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 $\mu$?

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

Option (b) is correct.

Step-by-step solution

Given Information

It is given that confidence interval is $90\%\text{and}95\%$

$25,50,100$are sample size

Concept Used

Formula to be used is

$\text{Margin of error}=z_{a/2}\times \frac{\sigma }{\sqrt{n}}$

Selecting the Combination

Standard Deviation and Confidence Level are positively related.

Sample size and margin of error are negatively related.

For less margin of error, less confidence level and greater sample size is needed.

Hence the perfect combination is option (b).

i.e.$90\%$confidence and$n=50$