Question

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. which of the following would result in the smallest margin of error in estimating the mean salt content $M$?

(a) $90\%$ confidence; $n=25$.

(b) $90\%$ confidence; $n=50$.

(c) $95\%$ confidence; $n=25$.

(d) $95\%$confidence; $n=50$.

(e) $n=100$ at any confidence level.

Short answer

The correct option is (d).

Step-by-step solution

Given Information

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production.

Explanation

Higher the confidence levelresults larger width of the confidence interval and thus increase in margin of error.Similarly, as the sample size increases more narrowwill be the confidence interval and thus margin of error decreases.

Thus for the smaller margin of error confidence level should be low and the sample size should be high.

Hence, the correct option is (b).