Question

A bank makes loans to small businesses and on average 4.1​% of them default on their loans within five years. The bank makes provision for these losses when it makes its financial plans. The Vice President in charge of small business loans thinks that the default rate may be going down and gives you a random sample of 255 recent loans of which 7 defaulted within five years. What advice do you give to the Vice​ President?

The probability that 7 or fewer of the 255 small businesses default on their loans is ( ). Using​ 5% as the criterion for an unlikely​ event, there is a relatively ( ) probability that 7 or fewer of the 255 small businesses would​ default, so there is ( )  to support the claim that the default rate may be going down.

​(Round to three decimal places as​ needed.)

Answer 1

Given that . Out of 255 loans, 7 defaulted within 5 years.

  

Level of significance :

Test statistic:

  

  

Critical value of Z is -1.6449. Since the calculated value of Z is greater than the critical value, we do not reject the null hypothesis.

The p-value is p=0.1376.

The probability that 7 or fewer of the 255 small businesses default on their loans is 0.1376 . Using​ 5% as the criterion for an unlikely​ event, there is a relatively more probability that 7 or fewer of the 255 small businesses would​ default, so there is not enough evidence to support the claim that the default rate may be going down.