Question

An epidemiologist wishes to know what proportion of adults living in a large metropolitan area have subtype ayr hepatitis B virus. Determine the sample size that would be required to estimate the true proportion to within 3% margin of error with 95 percent confidence.

Answer 1

Sample size 'n' = 1067

Explanation:

Explanation:-

Given margin of error of the true proportion

M.E = 0.03

The margin of error is determined by

`M.E =Z_(\alpha ) (√(p(1-p)) )/(√(n) )`

Level of significance = 0.95

The critical value Z₀.₀₅ = 1.96

The margin of error is

`0.03 =1.96 (√(p(1-p)) )/(√(n) )`

we know that

`√(p(1-p) \leq (1)/(2)`

`0.03 =(1.96 X(1)/(2) )/(√(n) )`

on cross multiplication , we get

√n = 32.66

Squaring on both sides, we get

n = 1066.6≅1067