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

© 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.

© 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.

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

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

© 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

© 2002 Thomson / South-Western Slide 10-7 Example: Hypothesis Testing for Differences Between Means (Part 1) Computer Analysts Registered Nurses

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

© 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

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

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

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

© 2002 Thomson / South-Western Slide 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

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

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

© 2002 Thomson / South-Western Slide Hernandez Manufacturing Company (Part 2) Training Method A Training Method B

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

© 2002 Thomson / South-Western Slide Dependent Samples Before and After Measurements on the same individual Studies of twins Studies of spouses Individual Before After d

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

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

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

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

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

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

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

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

© 2002 Thomson / South-Western Slide A Portion of the F Distribution Table for  = Numerator Degrees of Freedom Denominator Degrees of Freedom

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

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

© 2002 Thomson / South-Western Slide Sheet Metal Example (Part 3) Machine Machine