A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained if he wishes the estimate to be within two percentage points with 99​% ​confidence, assuming that
​(a) he uses the estimates of 22.5​% male and 18.3​% female from a previous​ year?
​(b) he does not use any prior​ estimates?