11. (4 points) A survey is taken to determine what fraction of freshman computer science majors have prior programming experience. Call this unknown fraction p. Out of the nationwide pool of computer science freshmen, 100 are chosen at random. Of them, 40% had prior programming experience.

(a) The natural estimate of p is 0.4. Give a 95% confidence interval for the estimate.

(b) Suppose we now want to estimate p more accurately, to within a 95% confidence interval of 0.01. What sample size should we use?