In 2012, the average credit score for loans that were purchased through Fannie Mae was 766. A random sample of 35 mortgages were selected, and it was found that the average credit score was 771with a sample standard deviation of 21.

Using alpha =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?

What is the p value for this test?

What assumptions need to be made to perform this analysis?