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 she wishes the estimate to be within five percentage points with 90​% ​confidence, assuming that ​(a) she uses the estimates of 22.8​% male and 19.8​% female from a previous​ year?
​(b) she does not use any prior​ estimates?