Provide an appropriate response.
-A local outdoor equipment store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers. Approximately how large a sample do the buyers need in order to insure that they are $98 \%$ confident that the margin of error is within $2 \%$ ?
A) 3394
B) 6787
C) 13,573
D) 1457

Question

Quizplus · Accepted Answer

To ensure a 98% confidence level with a margin of error of 2%, the sample size can be calculated using the formula for the sample size of a proportion, which simplifies to $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the confidence level (approximately 2.33 for 98%), $p$ is the estimated proportion (0.5 for maximum variability), and $E$ is the margin of error (0.02). Plugging these values in, we get a sample size of approximately 3391, which rounds to the nearest given option, 3394.

Provide an Appropriate Response 98%98 \%98% Confident That the Margin of Error Is Within

Provide an Appropriate Response $98 \%$ Confident That the Margin of Error Is Within