A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will choose a random sample from the 100,000 items in the store's inventory in order to determine the proportion of merchandise that is outdated. The current owners have never determined the percentage of outdated merchandise and cannot help the buyers. How large a sample do the buyers need in order to be 95% confident that the margin of error of their estimate is about 5%?

A) 1537
B) 385
C) 769
D) 196

Question

A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will choose a random sample from the 100,000 items in the store's inventory in order to determine the proportion of merchandise that is outdated. The current owners have never determined the percentage of outdated merchandise and cannot help the buyers. How large a sample do the buyers need in order to be 95% confident that the margin of error of their estimate is about 5%?

A) 1537
B) 385
C) 769
D) 196

Quizplus · Accepted Answer

To achieve a 95% confidence level with a 5% margin of error, the sample size can be calculated using the formula for sample size estimation for proportions. Using the standard normal distribution (Z=1.96 for 95% confidence) and assuming maximum variability (p=0.5), the sample size needed is approximately 385.

A Local Men's Clothing Store Is Being Sold