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 home-ownership rates. As lending standards have tightened during the most recent housing market crisis, credit scores for borrowers of approved mortgages have increased. In 2017 the average credit score for loans that were purchased by Fannie Mae was 745. A random sample of 35 mortgages recently purchased by Fannie Mae was selected, and it was found that the average credit score was 755 with a sample standard deviation of 21.

a. Using α = 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 2017?

b. Determine the precise p-value for this test using Excel.

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