Question

Recently, Experian 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 Experian report. A random sample of 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 α = 0.05. The p-value for this hypothesis test would be ________ .

Answer 1

Solution :

Null and alternative hypotheses :

The null and alternative hypotheses are as follows :

Where, μ_{​​​​​​} is population mean credit score of the new car loans.

Test statistic :

To test the hypothesis the most appropriate test is one sample t-test. The test statistic is given as follows :

Where, x̅ is sample mean, s is sample standard deviation, n is sample size and μ is hypothesized value of population mean under H_{​​​​​​0}.

We have,  x̅ = 764.2, s = 34.5, n = 20 and  μ = 753

The value of the test statistic is 1.4518.

P-value :

Since, our test is right-tailed test, therefore we shall obtain right-tailed p-value for the test statistic. The right-tailed p-value is given as follows :

P-value = P(T > t)

P-value = P(T > 1.4518)

P-value = 0.0814

The p-value for the test is 0.0814.

Decision :

Significance level = 0.05

P-value = 0.0814

(0.0814 > 0.05)

Since, p-value is greater than the significance level of 0.05, therefore we shall be fail to reject the null hypothesis (H_{​​​​​​0}) at 0.05 significance level.

Conclusion :

At 0.05 significance level there is not sufficient evidence to conclude that the average credit score has increased since the Experian report.

Please rate the answer. Thank you.