Before lending someone money, banks must decide whether they believe the applica

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?

Explanation / Answer

From the point of view of the Bank, If it loses money by lending loan to someone whom it think to be able to repay is a the error of I type.And if it rejects somebody who is actually able to repay but is denied a loan and thereby the bank misses a chance to make a profit is an error of type II.

So, (a) When a person defaults a loan bank makes Type-I error.

(b) This is as above mentioned a type-II error.

(c) If the bank lowers the cut-off from 250 to 200 in their scale then it allows more number of persons under the loan facilityso invites more chance OR technically probability of type-I error .It is analogous to choosing a lower value ( mean the p-value) for a hypothesis test, since we are allowing lower values.

(d) As the cut-off value changes the probability of type-I error has increased and probability of type-II error has decreased.

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