After elections were held, it was desired to estimate the proportion of voters who regretted that they did not vote. How many voters must be sampled in order to estimate the true proportion to within $2 \% ($ e.g., $\pm 0.02$ ) at the $90 \%$ confidence level? Assume that we believe this proportion lies close to $30 \%$.
A) $n = 2401$
B) $n = 1421$
C) $\mathrm { n } = 1692$
D) $n = 2017$
E) Cannot determine because no estimate of $\mathrm { p }$ or $\mathrm { q }$ exists in this problem.

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 (for 90%, $Z \approx 1.645$), $p$ is the estimated proportion (0.30 in this case), and $E$ is the margin of error (0.02). Plugging in the values: $n = \left(\frac{1.645^2 \cdot 0.30 \cdot (1-0.30)}{0.02^2}\right) \approx 1421$.

After Elections Were Held, It Was Desired to Estimate the Proportion