Of n, randomly selected male smokers, X, smoked filter cig- arettes, whereas of n, randomly selected female smokers, X, smoked filter cigarettes. Let p, and p2 denote the probabili- ties that a randomly selected male and female, respectively, smoke filter cigarettes.

a. Show that (X,/n)-(X/n) is an unbiased estimator for P1 P2. [Hint: E(X) =n,p, for i = 1, 2.]

b. What is the standard error of the estimator in part (a)?

c. How would you use the observed values x, and x, to esti- mate the standard error of your estimator?

d. If n = n = 200, x = 127, and x2 = 176, use the esti- mator of part

(a) to obtain an estimate of p - P2-

e. Use the result of part

(c) and the data of part

(d) to esti- mate the standard error of the estimator.