Question

A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity.

a. What sample size should be obtained if she wishes the estimate to be within two percentage points with 99​% ​confidence, assuming that she uses the estimates of 22.9​% male and 19.1​% female from a previous year?

b. What sample size should be obtained if she wishes the estimate to be within two percentage points with 99​% ​confidence, assuming that she does not use any prior​ estimates?

Answer 1

a) Given that, p₁ = 0.229 and p₂ = 0.191

margin of error ( E ) = 2% = 0.02

A 99% confidence level has significance level = 0.01 and critical value is,

We want to find, the sample size ( n ),

Therefore, required sample size is 5488

b) Assuming that she does not use any prior estimates.

So, p₁ = p₂ = 0.5 and sample size ( n ) is,

Therefore, required sample size is 8288