Question

We are interested in conducting a study to determine the percentage of voters of a state would vote for the incumbent governor. what is the minimum sample size needed to estimate the population proportion with a margin of error of .05 or less at 95% confidence? hint: use a planning proportion of p*=0.50
a. 200.
b. 100.
c. 385.
d. 58.

Answer 1

Finding the sample size for estimating a population proportion.

The formula is:

n = (z/m)^2 p~(1−p~)

where:
Z is the z value of the confidence level where 95% is equal to 1.96

M is the margin of error where 0.05

And p~ is the estimated value of the proportion where it is 0.50

Solution:

n = (1.96/0.05)^2 (0.5) (1-0.5)

= 1.536.64 (0.5) (0.5)

= 768.32 (0.5)

= 384.16

This is the minimum sample size, therefore we should round it up to 385. The answer is letter c.