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 two percentage points with 99​% ​confidence, assuming that

​(a) he uses the estimates of 22.6​% male and 18.9​% female from a previous​ year?

n=____

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

n=____

Answer 1

a)

p1          =	0.226
q1=1-p1=	0.774
p2          =	0.189
q2=1-p2=	0.811
here margin of error E =	0.02
for99% CI crtiical Z          =	2.576
required sample size n =	(p1q1+p2q2)*(Z/E)2=	5445.00

( please try 5444 if this comes wrong)

b)

p1          =	0.5
q1=1-p1=	0.5
p2          =	0.5
q2=1-p2=	0.5
here margin of error E =	0.02
for99% CI crtiical Z          =	2.576
required sample size n =	(p1q1+p2q2)*(Z/E)2=	8295.00

( please try 8294 if this comes wrong)