1. © 2002 Thomson / South-Western Slide 10-1 Chapter 10 Hypothesis Testing with Two Samples

2. © 2002 Thomson / South-Western Slide 10-2 Learning Objectives Test hypotheses about the difference in two population means using data from large independent samples. Test hypotheses about the difference in two population means using data from small independent samples when the populations are normally distributed.

3. © 2002 Thomson / South-Western Slide 10-3 Learning Objectives, continued Test hypotheses about the mean difference in two related populations when the populations are normally distributed. Test hypotheses about the differences in two population proportions. Test hypotheses about two population variances when the populations are normally distributed.

4. © 2002 Thomson / South-Western Slide 10-4 Hypothesis Testing about the Difference in Two Sample Means Population 1 Population 2

5. © 2002 Thomson / South-Western Slide 10-5 Hypothesis Testing about the Difference in Two Sample Means

6. © 2002 Thomson / South-Western Slide 10-6 Z Formula for the Difference in Two Sample Means for n 1  30, n 2  30, and Independent Samples

7. © 2002 Thomson / South-Western Slide 10-7 Example: Hypothesis Testing for Differences Between Means (Part 1) Computer Analysts 24.10 25.0024.25 23.75 22.7021.75 24.25 21.3022.00 22.5518.00 23.50 23.2523.50 22.80 22.1022.70 24.00 24.2521.50 23.85 23.5023.80 24.20 22.7525.60 22.90 23.8024.10 23.20 23.55 Registered Nurses 20.75 23.80 22.00 21.85 24.16 21.10 23.30 24.00 21.75 21.50 20.40 23.25 22.75 23.00 21.25 20.00 21.75 20.50 23.75 22.50 25.00 22.70 23.25 21.90 19.50 21.75 20.80 20.25 22.45 19.10 22.60 21.70 20.75 22.50

8. © 2002 Thomson / South-Western Slide 10-8 Example: Hypothesis Testing for Differences Between Means (Part 2) Rejection Region Nonrejection Region Critical Values Rejection Region

9. © 2002 Thomson / South-Western Slide 10-9 Example: Hypothesis Testing for Differences Between Means (Part 3) Rejection Region Nonrejection Region Critical Values Rejection Region 0

10. © 2002 Thomson / South-Western Slide 10-10 Example: Hypothesis Testing for Differences between Means (Part 4) Rejection Region Nonrejection Region Critical Values Rejection Region 0

11. © 2002 Thomson / South-Western Slide 10-11 Demonstration Problem 10.1 (Part 1) Nonrejection Region Critical Value Rejection Region 0

12. © 2002 Thomson / South-Western Slide 10-12 Demonstration Problem 10.1 (Part 2) Nonrejection Region Critical Value Rejection Region 0

13. © 2002 Thomson / South-Western Slide 10-13 The t Test for Differences in Population Means Each of the two populations is normally distributed. The two samples are independent. At least one of the samples is small, n < 30. The values of the population variances are unknown. The variances of the two populations are equal,  1 2 =  2 2

14. © 2002 Thomson / South-Western Slide 10-14 t Formula to Test the Difference in Means Assuming  1 2 =  2 2

15. © 2002 Thomson / South-Western Slide 10-15 Hernandez Manufacturing Company (Part 1) Rejection Region Nonrejection Region Critical Values Rejection Region 0

16. © 2002 Thomson / South-Western Slide 10-16 Hernandez Manufacturing Company (Part 2) Training Method A 56 5145 47 5243 42 5352 5042 48 4744 Training Method B 59 52 53 54 57 56 55 64 53 65 53 57

17. © 2002 Thomson / South-Western Slide 10-17 Hernandez Manufacturing Company (Part 3)

18. © 2002 Thomson / South-Western Slide 10-18 Dependent Samples Before and After Measurements on the same individual Studies of twins Studies of spouses Individual 123456123456 Before 32 11 21 17 30 38 After 39 15 35 13 41 39 d -7 -4 -14 4 -11

19. © 2002 Thomson / South-Western Slide 10-19 Formulas for Dependent Samples

20. © 2002 Thomson / South-Western Slide 10-20 Sampling Distribution of Differences in Sample Proportions

21. © 2002 Thomson / South-Western Slide 10-21 Z Formula for the Difference in Two Population Proportions

22. © 2002 Thomson / South-Western Slide 10-22 Z Formula to Test the Difference in Population Proportions

23. © 2002 Thomson / South-Western Slide 10-23 Testing the Difference in Population Proportions: Demonstration Problem 10.4 Rejection Region Nonrejection Region Critical Values Rejection Region 0

24. © 2002 Thomson / South-Western Slide 10-24 Demonstration Problem 10.4, continued

25. © 2002 Thomson / South-Western Slide 10-25 Hypothesis Testing about the Difference in Two Population Variances F Test for Two Population Variances

26. © 2002 Thomson / South-Western Slide 10-26 Example: An F Distribution for 1 = 10 and 2 = 8

27. © 2002 Thomson / South-Western Slide 10-27 A Portion of the F Distribution Table for  = 0.025 Numerator Degrees of Freedom Denominator Degrees of Freedom 123456789 1647.79799.48864.15899.60921.83937.11948.20956.64963.28 238.5139.0039.1739.2539.3039.3339.3639.3739.39 317.4416.0415.4415.1014.8814.7314.6214.5414.47 412.2210.659.989.609.369.209.078.988.90 510.018.437.767.397.156.986.856.766.68 68.817.266.606.235.995.825.705.605.52 78.076.545.895.525.295.124.994.904.82 87.576.065.425.054.824.654.534.434.36 97.215.715.084.724.484.324.204.104.03 106.945.464.834.474.244.073.953.853.78 116.725.264.634.284.043.883.763.663.59 126.555.104.474.123.893.733.613.513.44

28. © 2002 Thomson / South-Western Slide 10-28 Hypothesis Test for Equality of Two Population Variances: Sheet Metal Example (Part 1)

29. © 2002 Thomson / South-Western Slide 10-29 Sheet Metal Example (Part 2) Rejection Regions Critical Values Nonrejection Region

30. © 2002 Thomson / South-Western Slide 10-30 Sheet Metal Example (Part 3) Machine 1 22.3 21.822.2 21.8 21.921.6 22.3 22.4 21.622.5 Machine 2 22.0 22.1 21.8 21.9 22.2 22.0 21.7 21.9 22.0 22.1 21.9 22.1