Question

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. That is, the null hypothesis is H0: ? ? 25. a. What a 0.02 level of significance and a sample of 30 cars, what is the rejection rule based on the value of the sample mean x? for the test to determine whether the manufacturer's claim should be rejected? Assume that ? is 3 miles per gallon. b. What is the probability of committing a Type II error if the actual mileage is 23 miles per gallon? c. What is the probability of committing a Type II error if the actual mileage is 24 miles per gallon? d. What is the probability of committing a Type II error if the actual mileage is 25.5 miles per gallon? e. What happens to the power of the statistical test when we go from (a) to (b) to (c)? Explain why using your own words.

          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. That is, the null hypothesis is H0: ? ? 25.
a. What a 0.02 level of significance and a sample of 30 cars, what is the rejection rule based on the value of the sample mean x? for the test to determine whether the manufacturer's claim should be rejected? Assume that ? is 3 miles per gallon.
b. What is the probability of committing a Type II error if the actual mileage is 23 miles per gallon?
c. What is the probability of committing a Type II error if the actual mileage is 24 miles per gallon?
d. What is the probability of committing a Type II error if the actual mileage is 25.5 miles per gallon?
e. What happens to the power of the statistical test when we go from (a) to (b) to (c)? Explain why using your own words.

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. That is, the null hypothesis is H0: ? ? 25.
a. What a 0.02 level of significance and a sample of 30 cars, what is the rejection rule based on the value of the sample mean x? for the test to determine whether the manufacturer's claim should be rejected? Assume that ? is 3 miles per gallon.
b. What is the probability of committing a Type II error if the actual mileage is 23 miles per gallon?
c. What is the probability of committing a Type II error if the actual mileage is 24 miles per gallon?
d. What is the probability of committing a Type II error if the actual mileage is 25.5 miles per gallon?
e. What happens to the power of the statistical test when we go from (a) to (b) to (c)? Explain why using your own words.

Added by Virginia A.

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