Question

We are interested in conducting a study in order to determine what percentage of

voters of a state would vote for the incumbent governor. What is the minimum size

sample needed to estimate the population proportion with a margin of error of 0.04 at

95% confidence? Use a planning value of p∗= 0.5.

a. 601

b. 600

c. 385

d. 307

Answer 1

Solution :

Given that,

$\hat p$= 0.5

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

margin of error = E = 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 = Z_0.025 = 1.96

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

= (1.96 / 0.04)² * 0.5 * 0.5

= 600

Sample size = 600