Consider the following samples obtained from two normally distributed populations whose variances are equal:

Sample 1: 11.2 11.2 7.4 8.7 8.5 13.5 4.5 11.9 Sample 2: 11.7 9.5 15.6 16.5 11.3 17.6 17.0 8.5

a. Suppose that the samples were independent.

Perform a test of hypothesis to determine if there is a difference in the two population means. Use a significance level of 0.05.

b. Now suppose that the samples were paired samples.

Perform a test of hypothesis to determine if there is a difference in the two population means.

c. How do you account for the difference in the outcomes of part a and part b? Support your assertions with a statistical rationale.