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 she wishes the estimate to be within four percentage points with 95% confidence, assuming that

a) she uses the estimates of 21.8% male and 19.6% female from a previous year?

b) she does not use any prior estimates?

Answer 1

Given that,

a) p1 = 0.218, q1 = 1 - 0.218 = 0.782

p2 = 0.196, q2 = 1 - 0.196 = 0.804

E = 0.04

Sample size required is

n=(p1 * (1-p1) +(p2 * (1-p2) ) * ((Zalpha/2)/E)²

for 95% confidence, the critical value=Zalpha/2=1.96

then,

n= (0.218 * (0.782) +(0.196 * (0.804) ) * ((1.96)/0.04)²

Sample size =n =402

b) p1 = q1 = p2 = q2 = 0.50

E = 0.04

For 99% confidence, z = 1.96

Hence,

Sample size required is

n=(0.50* (0.50) +(0.50 * (0.50) ) * ((1.96)/0.04)²

sample size=n = 1201