5. Independent random samples of n 540 1 and n 580 2 observations were selected from binomial populations 1 and 2, respectively. The number of successes in the two samples were x 517 1 and x 523 2 .

a. Find a 99% confidence interval for the difference between the two binomial population proportions.

Interpret this interval.

b. Suppose you wish to estimate p 2 p 1 2 ( ) correct to within .06, with probability equal to .99, and you plan to use equal sample sizes—that is, n 5n 1 2. How large should n1 and n2 be?