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 The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers.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.1457

c.6787

d.13,573

Question

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 The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers.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.1457
		
c.6787
		
d.13,573

kropot72 · Answer

A 98% confidence interval for the mean is given by
$$\bar{x}-2.33\frac{\sigma}{\sqrt{n}}<\mu<\bar{x}+2.33\frac{\sigma}{\sqrt{n}}$$
This expression can be used to find n the sample size.