The document discusses two-sample hypothesis tests, including tests for differences between two population means and two population proportions. It provides examples of hypothesis tests comparing means and proportions from two independent samples, including the steps to set up null and alternative hypotheses, determine the appropriate test statistic, identify the rejection region, and make a conclusion. It also discusses tests for paired or dependent samples.

1. Testing Hypotheses: Two-Sample Tests Chapter 9 Statistics for Management Levin and Rubin

3. Different Parameters

5. Mary Jo Fitzpatric is the Vice President for Nursing Services at St. Luke’s Memorial Hospital. Recently she noticed in the job posting for nurses that those that are unionised seem to offer higher wages. She decided to investigate and gathered the following sample information. Would it be reasonable for her to conclude that there is significant difference in earning between union and non-union nurses? Use the .01 significance level. 45 $1.90 $19.80 Nonunion 40 $2.25 $20.75 Union Sample Size Sample Standard Deviation Mean Wage Group

8. Step 4: Sketch the distribution, locate the critical values and the test statistic. Step 5: Decide! Since the test statistic values lies within the rejection region then there is sufficient statistical evidence based on this sample to reject H 0 . The test for a difference between parameters does not have to be zero, it can be non-zero. For example: H 0 : μ 1 - μ 2 ≤ 0.10 versus H 1 : μ 1 - μ 2 > 0.10

12. Testing Hypothesis about Difference between Two Population Proportion: Pooled

17. Tests for Difference Between Two Means: Small Sample Size

19. Solution Step 1: This is a one-tailed test. The hypothesis is stated below. The significance level is 0.05 (given) H 0 : μ 1 ≤ μ 2 versus H 1 : μ 1 > μ 2 Step 2: Since this is a test of the means and neither n 1 or n 2 is in excess of 30, a t test is appropriate. The critical value is 1.708 (from a t table with 25 degrees of freedom). Step 3:

20. Step 4: Sketch the distribution, locate the critical values and the test statistic. Step 5: Decide! Since the test statistic values lies within the retention region then there is no sufficient statistical evidence based on this sample to reject H 0 .

21. Example:

24. Paired Difference Test: Dependent Samples

29. Decision rule using p-values