Chapter 9 Two Population Tests Prepared by Chhay

Chapter 9 Two Population Tests Prepared by Chhay Phang H/P: 012 840 102 E-mail: phangg 2002@yahoo. com

Chapter Blueprint Many business problems require the comparison of two populations. This chapter discusses the situations in which such a comparison can be made. Illustration show the circumstances in which it is essential to compare two populations, and the proper manner in which to make these comparisons.

Inferences about Two Populations Interval estimation Hypothesis tests Independent sampling Large sample estimation Large sample tests Equal variances pooled data Unequal variances Paired sampling Differences between two proportion Test for differences in population

9. 1 INTRODUCTION Sample for two-population test can be either n Independent n Paired A. 9. 2 Interval Estimates with Independent Sampling Large Sample Estimation

Standard error of the differences between sample means Estimate of Standard error of the differences between sample means Confidence interval when population variances are unknown

B. Small Sample Estimation: The t. Distribution 1. The population are normal or near normally distributed and 2. The population variances are known 3. The Assumption of Equal but Unknown Variance

interval for the deference in population mean using pooled data Unequal variances

9. 3 Interval Estimate with Paired Sampling Paired Sample: Matches pairs are two observation that are as similar as possible to each other. They differ in only one relevant aspect. (See Table 9. 1 Page 235)

9. 4 Confidence Interval for the difference between Two Proportions

9. 5 Selecting the proper Sample size A. Sample size for 1 - 2 B. Sample size for 1 - 2

9. 6 Tests of Hypotheses about two means with Independent Sampling A. Large Sample size

Step 1: State the hypotheses. Step 2: Base on sample results, calculate the value of the statistic, Z-test. Step 3: Determine the decision rule based on the critical Z-value. Step 4: Note the finding and conclusion.

B. Large Sample size

9. 7 Hypotheses With Paired Data 9. 8 A Test for the Difference between Two Proportions

9. 9 Comparing the variance of two Normal Populations see fig. 9. 5 The F-distribution page 249 The -value When controlling the F-ratio to ensure F>1, we are conducting the two tailed test of the hypotheses Ho: 1^2= 2^2 as if it were a one tailed test. It is therefore necessary to divide the -value by 2.

Chapter Exercises 1, 2, 3, 4, 6, 7, 8, 9, 13, 16, 17 22, 23, 25, 26, 27, 28, 29 30, 31, 32, 33

Thank You thank you all for your attention.