Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 95% confident that you esimate is within 4% of the true population proportion. How large of a sample size is required?

n=?

Do not round mid-calculation. However, use a critical value accurate to three decimal places.

Answer 1

Solution :

Given that,

$\hat p$= 0.5 ( assume 0.5)

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

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 = 1.960 ( Using z table )

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

= (1.960 / 0.04)2 * 0.5 * 0.5

= 600.25

Sample size =601