A survey of 499 women for the American Orthopedic Foot and Ankle Society revealed that 38% wear flats to work. Suppose the society also wishes to estimate the proportion of women who wear athletic shoes to work with a margin of error of 0.01 with 95% confidence. Determine the sample size required.

Question

Quizplus · Accepted Answer

To determine the sample size required for estimating a proportion with a specified margin of error and confidence level, we use the formula: $n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right)$, where $Z$ is the Z-score corresponding to the confidence level, $p$ is the estimated proportion (if unknown, 0.5 is used for maximum sample size), and $E$ is the margin of error. For a 95% confidence level, $Z = 1.96$. Since the proportion of women who wear athletic shoes to work is not given, we use $p = 0.5$ for the worst-case scenario (maximum variance). Plugging in the values: $n = \left(\frac{1.96^2 \cdot 0.5 \cdot (1-0.5)}{0.01^2}\right) = 9604$.

A Survey of 499 Women for the American Orthopedic Foot