4. you work for a company that is trying out two different sales pitches. the company tries pitch a on 200 potential clients, and pitch b on 200 potential clients. let pa be the probability of making a sale with pitch a, and pb be the probability of making a sale with pitch b as the company's statistical guru, you are tasked with determining if one of the pitches is in fact better than the other. let d -p hypothesis in terms of d. so that (a) is it a one-sided or two-sided test? (b) a friend suggests estimating d with the following estimator where pa is the fraction of the 200 clients who received pitch a who make a purchase and pb is the fraction of the 200 clients who receive pitch b who make a purchase. is d an unbiased estimator? (c) assuming the null hypothesis is true and pa pb, there is some value p that is equal to both pa and pb. find the standard deviation of d (from now on denoted by ơd) in terms of p hint: find var(pa+-1)xpb) and then find its square root. you may assume that pa and pb are independent random variables (d) find an unbiased estimator for p that is more efficient than pa or pb (e) 105 of the 200 clients receiving pitch a made a purchase, and 95 of the clients receiving pitch b made a purchase. estimate p using the estimator from the previous question, and then use that estimate of p to create an estimate of ơd (using your answer to part (c)) (f) calculate d (g) perform your hypothesis test. use a-.05