A pollster wishes to estimate the proportion of United States voters who favor capital punishment. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true
Proportion by more than 3%?
A)1509
B)1068
C)20
D)3017

Question

Quizplus · Accepted Answer

To estimate the sample size needed for a proportion with a specific margin of error and confidence level, the formula is $n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right)$, where $Z$ is the Z-score corresponding to the confidence level, $p$ is the estimated proportion (0.5 if unknown, to maximize sample size), and $E$ is the margin of error. For a 98% confidence level, the Z-score is approximately 2.33. Assuming $p = 0.5$ for maximum sample size and $E = 0.03$, the calculation is $n = \left(\frac{(2.33)^2 \cdot 0.5 \cdot (1-0.5)}{(0.03)^2}\right) \approx 1509$.

A Pollster Wishes to Estimate the Proportion of United States