EXAMPLE 8 Decreasing the margin of error by decreasing the confidence level

For the confidence interval for the population mean city gas mileage in Example 5, suppose we reduce the confidence level from 90% to 80% and leave everything else unchanged. Find the new margin of error. Describe how the margin of error has changed.

Solution

From Example 5, we have the margin of error for the 90% confidence interval for as follows:

Decreasing the confidence level from 90% to 80% decreases from 1.645 to 1.28. This gives us the margin of error for the 90% confidence interval as:

Decreasing the confidence level from 90% to 80% decreases the margin of error from 0.93 mpg to 0.72 mpg.