Exam 10: Statistical Inference Concerning Two Populations

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.

When constructing a confidence interval for the mean difference ,we follow the same general format of point estimate ± _________ .

Assume the competing hypotheses take the following form: H₀: µ₁- µ₂ = 0,H_A: µ₁- µ₂ ≠ 0,where µ₁ is the population mean for population 1 and µ₂ is the population mean for population 2.Also assume that the populations are normally distributed and we use independent sampling.The population variances are not known and cannot be assumed equal.Which of the following expressions is appropriate test statistic?

If testing the difference between two population proportions under independent sampling,you pool the sample proportions and compute as _________ .