Question

You may need to use the appropriate appendix table or technology to answer this question.

A consumer research group is interested in testing an automobile manufacturer's claim that a new economy model will travel at least 23 miles per gallon of gasoline (H₀: μ ≥ 23).

(a)

With a 0.02 level of significance and a sample of 40 cars, what is the rejection rule based on the value of

x̄

for the test to determine whether the manufacturer's claim should be rejected? Assume that σ is 4 miles per gallon.

State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

x ≤ ?

x ≥ ?

(b)

What is the probability of committing a type II error if the actual mileage is 21 miles per gallon? (Round your answer to four decimal places. If it is not possible to commit a type II error enter NOT POSSIBLE.)

(c)

What is the probability of committing a type II error if the actual mileage is 22 miles per gallon? (Round your answer to four decimal places. If it is not possible to commit a type II error enter NOT POSSIBLE.)

(d)

What is the probability of committing a type II error if the actual mileage is 23.5 miles per gallon? (Round your answer to four decimal places. If it is not possible to commit a type II error enter NOT POSSIBLE.)

Answer 1