1. Inference Procedures for Two Populations Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

2. Independent versus Dependent Samples Independent Samples The occurrence of an observation in the first sample has no effect on the value(s) in the other sample. Dependent Samples or paired samples –The occurrence of an observation in the first sample has an impact on the corresponding value in the second sample. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

3. (1 -  ) * 100% Confidence Interval for  1 -  2 For large samples where  ’s are known Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

4. (1 -  ) * 100% Confidence Interval for  1 -  2 For large samples where  ’s are unknown Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

5. Sample Sizes To minimize total sample size: Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

6. Hypothesis Testing for  1 and  2 (Large Samples) Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

7. Example 9.2 Define the Hypothesis H o  1   2 (Texgas is less expensive) H a  1 >  2 (Quik-Chek is less expensive) Define the test statistic Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

8. Define the rejection region (  =.05) Reject H O if Z > 1.645 Figure 9.4 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

9. Evaluate the test statistic State the conclusion: Quik-Chek stores do charge less for gasoline(on the average) than do Texgas stations. Because 3.5 > 1.645 we reject H O Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

10. Large Sample Tests for  1 and  2 Two-Tail Test H o  1 =  2 H a  1   2 Reject H O if |Z| > Z  /2 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

11. Large Sample Tests for  1 and  2 One-Tail Test H o  1   2 H a  1 >  2 Reject H o if Z > Z  H o  1   2 H a  1 <  2 Reject H o if Z < - Z  Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

12. (1 -  ) * 100% Confidence Interval for  1 -  2 (Small Independent Samples) Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

13. Hypothesis Testing for  1 -  2 (Small, Independent Samples) Example 9.5 1. H o  1 =  2 H a  1   2 2. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

14. 3.Reject H O if |t’| > t  /2, df = t.05,22 = 1.717 4. Because |t’| = 3.25 > 1.717, we reject H O 5.There is a significant difference in the average blowout times for the two brands Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

15. Comparing Variances Assumptions Both populations are normal The samples are independent Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

16. Comparing Variances Figure 9.14 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

17. Hypothesis Test for  1 and  2 Two-Tail Test H o :  1 =  2 H a :  1   2 Reject H o if F > F  /2, v 1, v 2 or if F < F 1-  /2, v 1, v 2 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

18. Hypothesis Test for  1 and  2 One-Tail Test H o :  1   2 H a :  1 >  2 H o :  1   2 H a :  1 <  2 Reject H o if F > F , v 1, v 2 F 1- , v 1, v 2 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

19. Confidence Interval for  1 2 /  2 2 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

20. Confidence Interval for  d Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

21. Hypothesis Test for  d H o :  d = 0 H a :  d  0 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing