Motor-Vehicle Theft. The mean length of imprisonment for motor-vehicle theft offenders in this country is 21.5 months. A hypothesis test is to be performed to decide whether the mean length of imprisonment in this city differs from the national mean. The null and alternative hypotheses are H0: μ = 21.5 months, Ha: μ = 21.5 months.

a. Explain what it would mean to make a type I error.

b. Explain what it would mean to make a type II error.

c. Explain what it would mean to make a correct decision.

d. Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean length of imprisonment for motor-vehicle theft offenders in this city equals the national mean of 21.5 months.

e. Suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify the conclusion by error type or as a correct decision if in fact the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 21.5 months.