Refer to the gas mileage hypothesis test of Example 9 23 on page 422 Recall that the null and alternative hypotheses are H0 26 mpg (manufacturer 's claim) Ha 26 mpg (consumer group 's conjecture), Where is the mean gas mileage of all Orions Also recall that the mileages are normally distributed wit...

a Note Since this is a lefttailed test reject H 0 if ...

Refer to the gas mileage hypothesis test of Example 9.23 on page 422. Recall that the null

Question:

Refer to the gas mileage hypothesis test of Example 9.23 on page 422. 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 423 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. For the 100 samples obtained in part (b), about how many would you expect to lead to non-rejection of the null hypothesis? Explain your answer.