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

Question

Quizplus · Accepted Answer

The formula for the minimum sample size needed to estimate a population proportion with a margin of error of E at a confidence level of C% is n = (Z^2*P*(1-P))/E^2, where Z is the critical value for the chosen confidence level, P is the estimated proportion, and E is the margin of error. For this problem, we want a margin of error of 0.05 or less at 95% confidence, which means that Z = 1.96. We do not have an estimated proportion, so we use the worst-case scenario of P = 0.5 (which yields the largest sample size). Substituting these values into the formula, we get n = (1.96^2*0.5*(1-0.5))/0.05^2 = 384.16. Rounding up to the nearest whole number, we get a minimum sample size of 385. Therefore, the best choice is D).

We Are Interested in Conducting a Study to Determine the Percentage