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 0.05 or less at 95% confidence? Use planning value of p=0.5.

Select one:

A.200

B.100

C.58

D.385

Answer 1

To estimate the population proportion with a margin of error at 95% confidence, the minimum sample size needed is 385.

Step-by-step explanation:

To determine the minimum sample size needed to estimate a population proportion with a margin of error at 95% confidence, we can use the formula:

n = (Z^2 * p * (1-p))/(E^2)

where n is the sample size, Z is the Z-score corresponding to the desired confidence level (Z = 1.96 for 95% confidence), p is the planning value (0.5), and E is the margin of error (0.05).

Plugging in the values into the formula:

n = (1.96^2 * 0.5 * (1-0.5))/(0.05^2) = 385

Therefore, the minimum sample size needed is 385. So, the correct answer is D. 385.