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 two percentage points with \(90 \%\) confidence, assuming that

(a) she uses the estimates of \(22.4 \%\) male and \(19.1 \%\) female from a previous year?

(b) she does not use any prior estimates?