Question

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3 percentage points with 95% confidence if (a) he uses a previous estimate of 26%? (b) he does not use any prior estimates? (a) na (Round up to the nearest integer.) (b)(Round up to the nearest integer.)

Answer 1

Solution :

margin of error = E = 0.03

Z_$\alpha$/2 = 1.96

(a)

$\hat p$ = 0.26

1 - $\hat p$ = 0.74

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

= (1.96 / 0.03)² * 0.26 * 0.74

= 822

sample size = n = 822

(b)

$\hat p$ = 0.5

1 - $\hat p$ = 0.5

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

= (1.96 / 0.03)² * 0.5 * 0.5

= 1067.1

sample size = n = 1068