List the assumptions necessary for each of the following inferential techniques:

a. Large-sample inferences about the difference

(p, - p2) bctween population means using a twosample z statistic

b. Small-sample inferences about (p, - p2) using an independent samples design and a two-sample t statistic

c. Small-sample inferences about (p, - p,) using a paired difference design and a single-sample t statistic to analyze the differences

*d. Inferences about the ratio a:/u; of two population variances using an F-test.