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?