Chapter 9.7, Problem 49E

A consumer research group is interested in testing an automobile manufacturer’s claim that a new economy model will travel at least 25 miles per gallon of gasoline (H₀: μ ≥ 25).

1. a. With a .02 level of significance and a sample of 30 cars, what is the rejection rule based on the value of $\bar{x}$ for the test to determine whether the manufacturer’s claim should be rejected? Assume that σ is 3 miles per gallon.
2. b. What is the probability of committing a Type II error if the actual mileage is 23 miles per gallon?
3. c. What is the probability of committing a Type II error if the actual mileage is 24 miles per gallon?
4. d. What is the probability of committing a Type II error if the actual mileage is 25.5 miles per gallon?