Question

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 the company was 796. A random sample of 20 mortgages recently purchased by the company was selected and it was found that the average credit score was 800 with a sample standard deviation of 35. Complete parts​ (a) through​ (c) below.

a. Using alphaequals0.02​, is there enough evidence from this sample to conclude that the average credit score increased as the lending standards have tightened​?

b. Determine the critical values.

c. Determine the test Statistic.

d. determine the p-value

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 796
Alternative Hypothesis, Ha: μ > 796

Rejection Region
This is right tailed test, for α = 0.02 and df = 19
Critical value of t is 2.205.
Hence reject H0 if t > 2.205

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (800 - 796)/(35/sqrt(20))
t = 0.511

P-value Approach
P-value = 0.3076
As P-value >= 0.02, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the average credit score increased as the lending standards have tightened