The data for a random sample of eight paired observations are shown in the table below:
| Pair 1 |
Population 1 |
Population 2 |
| 1 |
32 |
38 |
| 2 |
20 |
24 |
| 3 |
49 |
53 |
| 4 |
53 |
53 |
| 5 |
28 |
34 |
| 6 |
39 |
46 |
| 7 |
18 |
20 |
|
8
|
22 |
28 |
a. What are the appropriate null and alternative hypotheses to test whether the mean for population 2 is larger that that for population 1.
b. Conduct the test identified in part a using a = 0.05
c. Find a 95% confidence interval for ud. Interpret this result.
d. What assumptions are necessary to ensure the validity of this analysis?