Question

Before lending someone money, banks must decide whether they believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess information about the applicant, totalling points they award for the persons income level, credit history, current debt burden, and so on. The higher the point total, the more convinced the bank is that it’s safe to make the loan. Any applicant with a lower point total than a certain cut-off score is denied a loan. We can think of this decision as a hypothesis test. Since the bank makes its profit from the interest collected on repaid loans, their null hypothesis is that the applicant will repay the loan and therefore should get the money. Only if the persons score falls below the minimum cut-off will the bank reject the null and deny the loan. This system is reasonably reliable, but, of course, sometimes there are mistakes.a) When a person defaults on a loan, which type of error did the bank make?b) Which kind of error is it when the bank misses an opportunity to make a loan to someone who would have repaid it?c) Suppose the bank decides to lower the cut-off score from 250 points to 200. Is that analogous to choosing a higher or lower value of for a hypothesis test? Explain.d) What impact does this change in the cut-off value have on the chance of each type of error?

Answer 1

Answer:

(a) Type II error

(b) Type I error

(c) It is analogous to choosing a lower value for a hypothesis test

(d) There will be more tendency of making type II error and less tendency of making type I error

Step-by-step explanation:

(a) The bank made a type II error because they accepted the null hypothesis when it is false

(b) The bank made a type I error because they rejected the null hypothesis when it is true

(c) By lowering the value for the hypothesis test, they give applicants who do not meet the initial cut-off point the benefit of doubt of repaying the loan thus increasing their chances of making more profit

(d) There will be more tendency of making type II error because the bank accepts the null hypothesis though they are not fully convinced the applicants will repay the loan and less tendency of making type I error because the bank rejects the null hypothesis knowing the applicants might not be able to repay the loan