A recent study reported that the average credit score for a new-car loan was 753
ID: 3289449 • Letter: A
Question
A recent study reported that the average credit score for a new-car loan was 753. Suppose Ally Financial, a bank holding company that finances car loans, would like to test the hypothesis that the average credit score has increased since the study. A random sample 20 new-car loans had an average credit score of 764.2 with a sample standard deviation of 34.5. Ally Financial would like to set alpha = 0.05. What is the conclusion for this hypothesis test? Would be that because the last statistic is ______. A. Since the test statistic is more than the critical value, we can conclude that the average credit score for a new car-loan is more than 753. B. Since the test statistic is more than the critical value, we cannot conclude that the average credit score for a new-car loan is not more than 753. C. Since the test statistic is less than the critical value, we cannot conclude that the average credit score for a new-car loan is not more than 753. D. Since the test statistic is less than the critical value, we can conclude that the average credit score for a new-car loan is more than753.Explanation / Answer
Solution:
Set Up Hypothesis
Null, H0: U<=753
Alternate,average credit score for a new-car loan is more than 753 H1: U>753
Test Statistic
Population Mean(U)=753
Sample X(Mean)=764.2
Standard Deviation(S.D)=34.5
Number (n)=20
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =764.2-753/(34.5/Sqrt(20))
to =1.452
| to | =1.452
Critical Value
The Value of |t | with n-1 = 19 d.f is 1.729
We got |to| =1.452 & | t | =1.729
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Right Tail - Ha : ( P > 1.4518 ) = 0.08143
Hence Value of P0.05 < 0.08143,Here We Do not Reject Ho
[ANSWER]
C.Since the test statistic is less than the critical value, we cannot conclude that the average credit score for a new-car loan is not more than 753.