A physical therapist wants to determine the difference in the proportion of men

Question

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 four percentage points with 95?% confidence, assuming that

?(a) he uses the estimates of 21.2?% male and 18.1?% female from a previous? year??

(b)he does not use any prior? estimates?

Complete answer below

?(a) n= ( ) (Round up to the nearest whole? number.)

?(b) n= (    ) (Round up to the nearest whole? number.)

Explanation / Answer

Solution:- Given that information : 95% confidence for Z = 1.96 , E = 0.04

(a) male = 0.212 , female = 0.181

Formula n = (Z/E)^2*p1*(1-p1)*p2*(1-p2)
= (1.96/0.04)^2*0.212*(1-0.212)*(0.181)*(1-0.181)
= 59.4588
n = 60

(b) n = (1.96/0.04)^2*0.5*0.5*0.5*0.5
= 150.0625
n = 150

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