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 785. A random sample of 20 mortgages recently purchased by the company was selected and it was found that the average credit score was 794 with a sample standard deviation of 25. Complete parts (a) through (c) below.
A. H0: μ ≥ 785 and H1: μ < 785
B. H0: μ ≤ 785 and H1: μ > 785
C. H0: μ ≠ 785 and H1: μ = 785
D. H0: μ = 785 and H1: μ ≠ 785
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. Reject H0. There is not 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. Do not reject H0. There is 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. Because the sample size is less than 30, the population needs to be normally distributed.
B. That the median was less than the mean value.
C. That there was less than 30 users sampled.
D. No assumptions were needed to preform the analysis.