When constructing confidence interval estimate of μ,doubling the sample size n decreases the width of the interval by half.

Question

Quizplus · Accepted Answer

Doubling the sample size decreases the standard error of the mean (since it is inversely proportional to the square root of the sample size), which in turn decreases the width of the confidence interval, but not by half. The decrease is less than half because the relationship is not linear but based on the square root of the sample size.

When Constructing Confidence Interval Estimate of μ,Doubling the Sample Size