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

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.