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- 1. 18-1Hypothesis Testing and the Research Process
- 2. 18-2 Types of Hypotheses• Null – H0: µ = 50 mpg – H0: µ < 50 mpg – H0: µ > 50 mpg• Alternate – HA: µ = 50 mpg – HA: µ > 50 mpg – HA: µ < 50 mpg
- 3. 18-3Two-Tailed Test of Significance
- 4. 18-4One-Tailed Test of Significance
- 5. 18-5 Decision RuleTake no corrective action if theanalysis shows that one cannotreject the null hypothesis.
- 6. 18-6Statistical Decisions
- 7. 18-7 Factors Affecting Probability of Committing a β ErrorTrue value of parameterTrue value of parameter Alpha level selected Alpha level selected One or two-tailed test used One or two-tailed test used Sample standard deviation Sample standard deviation Sample size Sample size
- 8. 18-8 Statistical Testing Procedures State null State null hypothesis hypothesis s a ho s C tta sho os ttiistt c os eInterpret the Interpret the C iica l e test test al Stages Stages ttes t es tObtain criticalObtain critical Select level of Select level of test value test value significance significance Compute Compute difference difference value value
- 9. 18-9 Tests of SignificanceParametric Nonparametric
- 10. 18-10 Assumptions for Using Parametric TestsIndependent observations Independent observations Normal distribution Normal distribution Equal variances Equal variances Interval or ratio scales Interval or ratio scales
- 11. 18-11
- 12. 18-12
- 13. 18-13 Advantages of Nonparametric TestsEasy to understand and useEasy to understand and use Usable with nominal data Usable with nominal data Appropriate for ordinal data Appropriate for ordinal data Appropriate for non-normal Appropriate for non-normal population distributions population distributions
- 14. 18-14 How To Select A Test How many samples are involved? If two or more samples are involved,are the individual cases independent or related? Is the measurement scale nominal, ordinal, interval, or ratio?
- 15. 18-15 Recommended Statistical Techniques Two-Sample Tests k-Sample Tests ____________________________________________ ____________________________________________Measurement Independent IndependentScale One-Sample Case Related Samples Samples Related Samples SamplesNominal • Binomial • McNemar • Fisher exact test • Cochran Q • x2 for k samples • x2 one-sample test • x2 two-samples testOrdinal • Kolmogorov-Smirnov • Sign test • Median test • Friedman two- • Median one-sample test way ANOVA extension • Runs test •Wilcoxon •Mann-Whitney U •Kruskal-Wallis matched-pairs •Kolmogorov- one-way ANOVA test Smirnov •Wald-WolfowitzInterval and • t-test • t-test for paired • t-test • Repeated- • One-wayRatio samples measures ANOVA • Z test • Z test ANOVA • n-way ANOVA
- 16. 18-16 Questions Answered by One-Sample Tests• Is there a difference between observed frequencies and the frequencies we would expect?• Is there a difference between observed and expected proportions?• Is there a significant difference between some measures of central tendency and the population parameter?
- 17. 18-17 Parametric TestsZ-test t-test
- 18. 18-18 One-Sample t-Test ExampleNull Ho: = 50 mpgStatistical test t-testSignificance level .05, n=100Calculated value 1.786Critical test value 1.66 (from Appendix C, Exhibit C-2)
- 19. 18-19 One Sample Chi-Square Test Example Expected Intend to Number Percent Frequencies Living Arrangement Join Interviewed (no. interviewed/200) (percent x 60)Dorm/fraternity 16 90 45 27Apartment/rooming 13 40 20 12house, nearbyApartment/rooming 16 40 20 12house, distantLive at home 15 30 15 9 _____ _____ _____ _____Total 60 200 100 60
- 20. 18-20 One-Sample Chi-Square ExampleNull Ho: 0 = EStatistical test One-sample chi-squareSignificance level .05Calculated value 9.89Critical test value 7.82 (from Appendix C, Exhibit C-3)
- 21. 18-21 Two-SampleParametric Tests
- 22. 18-22 Two-Sample t-Test Example A Group B GroupAverage hourly sales X1 = $1,500 X2 = $1,300Standard deviation s1 = 225 s2 = 251
- 23. 18-23 Two-Sample t-Test ExampleNull Ho: A sales = B salesStatistical test t-testSignificance level .05 (one-tailed)Calculated value 1.97, d.f. = 20Critical test value 1.725 (from Appendix C, Exhibit C-2)
- 24. 18-24 Two-Sample Nonparametric Tests: Chi-Square On-the-Job-Accident Cell Designation Count Expected Values Yes No Row TotalSmoker 1,1 1,2 Heavy Smoker 12, 4 16 8.24 7.75 2,1 2,2 Moderate 9 6 15 7.73 7.27 3,1 3,2 Nonsmoker 13 22 35 18.03 16.97 Column Total 34 32 66
- 25. 18-25 Two-Sample Chi-Square ExampleNull There is no difference in distribution channel for age categories.Statistical test Chi-squareSignificance level .05Calculated value 6.86, d.f. = 2Critical test value 5.99 (from Appendix C, Exhibit C-3)
- 26. 18-26 Two-Related-Samples TestsParametric Nonparametric
- 27. 18-27 Sales Data for Paired- Samples t-Test Sales SalesCompany Year 2 Year 1 Difference D D2GM 126932 123505 3427 11744329GE 54574 49662 4912 24127744Exxon 86656 78944 7712 59474944IBM 62710 59512 3192 10227204Ford 96146 92300 3846 14971716AT&T 36112 35173 939 881721Mobil 50220 48111 2109 4447881DuPont 35099 32427 2632 6927424Sears 53794 49975 3819 14584761Amoco 23966 20779 3187 10156969 Total ΣD = 35781 . ΣD = 157364693 .
- 28. 18-28 Paired-Samples t-Test ExampleNull Year 1 sales = Year 2 salesStatistical test Paired sample t-testSignificance level .01Calculated value 6.28, d.f. = 9Critical test value 3.25 (from Appendix C, Exhibit C-2)
- 29. 18-29 k-Independent-Samples Tests: ANOVA• Tests the null hypothesis that the means of three or more populations are equal• One-way: Uses a single-factor, fixed- effects model to compare the effects of a treatment or factor on a continuous dependent variable
- 30. 18-30 ANOVA Example __________________________________________Model Summary_________________________________________ Source d.f. Sum of Squares Mean Square F Value p Value Model (airline) 2 11644.033 5822.017 28.304 0.0001 Residual (error) 57 11724.550 205.694 Total 59 23368.583 _______________________Means Table________________________ Count Mean Std. Dev. Std. Error Delta 20 38.950 14.006 3.132 Lufthansa 20 58.900 15.089 3.374 KLM 20 72.900 13.902 3.108All data are hypothetical
- 31. 18-31 ANOVA Example ContinuedNull µA1 = µA2 = µA3Statistical test ANOVA and F ratioSignificance level .05Calculated value 28.304, d.f. = 2, 57Critical test value 3.16 (from Appendix C, Exhibit C-9)
- 32. 18-32 k-Related-Samples TestsMore than two levels in grouping factor Observations are matched Data are interval or ratio

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