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. A) H₀: p₁ - p₂ ≤ 0, H_A: p₁ - p₂ 0 B) H₀: p₁ - p₂ ≥ 0, H_A: p₁ - p₂ 0, H_A: p₁ - p₂ ≤ 0

Question

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. 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

Quizplus · Accepted Answer

The null hypothesis should state that there is no difference in default rates between borrowers who received HAMP modifications and non-HAMP modifications. Therefore, the correct null hypothesis is H₀: p₁ - p₂ ≥ 0. The alternative hypothesis should state that borrowers who received HAMP modifications default less than borrowers who received non-HAMP modifications, which corresponds to the directionality of a one-tailed test. Therefore, the correct alternative hypothesis is H_A: p₁ - p₂ < 0. Among the given choices, only option B correctly presents both hypotheses.

A Particular Bank Has Two Loan Modification Programs for Distressed