A? government-sponsored organization that was established in 1938after the Depression to provide local banks with money from thefederal government to be used for residential mortgages in aneffort to increase homeownership rates. As lending standards havetightened during the most recent housing market? crisis, creditscores for borrowers of approved mortgages have increased. In?2012, the average credit score for loans that were purchased by thecompany was 782. A random sample of 25 mortgages recently purchasedby the company was selected and it was found that the averagecredit score was 789 with a sample standard deviation of 25.Complete parts? (a) through? (c) below. a. Using alphaequals0.05?,is there enough evidence from this sample to conclude that theaverage credit score increased as the lending standards havetightened?? Determine the null and alternative hypotheses. Choosethe correct answer below. A.Upper H 0?: mu not equals 782 and UpperH 1?: mu equals 782 B.Upper H 0?: mu greater than or equals 782 andUpper H 1?: mu less than 782 C.Upper H 0?: mu less than or equals782 and Upper H 1?: mu greater than 782 D.Upper H 0?: mu equals 782and Upper H 1?: mu not equals 782 Determine the critical? value(s).The critical? value(s) is(are) nothing. ?(Round to three decimalplaces as needed. Use a comma to separate answers as? needed.)Determine the test? statistic, t Subscript x overbar. t Subscript xoverbarequals nothing ?(Round to two decimal places as? needed.)What conclusion should be? drawn? A.Do not reject Upper H 0. Thereis not sufficient evidence to conclude that the average creditscore increased as the lending standards have tightened. B.Do notreject Upper H 0. There is sufficient evidence to conclude that theaverage credit score increased as the lending standards havetightened. C.Reject Upper H 0. There is sufficient evidence toconclude that the average credit score increased as the lendingstandards have tightened. D.Reject Upper H 0. There is notsufficient evidence to conclude that the average credit scoreincreased as the lending standards have tightened. b. Usetechnology to determine the? p-value for this test. ?p-valueequalsnothing ?(Round to three decimal places as? needed.) c. Whatassumptions need to be made to perform this? analysis? A.That therewas less than 30 users sampled. B.Because the sample size is lessthan? 30, the population needs to be normally distributed. C.Thatthe median was less than the mean value. D.No assumptions wereneeded to preform the analysis. Click to select your answer(s).
