Question

The Fair Isaac Corporation (FICO) credit score is used by banks and other lenders to determine whether someone is a good credit risk. Scores range from 300 to 850, with a score of 720 or more indicating that a person is a very good credit risk. An economist wants to determine whether the mean FICO score is more than the cutoff of 720. She finds that a random sample of 40 people had a mean FICO score of 760 with a standard deviation of 95. Can the economist conclude that the mean FICO score is greater than 720? Use the =α0.01 level of significance and the critical value method.

a. state hypothesis

b. critical values/ test statistic

c. conclusion

Answer 1

Solution:

The provided sample mean is à = 760 and the sample standard deviation is s = 95, and the sample size is n = 40. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: p = 720 Ha: u > 720 This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.01, and the critical value for a right-tailed test is to = 2.426. The rejection region for this right-tailed test is R=t:t> 2.426 (3) Test Statistics The t-statistic is computed as follows: t=2 X - Mo s/n 760 – 720 _ 2 663 95/V40 (4) Decision about the null hypothesis Since it is observed that t = 2.663 > tc = 2.426, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0.0056, and since p= 0.0056 < 0.01, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean u is greater than 720, at the 0.01 significance level.