EXAMPLE 9 Decreasing the margin of error by increasing the sample size

For the confidence interval for the population mean city gas mileage in Example 5, suppose the results were based on a sample of size instead of . Leaving everything else unchanged, find the new margin of error, and describe how the margin of error has changed.

Solution

For , the margin of error is

Increasing the sample size from to has decreased the margin of error from 0.93 mpg to 0.46 mpg.