Question

A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 99% confidence if (a) she uses a previous estimate of 0.54? (b) she does not use any prior estimates? Х i Table of critical values Click the icon to view the table of critical values. (a) n= (Round up to the nearest integer.) Level of Confidence, (1 - «). 100% Area in Each Tail, Critical Value, z 90% 0.05 1.645 95% 0.025 1.96 99% 0.005 2.575 Print Done

Answer 1

Solution :

Given that,

(a)

$\hat p$ = 0.54

1 - $\hat p$ = 1 - 0.54 = 0.46

margin of error = E = 0.04

Z_$\alpha$/2 = 2.576

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

= (2.576 / 0.04)² * 0.54 * 0.46

= 1030

sample size = n = 1030

(b)

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

margin of error = E = 0.04

Z_$\alpha$/2 = 2.576

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

= (2.576 / 0.04)² * 0.5 * 0.5

= 1037

sample size = n = 1037