EXAMPLE 33 Using confidence intervals for to conduct two-tailed tests for

A 95% confidence interval for the population mean sodium content of breakfast cereals, in milligrams (mg) per serving, is given by

Assume that the data are normally distributed. Test, using level of significance , whether differs from the following.

  1. 80 mg
  2. 40 mg

Solution

  1. For the hypothesis test versus lies between the lower bound 44.53 and the upper bound 81.50 of the confidence interval, and we therefore do not reject . There is insufficient evidence that the population standard deviation of sodium content differs from 80 mg.
  2. For the hypothesis test lies outside the confidence interval, and we therefore reject . There is evidence that the population standard deviation of sodium content differs from 40 mg.

NOW YOU CAN DO

Exercises 19–22.