The mean length of imprisonment for motor-vehicle theft offenders in this country is 17.4 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 H\": u = 17.4 months, Ha: u17.4 months. a. Explain what it would mean to make a type I error. A. A type I error would occur if in fact p $17.4 months, but the results of the sampling fail to lead to the conclusion that p =17.4 months. .._,> B. A type I error would occur if in fact p =17.4 months, but the results of the sampling lead to the conclusion that p # 17.4 months. ' > C. A type I error would occur if in fact p =17.4 months, but the results of the sampling fail to lead to the conclusion that u $17.4 months. b. Explain what it would mean to make a type II error. \" A. A type II error would occur if in fact p = 17.4 months, but the results of the sampling lead to the conclusion that p a4 17.4 months. . ' B. A type II error would occur if in fact p a4 17.4 months, but the results of the sampling fail to lead to the conclusion that p a4 17.4 months. C. A type II error would occur if in fact p a4 17.4 months, but the results of the sampling lead to the conclusion that u# 17.4 months. 6. Explain what it would mean to make a correct decision. 1:; A. A correct decision would occur if p =17.4 months and the results of the sampling do not lead to the rejection of that fact; or if u#17.4 months and the results of the sampling lead to that conclusion. 1:; B. A correct decision would occur if p it 17.4 months and the results of the sampling lead to the rejection of that fact; or if p = 17.4 months and the results of the sampling do not lead to that conclusion. ' C. A correct decision would occur if p =17.4 months and the results of the sampling lead to the rejection of that fact; or if p 36 17.4 months and the results of the sampling do not lead to that conclusion. 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 17.4 months. 3 A. Type I error > B. Correct decision . >C. Typellermr 2. 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 17.4 months. 1:; A. Type I error 1', B. Correct decision -.,.' C. Type II error