Question: Perform the following hypothesis test. Note that you will do both a p-value hypothesis test and a critical-value hypothesis test.

The Motor Trend New Car Buyer’s Guide listed the Ford Taurus as having a highway fuel efficiency of 30 miles per gallon. A consumer interest group conducts automobile mileage tests seeking statistical evidence to identify instances where automobile manufacturers overstate the miles-per-gallon rating for a particular model.

a. State the hypotheses that would enable the consumer interest group to conclude that the Ford Taurus fuel efficiency is less than the published 30 miles per gallon.

b. A sample of 50 mileage tests with the Ford Taurus showed a sample mean of 29.6 miles per gallon and a sample standard deviation of 1.8 miles per gallon. What is the p-value? What conclusion should be drawn from the sample results? Use \(\alpha =0.01\)

c. Repeat the preceding hypothesis test using the critical value approach. Use \(\alpha =0.01\).