Chapter 21, Problem 15E

(a)

To determine

To explain which type of error did the blank make when a person defaults on a loan.

Answer to Problem 15E

It is a Type II error.

Explanation of Solution

It is given in the question that before lending someone money, banks must decide whether they believe the applicant will repay the loan. The strategy used is a point system. Thus, when a person defaults on a loan, then it is a Type II error as the null hypothesis was not rejected even though it was false.

(b)

To determine

To which kind of error is it when the blank misses an opportunity to make a loan to someone who would have repaid it.

Answer to Problem 15E

It is a Type I error.

Explanation of Solution

It is given in the question that before lending someone money, banks must decide whether they believe the applicant will repay the loan. The strategy used is a point system. Thus, when the blank misses an opportunity to make a loan to someone who would have repaid it then it is a Type I error because the null hypothesis was incorrectly rejected when it was true.

(c)

To determine

To explain is that analogous to choosing a higher or lower value of $\alpha$ for a hypothesis test.

Answer to Problem 15E

It is lower.

Explanation of Solution

It is given in the question that before lending someone money, banks must decide whether they believe the applicant will repay the loan. The strategy used is a point system. Thus, it is analogous to choosing a lower value of $\alpha$ for a hypothesis test because by making it easier to get the loan, the bank has reduced the alpha level.

(d)

To determine

To explain what impact does this change in the cut-off value have on the chance of each type of error.

Explanation of Solution

It is given in the question that before lending someone money, banks must decide whether they believe the applicant will repay the loan. The strategy used is a point system. Thus, the impact does this change in the cut-off value have on the chance of each type of error is that the risk of a Type I error decreases but the risk of a Type II error increases because the probability of a Type I error as alpha while the probability of a Type II error is $1-\alpha$ .