A particular bank has two loan modification programs for distressed borrowers: Home Affordable Modification Program (HAMP) modifications, where the federal government pays the bank $1,000 for each successful modification, and non-HAMP modifications, where the bank does not receive a bonus from the federal government. To qualify for a HAMP modification, borrowers must meet a set of financial suitability criteria. Define the null and alternative hypotheses to test whether borrowers who receive HAMP modifications default less than borrowers who receive non-HAMP modifications. Let p₁ and p₂ represent the proportion of borrowers who received HAMP and non-HAMP modifications that did not re-default, respectively.

Multiple Choice

H₀: p₁ p₂> 0, H_A: p₁ p₂ 0

H₀: p₁ p₂ 0, H_A: p₁ p₂> 0

H₀: p₁ p₂= 0, H_A: p₁ p₂ 0

H₀: p₁ p₂ 0, H_A: p₁ p₂< 0