The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within 3 percentage points of the true proportion. How large a sample is necessary?

Question

Quizplus · Accepted Answer

The sample size needed is 966. This is because the margin of error is 3 percentage points, and the confidence level is 98%. The formula for calculating the sample size is:n = (Z^2 * p * q) / e^2where:n is the sample sizeZ is the z-score for the desired confidence levelp is the proportion of women who wear shoes that are too small for their feetq is the complement of p (1 - p)e is the margin of errorPlugging in the values given in the question, we get:n = (2.326^2 * 0.8 * 0.2) / 0.03^2n = 966.04Therefore, the sample size needed is 966.

The Academy of Orthopedic Surgeons States That 80% of Women