A consultant for the mortgage lending industry has developed a new technique for assessing the risk involved in lending to those with less-than-stellar credit profiles. The technique involves using data-mining techniques to make a Personal Financial Responsibility (PFR) index. To evaluate the predictive power of this index, the consultant selected a random sample of borrowers and evaluated their risk using PFR. The consultant then compared borrowers' PFR to their mortgage payment performance (a rating based on a variety of factors with a range of 0 to 200). Data from the sample were as follows:

Payment

PFRPerformance

89188

99140

90108

3129

5482

6049

5220

6564

3241

6731

A)Conduct an appropriate hypothesis test to evaluate whether these data provide sufficient evidence regarding PFR's usefulness as a predictor of mortgage payment performance.

B)If you conclude PFR is a useful predictor of mortgage payment performance, how effective is it?

C)Construct a 95% confidence interval for the mean Payment Performance given a PFR score of 58.

D)Construct a 95% prediction interval for an individual's Payment Performance given his/her PFR score is 58.