Statistics A First Course Donald H. Sanders Robert K. Smidt Aminmohamed Adatia Glenn A. Larson © 2005 McGraw-Hill Ryerson Ltd.

Chapter 9 Inference: Two-Sample Procedures © 2005 McGraw-Hill Ryerson Ltd.

Chapter 9 - Topics Hypothesis Tests of Two Variances Inferences about Two Means Inferences about Two Proportions © 2005 McGraw-Hill Ryerson Ltd.

Hypothesis Tests of Two Variances Two-Variance Testing: Purpose and Assumptions Independent Samples Data sources used to generate the data sets from two populations that are unrelated to each other Dependent Samples Data sources used to generate the data sets from two populations that are related to each other © 2005 McGraw-Hill Ryerson Ltd.

Hypothesis Tests of Two Variances Hypothesis Testing Procedure Step1: State the null and alternative hypothesis Step 2: Select the significance level Step 3: Determine the test distribution to use Step 4: Define the rejection region Step 5: State the decision rule Step 6: Compute the test statistic Step 7: Make the statistical decision © 2005 McGraw-Hill Ryerson Ltd.

Hypothesis Tests of Two Variances Hypothesis Testing Procedure Null and alternative hypothesis Null Hypothesis Alternative Hypothesis Two tail test One tail test (right) One tail test (left) © 2005 McGraw-Hill Ryerson Ltd.

The general shape of F distributions. Figure 9.1 © 2005 McGraw-Hill Ryerson Ltd.

© 2005 McGraw-Hill Ryerson Ltd.

The critical F value of 4.53 defines the rejection region of the F distribution with 7 degrees of freedom in the numerator and 8 degrees of freedom in the denominator, at  = .05. Figure 9.2 © 2005 McGraw-Hill Ryerson Ltd.

© 2005 McGraw-Hill Ryerson Ltd.

Inferences about Two Means Procedures 1A: The Paired t Test for Dependent Populations 1B: The Confidence Interval for Dependent Populations 2A: The z Test for Independent Populations 2B: The Confidence Interval for Independent Populations © 2005 McGraw-Hill Ryerson Ltd.

Inferences about Two Means Procedures (continued) 3A: Small-Sample t Test for Independent Populations When σ1≠σ2 3B: Small-Sample Confidence Interval for Independent Populations When σ1≠σ2 4A: Small-Sample t Test for Independent Populations When σ1=σ2 4B: Small-Sample Confidence Interval for Independent Populations When σ1=σ2 © 2005 McGraw-Hill Ryerson Ltd.

Inferences about Two Means Four procedures followed to conduct hypothesis tests about the means of two normally distributed populations. The correct procedure to use in a given situation depends on the answers to the questions posed in the four diamond-shaped decision symbols. Figure 9.4 (2 slides) © 2005 McGraw-Hill Ryerson Ltd.

© 2005 McGraw-Hill Ryerson Ltd.

© 2005 McGraw-Hill Ryerson Ltd.

Conceptual schematic of the sampling distribution of the differences between sample means. Figure 9.7 © 2005 McGraw-Hill Ryerson Ltd.

© 2005 McGraw-Hill Ryerson Ltd.

The sampling differences between means when 1 and 2 are known or when n1 and n2 are both > 30. Figure 9.8 © 2005 McGraw-Hill Ryerson Ltd.

© 2005 McGraw-Hill Ryerson Ltd.

Inferences about Two Proportions Hypothesis Testing of Two Proportions Independent population and np ≥ 5 n(1-p) ≥ 5 Null Hypothesis Alternative Hypothesis Two tail test One tail test (right) One tail test (left) © 2005 McGraw-Hill Ryerson Ltd.

Inferences about Two Proportions Hypothesis Testing of Two Proportions Test Statistic © 2005 McGraw-Hill Ryerson Ltd.

Inferences about Two Proportions Confidence Interval for the Difference of Two Proportions Formula © 2005 McGraw-Hill Ryerson Ltd.

End of Chapter 9 Inference: Two-Sample Procedures © 2005 McGraw-Hill Ryerson Ltd.