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 768. A random sample of 20 mortgages recently purchased by the company was selected and it was found that the average credit score was 777 with a sample standard deviation of 35. Complete parts? (a) through? (c) below.
a. Using alpha α=0.01?, 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.
A. H0?:μ=768 and H1:μ≠768
B.H0?: μ≠768 and H1?: μ=768
C.H0?: μ≤768 and H1?:μ>768
D.H0?: μ≥768 andH1?: μ<768
Determine the critical value(s).
The critical? value(s) is(are) ______?(Round to three decimal places as needed. Use a comma to separate answers as? needed.)
Determine the test? statistic, tx
tx=______?(Round to two decimal places as? needed.)
What conclusion should be? drawn?
A.Do not reject H0. There is sufficient evidence to conclude that the average credit score increased as the lending standards have tightened.
B.Do not reject H0. There is not sufficient evidence to conclude that the average credit score increased as the lending standards have tightened.
C.Reject H0. There is not sufficient evidence to conclude that the average credit score increased as the lending standards have tightened.
D.Reject H0. There is sufficient evidence to conclude that the average credit score increased as the lending standards have tightened.
b. Use technology to determine the? p-value for this test.
?p-value =________(Round to three decimal places as? needed.)
c. What assumptions need to be made to perform this? analysis?
A. That the median was less than the mean value.
B. That there was less than 30 users sampled.
C. Because the sample standard deviation was used to approximate the population standard? deviation, the population needs to be normally distributed.
D. No assumptions were needed to preform the analysis.