Q.77 - The Practice of Statistics for AP

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.

Step-by-Step Solution

Answer

The correct option is (d).

Step 1: 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. 

Step 2: 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).