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 estimates to be within three percentage points with a 95% confidence, assuming that

a) he uses the estimate of 22.7% male and 19.1% female from a previous year?

b) he does not use any prior estimates?

Answer 1

a)

Proportion for sample 1, p̂₁ = 0.227  

Proportion for sample 2, p̂₂ = 0.191

Margin of error, E = 0.03

Confidence Level, CL = 0.95

Significance level, α = 1 - CL = 0.05

Critical value, z = NORM.S.INV(0.05/2) = 1.96

Sample size, n = (z² * (p̂₁*(1-p̂₁) + p̂₂*(1-p̂₂)) / E²

= 1408.54 = 1409

b)

Let Proportion for sample 1, p̂₁ = 0.5  

Proportion for sample 2, p̂₂ = 0.5

Margin of error, E = 0.03

Confidence Level, CL = 0.95

Significance level, α = 1 - CL = 0.05

Critical value, z = NORM.S.INV(0.05/2) = 1.96

Sample size, n = (z² * (p̂₁*(1-p̂₁) + p̂₂*(1-p̂₂)) / E²

= 2134.22 = 2134