Question

How large a sample is needed to estimate the population proportion for the following? ME = 0.03; α=0.05

a.) 962

b.) 1068

c.) 1297

d.) 1242

Answer 1

Solution :

Given that,

$\hat p$= 0.5

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

margin of error = E = 0.03

At confidence level the z is ,

$\alpha$ / 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 / 0.03)² * 0.5 * 0.5

= 1068

Sample size =