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

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

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

4. 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.

5. 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.

6. 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.

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

8. © 2005 McGraw-Hill Ryerson Ltd.

9. 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.

10. © 2005 McGraw-Hill Ryerson Ltd.

11. 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.

12. 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.

13. 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.

14. © 2005 McGraw-Hill Ryerson Ltd.

15. © 2005 McGraw-Hill Ryerson Ltd.

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

17. © 2005 McGraw-Hill Ryerson Ltd.

18. 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.

19. © 2005 McGraw-Hill Ryerson Ltd.

20. 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.

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

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

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