Exhibit 10.14.In August of 2010,Massachusetts enacted a 150-day right-to-cure period that mandates that lenders give homeowners who fall behind on their mortgage an extra five months to become current before beginning foreclosure proceedings.Policymakers claimed that the policy would result in a higher proportion of delinquent borrowers becoming current on their mortgages.To test this claim,researchers took a sample of 244 homeowners in danger of foreclosure in the time period surrounding the enactment of this law.Of the 100 who fell behind just before the law was enacted,30 were able to avoid foreclosure,and of 144 who fell behind just after the law was enacted,48 were able to avoid foreclosure.Let and represent the proportion of delinquent borrowers who avoid foreclosure just before and just after the right-to-cure law is enacted,respectively. Refer to Exhibit 10.14.Assuming α = 0.10,does the evidence support the policymakers' claim?
A)Yes,since the p-value is less than the critical value.
B)No,since the test statistic value is less than the critical value.
C)No,since the p-value is greater than the significance level.
D)Yes,since the test statistic value is greater than the critical value.

Question

Exhibit 10.14.In August of 2010,Massachusetts enacted a 150-day right-to-cure period that mandates that lenders give homeowners who fall behind on their mortgage an extra five months to become current before beginning foreclosure proceedings.Policymakers claimed that the policy would result in a higher proportion of delinquent borrowers becoming current on their mortgages.To test this claim,researchers took a sample of 244 homeowners in danger of foreclosure in the time period surrounding the enactment of this law.Of the 100 who fell behind just before the law was enacted,30 were able to avoid foreclosure,and of 144 who fell behind just after the law was enacted,48 were able to avoid foreclosure.Let  and  represent the proportion of delinquent borrowers who avoid foreclosure just before and just after the right-to-cure law is enacted,respectively. Refer to Exhibit 10.14.Assuming α = 0.10,does the evidence support the policymakers' claim?
A)Yes,since the p-value is less than the critical value. 
B)No,since the test statistic value is less than the critical value. 
C)No,since the p-value is greater than the significance level. 
D)Yes,since the test statistic value is greater than the critical value.

Quizplus · Accepted Answer

To test the policymakers' claim, we need to conduct 2-proportion z-test using the formula:

z = (p1-p2)/ sqrt{p_hat * (1-p_hat) * (1/n1 + 1/n2)}

where,
p1 = 30/100 = 0.3
p2 = 48/144 = 0.3333
p_hat = (30+48)/(100+144) = 0.3192
n1 = 100 and n2 = 144
α = 0.10

Plugging in the values, we get z = -1.034 and the corresponding p-value is 0.1507, which is greater than the significance level α = 0.10. Therefore, we fail to reject the null hypothesis that the proportion of delinquent borrowers who avoid foreclosure just before and just after the right-to-cure law is enacted are equal. Hence, the evidence does not support the policymakers' claim. The correct choice is C.