A researcher recruited a sample of 5 women who were interestedin trying a new six-week program of diet and exercise designed topromote healthy weight loss. She plans to use the .01 significancelevel to test whether weight decreases (on average) forwomen using this program. The table below gives the starting andend weights (in pounds) for each of the five women.
| Subject | Starting Wt. (Sample 1) | Ending Wt. (Sample 2) |
| 1 | 174 | 156 |
| 2 | 122 | 110 |
| 3 | 169 | 160 |
| 4 | 181 | 165 |
| 5 | 147 | 139 |
| | |
a. Should these samples be considered paired or independent?Why?
b. Chose the appropriate formula for the test statistic andfinds its value.
c. Describe the rejection region for this test.
d. What should the researcher conclude?
e. Find a 95% confidence interval for the mean weight-loss ofwomen using this program. What mean weightless would you predictfor women who follow this program?
An independently selected sample of five men also participatedin the same study. The table below shows results for the numberof pounds lost by the five men and the five women in thestudy. The researcher will use the .01 significance level to testwhether (on average) the program produces different weight lossresults for men and women. You may assume the population variancesare equal (although the sample variances are not).
| Weight Loss (in pounds) | |
|---|
| Men (Sample 1) | Women (Sample 2) |
| Sample Size | 5 | 5 |
| Sample mean | 19.2 | 12.6 |
| Standard deviation | 4.970 | 4.336 |
| | |
f. Formulate the hypothesis for this test.
g. Should the pooled-sample variance be used in this situation?Why?
h. Choose the appropriate formula for the test statistic andfind its value.
i. What is the rejection region for this test?
j. What should the researcher conclude?
