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 778. A random sample of 25 mortgages recently purchased by the company was selected and it was found that the average credit score was 784 with a sample standard deviation of 35. Complete parts​ (a) through​ (c) below. a. Using alphaequals0.01​, 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. Upper H 0​: mu equals 778 and Upper H 1​: mu not equals 778 B. Upper H 0​: mu not equals 778 and Upper H 1​: mu equals 778 C. Upper H 0​: mu greater than or equals 778 and Upper H 1​: mu less than 778 D. Upper H 0​: mu less than or equals 778 and Upper H 1​: mu greater than 778 Determine the critical​ value(s). The critical​ value(s) is(are) nothing. ​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

Answer 1

from above

for hypothesis: option D is correct

the critical value is =2.492

test statistic t =0.857

as test statistic does not fall in rejection region, we can not reject null hypothesis