A local outdoor equipment store is being sold. The buyers are trying to estimate the percentage of items thatare outdated. They will randomly sample among its 100,000 items in order to determine the proportion ofmerchandise that is outdated. The current owners have never determined their outdated percentage and cannot help the buyers. Approximately how large a sample do the buyers need in order to insure that they are 95%confident that the margin of error is within 3%?

Question

Quizplus · Accepted Answer

To achieve a 95% confidence level with a margin of error of 3%, the sample size can be calculated using the formula for a proportion: $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score for the confidence level (1.96 for 95%), $p$ is the estimated proportion (0.5 for maximum variability), and $E$ is the margin of error (0.03). Substituting these values, we get $n = \frac{(1.96)^2 \cdot 0.5 \cdot (1-0.5)}{(0.03)^2}$, which calculates to approximately 1067.11, rounded up to 1068 for a whole number of items.

A Local Outdoor Equipment Store Is Being Sold