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 784. A random sample of 25 mortgages recently purchased by the company was selected and it was found that the average credit score was 793 with a sample standard deviation of 20. 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​?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 784

H_a : > 784

Test statistic =t

= ( - ) / s / n

= (793 - 784) / 20 / 25

Test statistic =2.25

df = 24

P-value = 0.0169

= 0.02

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the this sample to conclude that the average credit score increased as

the lending standards have tightened .