Loans Before lending someone money, banks must decidewhether they believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess infor-mation about the applicant, totaling points they award for the person’s income level, credit history, current debt burden,and so on. The higher the point total, the more convinced thebank is that it’s safe to make the loan. Any applicant with alower point total than a certain cutoff score is denied a loan.We can think of this decision as a hypothesis test. Sincethe bank makes its profit from the interest collected onrepaid loans, their null hypothesis is that the applicant willrepay the loan and therefore should get the money. Only ifthe person’s score falls below the minimum cutoff will the bank reject the null and deny the loan. This system is reason-ably reliable, but, of course, sometimes there are mistakes. a) When a person defaults on a loan, which type of errordid the bank make?b) Which kind of error is it when the bank misses anopportunity to make a loan to someone who wouldhave repaid it?c) Suppose the bank decides to lower the cutoff score from250 points to 200. Is that analogous to choosing a higheror lower value of a for a hypothesis test? Explain.d) What impact does this change in the cutoff value haveon the chance of each type of error?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Loans 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 infor-
mation about the applicant, totaling points they award for the

person’s 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 cutoff 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 person’s score falls below the minimum cutoff will the

bank reject the null and deny the loan. This system is reason-
ably 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 cutoff score from
250 points to 200. Is that analogous to choosing a higher
or lower value of a for a hypothesis test? Explain.
d) What impact does this change in the cutoff value have
on the chance of each type of error?

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