[8] Q 3. rl'he manager of a supermarket wants to obtain information about the proportion of customers who dislike a new policy on cashing checks. (a) How many customers should the manager sample if she wants the sample propor tion to be within (11 of the true proportion, with probability [LEI]? [b] If the manager samplesn = 50 customers and finds that 42 of them dislike the policy, give a 95% oonfidenoe interval for the true proportion of customers who dislike the policy. {c} If the manager samplesn = El] customers and if the true proportion of customers who dislike the policy is approximately {18? estimate the probability that the sample proportion will be within {1.1 of the true proportion. [8] Q 4. Let Y1, Y2, . . . , 1; denote a random sample of size-'1 from a population whose cumulative distribution function is given by D. a *1 x3. F(y] = { d l 13 I} (E) . y _ :3. where ,8 1:- [l is an unknown parameter. Consider the estimaton = minlyl, 13,. . . , K} {a} Find the bias as. [b] Find the mean square error of. [8] Q 5. In a large high school, a radome sample of 1121] students are selected. Among them 33 play footballs. (a) Find a twdsided 95% condence interval on the proportion of students in that high school who play football. [b] If you want the error of estimation to be less than [D5 in part {a}, find the minimum sample size. {c} Estimate the probability that there are at least 12 students who play football if you choose 25 students randomly. [] Q 6. Let 1/1,. . ., 3:; be a random sample from a population with density 2 1. Digit}, y] ={3?Y elsewhere. Find a minimumvariance unbiased estimator fort}