A population proportion is to be estimated. Estimate the minimum sample size needed to achieve the specified margin of error with a 95% degree of confidence.
-$\mathrm { E } = 0.013$
A)5917
B)2959
C)77
D)11,834

Question

Quizplus · Accepted Answer

The minimum sample size needed to achieve a specified margin of error (E) with a 95% confidence level for estimating a population proportion can be calculated using the formula $n = \left( \frac{Z_{\alpha/2}}{E} \right)^2 p(1-p)$, where $Z_{\alpha/2}$ is the Z-score corresponding to the desired confidence level (for 95% confidence, $Z_{\alpha/2} = 1.96$), $E$ is the margin of error, and $p$ is the estimated proportion (if unknown, using 0.5 maximizes the sample size, providing a conservative estimate). Plugging in the values: $n = \left( \frac{1.96}{0.013} \right)^2 \times 0.5 \times 0.5 \approx 5917$.

A Population Proportion Is to Be Estimated E=0.013\mathrm { E } = 0.013E=0.013

A Population Proportion Is to Be Estimated $\mathrm { E } = 0.013$