Question

UTVU 4. If a researcher wants to estimate a population proportion to be within 4 percentage points with a 95% confidence if she uses the estimate from a recent study that showed its value to be 85%, what size sample should she obtain?

Answer 1

Solution :

Given that,

$\hat p$= 0.85

1 - $\hat p$ = 1 - 0.85 = 0.15

margin of error = E = 4% = 0.04

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z$\alpha$/2 = Z0.025 = 1.96 ( Using z table )

Sample size = n = (Z$\alpha$/2 / E)2 * $\hat p$ * (1 - $\hat p$ )

= (1.96 / 0.04)2 * 0.85 * 0.15

= 306.12

=306 rounded