Question

In August 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 p1 and p2 represent the proportion of delinquent borrowers who avoid foreclosure just before and just after the right-to-cure law is enacted, respectively. Which of the following is the correct competing hypotheses that will test the policymakers’ claim?

a. H₀: p₁ – p₂≥ 0, H_A: p₁ – p₂< 0

b. H₀: p₁ – p₂> 0, H_A: p₁ – p₂≤ 0

c. H₀: p₁ – p₂≤ 0, H_A: p₁ – p₂> 0

d. H₀: p₁ – p₂= 0, H_A: p₁ – p₂≠ 0

Answer 1

here claim is  the policy would result in a higher proportion of delinquent borrowers becoming current on their mortgage

Let p1 represent the proportion of delinquent borrowers who avoid foreclosure just before the right-to-cure law is enacted.

p2 represent the proportion of delinquent borrowers who avoid foreclosure just after the right-to-cure law is enacted.

the null and alternative hypothesis is given by option c

c. H0: p1 – p2 ≤ 0, HA: p1 – p2 > 0