A government-sponsored organization that was established in 1938 after the Depre

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 775. A random sample of 40 mortgages recently purchased by the company was selected and it was found that the average credit score was 780 with a sample standard deviation of 20. Complete parts (a) through (c) below. a. Using = 0.02, is there enough evidence from this sample to conclude that the average credit score increased as the lending standards have tightened? Determine the null and alternative hypotheses. Choose the correct answer below. OA, Ho: 2775 and H1: 775 O c. H04-775 and H1 : #775 O D. Ho : 775 and H 1 : = 775 Determine the critical value(s). The critical value(s) is(are)

Explanation / Answer

The statistical software output for this problem is:

One sample T summary hypothesis test:
: Mean of population
H0 : = 775
HA : > 775

Hypothesis test results:

Hence,

Null and Alternative hypotheses: Option B is correct.

Critical value = 2.125

Test statistic = 1.58

Conclusion: Option D is correct.

p - value = 0.061

Assumptions: Option B is correct.

Mean Sample Mean Std. Err. DF T-Stat P-value 780 3.1622777 39 1.5811388 0.061

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