Fannie Mae is a government sponsored organization that was established in 1938 after the Depression to provide local banks with money from the federal government to be used for residential mortgages in an effort to increase homeownership rates. As lending standards have tightened during the most recent housing market crisis, credit scores for borrowers of approved mortgages have increased. In 2012, the average credit score for loans that were purchased by Fannie Mae was 766. A random sample of 35 mortgages recently purchased by Fannie Mae was selected, and it was found that the average credit score was 771 with a sample standard deviation of 21.

a. Using σ = 0.05, is there enough evidence from this sample to conclude that the average credit score for mortgages purchased by Fannie Mae has increased since 2012?

b. Estimate the p value for this test using Table 5 in Appendix A.

c. Determine the precise p value for this test using Excel.

d. Use PHStat to validate these results.

e. What assumptions need to be made to perform this analysis?