Question

Of n1 randomly selected male smokers, X1 smoked filter cigarettes, whereas of n2 randomly selected female smokers, X2 smoked filter cigarettes. Let P1 and P2 denote the probabilities that a randomly selected male and female, respectively, smoke filter cigarettes.

Answer 1

a. To show: ! is an unbiased estimator for p1-22 X, X E(X)-E 41-42 n2 = p1-p2 X. Thus, I 그 1-1-2 | is an unbiased estimator for pl-p2

b. To find: Standard error of the estimator obtained in part (a). V(X)-V 72 1 2 SE(xX) n, n2 Thus, the standard error of the estimator obtained in part (a) is 1+2-4

c. Explanation: The observed values x and x can be used in the standard error of estimate by finding the values of pı and p using the fomula given below Pfori-1,2 Also, 1- Thus, the necessary quantities are estimated and the values are used in the formula. Correct option: You would use them to estimate the necessary quantities and put them these in X, 72 to the formula.

d. To find: Estimate of p -p Given: n -208, xi -125, x2 -175 i n 125 175 208 208 0.6010-0.8413 -0.2403 Thus, the estimator of Pl - P is -0.240

e. To find: Estimate the standard error of the estimator using the result ofpart (c) and the data of part (d) 125 208 175 Pi--= 0.6010 1--0.6010 0.399 200.84134.1-P-1-08413-0.1587 Pa =-= 0.6010x 0.399 0.8413x 0.1587 208 208 0.239799 0.13351431 208 208 v0.00179 0.0424 Thus, the standard error of estimate is 0.042