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

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

(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

(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

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

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

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

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

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 > we reject H O Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

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

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

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

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

3.Reject H O if |t’| > t  /2, df = t.05,22 = 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

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

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

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

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

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

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

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