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?
A)200
B)100
C)58
D)385

Question

Quizplus · Accepted Answer

The formula to calculate the minimum sample size is:
n = [Z^2 * p * (1-p)] / E^2 
where Z is the z-score for the desired confidence level (in this case, 1.96 for 95% confidence), p is the estimated proportion (since we don't have any prior estimate, we can assume 0.5 for maximum variability), and E is the maximum margin of error we want to tolerate (in this case, 0.05). Plugging in the values, we get:
n = [(1.96)^2 * 0.5 * (1-0.5)] / (0.05)^2 = 384.16
Rounding up to the next whole number, we get a minimum sample size of 385.

We Are Interested in Conducting a Study in Order to Determine