Question

When we want confidence and use the conservative estimate of 95%, we can use the simple formula to roughly determine the sample size needed for a given margin of error p=.05. Use this formula to determine the sample size needed for a margin of error of 0.01 .

Answer 1

Solution :

Given that,

$\hat p$ = 0.05

1 - $\hat p$ = 0.95

margin of error = E = 0.01

Z_$\alpha$/2 = Z_0.025 = 1.96

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

= (1.96 / 0.01)² * 0.05 * 0.95

= 1825

sample size = n = 1825