Class Project: Questioning Gas Mileage. This exercise can be done individually or, better yet, as a class project. Refer to the gas mileage hypothesis test of Example 9.23 on page 444. Recall that the null and alternative hypotheses are H0: μ = 26 mpg (manufacturer’s claim)

Ha: μ < 26 mpg (consumer group’s conjecture),

where μ is the mean gas mileage of all Orions. Also recall that the mileages are normally distributed with a standard deviation of 1.4 mpg. Figure 9.30 on page 445 portrays the decision criterion for a test at the 5% significance level with a sample size of 30. Suppose that, in reality, the mean gas mileage of all Orions is 25.4 mpg.

a. Determine the probability of making a Type II error.

b. Simulate 100 samples of 30 gas mileages each.

c. Determine the mean of each sample in part (b).

d. For the 100 samples obtained in part (b), about how many would you expect to lead to nonrejection of the null hypothesis? Explain your answer.

e. For the 100 samples obtained in part (b), determine the number that lead to nonrejection of the null hypothesis.

f. Compare your answers from parts

(d) and (e), and comment on any observed difference.