Pollster problem. You plan to conduct a poll to determine the fraction of people interested in your new product. a. (5 points) Suppose you ask n people if they are interested in your new product. Let us denote the answers for i E {1,...,n}. (X = 1 means they are interested and X, = 0 means they are not). Given the responses, how would you estimate the fraction of people interested in your new product? а b. (10 points) Let W, denote your estimate based on n responses above. Using the Chebyshev inequality, find a lower bound for the number of people needed to ensure that P{ W-W. < 0.05) >0.95, where W denotes the actual underlying fraction of people interested in your product. c. (5 points) Approximate the distribution of VW-W) using the CLT. Assume that the variance of W is 1/4 d. (10 points) Using the CLT, determine an approximate lower bound for the number of people needed to ensure that P{ W - W. < 0.05) > 0.95, where W denotes the actual underlying fraction of people interested in your product. Hint: use the Q function table.
