3
15. 15.  1.096.10.3  196.0.3  196.3 Critical values of 
16. 16. Critical value - lower limit n S ZZSX -or-         225 5.1 96.1-0.3 Critical values of 
17. 17.  1.096.10.3  196.0.3  804.2 Critical values of 
18. 18. Region of Rejection LOWER LIMIT UPPER LIMIT 3.0
19. 19. Hypothesis Test  3.0 2.804 3.1963.0 3.78
20. 20. Accept null Reject null Null is true Null is false Correct- no error Type I error Type II error Correct- no error Type I and Type II Errors
21. 21. Type I and Type II Errors in Hypothesis Testing State of Null Hypothesis Decision in the Population Accept Ho Reject Ho Ho is true Correct--no error Type I error Ho is false Type II error Correct--no error
22. 22. Calculating Zobs xs x zobs  
23. 23. X obs S X Z   Alternate Way of Testing the Hypothesis
24. 24. X obs S Z   78.3 1. 0.378.3   1. 78.0  8.7 Alternate Way of Testing the Hypothesis
25. 25. Choosing the Appropriate Statistical Technique • Type of question to be answered • Number of variables – Univariate – Bivariate – Multivariate • Scale of measurement
26. 26. PARAMETRIC STATISTICS NONPARAMETRIC STATISTICS
27. 27. t-Distribution • Symmetrical, bell-shaped distribution • Mean of zero and a unit standard deviation • Shape influenced by degrees of freedom
28. 28. Degrees of Freedom • Abbreviated d.f. • Number of observations • Number of constraints
29. 29. or Xlc StX .. n S tX lc ..limitUpper  n S tX lc ..limitLower  Confidence Interval Estimate Using the t-distribution
30. 30. = population mean = sample mean = critical value of t at a specified confidence level = standard error of the mean = sample standard deviation = sample size ..lct  X X S S n Confidence Interval Estimate Using the t-distribution
31. 31. xcl stX  17 66.2 7.3    n S X Confidence Interval Estimate Using the t-distribution
32. 32. 07.5 )1766.2(12.27.3limitupper  
33. 33. 33.2 )1766.2(12.27.3limitLower  
34. 34. Hypothesis Test Using the t-Distribution
35. 35. Suppose that a production manager believes the average number of defective assemblies each day to be 20. The factory records the number of defective assemblies for each of the 25 days it was opened in a given month. The mean was calculated to be 22, and the standard deviation, ,to be 5. X S Univariate Hypothesis Test Utilizing the t-Distribution
36. 36. 20: 20: 1 0     H H
37. 37. nSSX / 25/5 1
38. 38. The researcher desired a 95 percent confidence, and the significance level becomes .05.The researcher must then find the upper and lower limits of the confidence interval to determine the region of rejection. Thus, the value of t is needed. For 24 degrees of freedom (n-1, 25-1), the t-value is 2.064. Univariate Hypothesis Test Utilizing the t-Distribution
39. 39. :limitLower  25/5064.220..  Xlc St  1064.220 936.17
40. 40. :limitUpper  25/5064.220..  Xlc St  1064.220 064.20
41. 41. X obs S X t   1 2022   1 2  2 Univariate Hypothesis Test t-Test
42. 42. Testing a Hypothesis about a Distribution • Chi-Square test • Test for significance in the analysis of frequency distributions • Compare observed frequencies with expected frequencies • “Goodness of Fit”
43. 43.    i ii )²( ² E EO x Chi-Square Test
44. 44. x² = chi-square statistics Oi = observed frequency in the ith cell Ei = expected frequency on the ith cell Chi-Square Test
45. 45. n CR E ji ij  Chi-Square Test Estimation for Expected Number for Each Cell
46. 46. Chi-Square Test Estimation for Expected Number for Each Cell Ri = total observed frequency in the ith row Cj = total observed frequency in the jth column n = sample size
47. 47.     2 2 22 1 2 112 E EO E EO X     Univariate Hypothesis Test Chi-square Example
48. 48.     50 5040 50 5060 22 2    X 4 Univariate Hypothesis Test Chi-square Example
49. 49. Hypothesis Test of a Proportion p is the population proportion p is the sample proportion p is estimated with p
50. 50. 5.:H 5.:H 1 0 p p Hypothesis Test of a Proportion
51. 51.    100 4.06.0 pS 100 24.  0024. 04899.
52. 52. pS p Zobs p  04899. 5.6.   04899. 1.  04.2
53. 53. 0115.Sp  000133.Sp  1200 16. Sp  1200 )8)(.2(. Sp  n pq Sp  20.p  200,1n  Hypothesis Test of a Proportion: Another Example
54. 54. 0115.Sp  000133.Sp  1200 16. Sp  1200 )8)(.2(. Sp  n pq Sp  20.p  200,1n  Hypothesis Test of a Proportion: Another Example
55. 55. Indeed .001thebeyondtsignificantisit level..05theatrejectedbeshouldhypothesisnulltheso1.96,exceedsvalueZThe 348.4Z 0115. 05. Z 0115. 15.20. Z S p Z p     p  Hypothesis Test of a Proportion: Another Example