Question

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.017 for the estimation of a population proportion? Assume that past data are not available for developing a planning value for p *. Round up to the next whole number.

Answer 1

Solution :

Given that,

$\hat p$= 0.5

1 - $\hat p$ = 1 - 0.5 = 0.5

margin of error = E = = 0.017

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 = Z_0.025 = 1.96

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

= (1.96 / 0.017)² * 0.5 * 0.5

= 3323

Sample size = 3323