Question

Help please, thank you!

A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What sze sample should be obtained if she wishes the estimate to be within 0.01 with 95% confidence if (a) she uses a previous estimate of 0.32? (b) she does not use any prior estimates? (a)n(Round up to the nearest integer)

Answer 1

Solution :

Given that,

margin of error = E = 0.01

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

(a)

$\hat p$ = 0.32

1 - $\hat p$ = 1 - 0.32 = 0.68

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

= (1.96 / 0.01)² * 0.32 * 0.68

= 8359.3

sample size = 8359

(b)

$\hat p$ = 0.5

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

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

= (1.96 / 0.01)² * 0.5 * 0.5

= 9604

sample size = 9604