Of n, randomly selected male smokers, X, smoked filter cigarettes, whereas of n2 randomly selected female smokers, X2 smoked filter cigarettes. Let p, and p, denote the probabilities that a randomly selected male and female, respectively, smoke filter cigarettes. (a) Show that (X1j) - (X22) is an unbiased estimator for P1 - P2. [Hint: E(X;) = np; for / = 1, 2.] E( X 1 X2 n2 n1 n1 = P1 - P2 (b) What is the standard error of the estimator in part (a)? (c) How would you use the observed values x, and x, to estimate the standard error of your estimator? O You would put them directly into the formula to obtain the estimate of the standard error. You can not use the observed values to estimate the standard error of your estimator. There is not enough information. O You would use them to estimate the necessary quantities and then put these into the formula. (d) If n, = n2 = 191, x, = 120, and x2 = 178, use the estimator of part (a) to obtain an estimate of P, - P2. (Round your answer to three decimal places.) (e) Use the result of part (c) and the data of part (d) to estimate the standard error of the estimator. (Round your answer to three decimal places.)