Good credit: 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 lower than the cutoff of 720 . She finds that a random sample of 100 people had a mean FICO score of 703 with a standard deviation of 92 . Can the economist conclude that the mean FICO score is less than 720 ? Use the $\alpha=0.01$ level of significance and the P-value method with the TI- 84 Plus calculator. Part: $0 / 4$ Part 1 of 4 State the appropriate null and alternate hypotheses. \[ \begin{array}{l} H_{0}: \mu>720 \\ H_{1}: \mu<720 \end{array} \] This hypothesis test is a $\square<\square \quad \square>\square \quad \square=\square$ $\square \neq \square \quad \mu$
Solution
Step 1 ：State the appropriate null and alternate hypotheses. The null hypothesis \(H_{0}: \mu \geq 720\) and the alternative hypothesis \(H_{1}: \mu < 720\).
Step 2 ：The question is asking to perform a hypothesis test to determine if the mean FICO score is less than 720. We are given a sample mean of 703, a standard deviation of 92, and a sample size of 100. We are also given a significance level of 0.01.
Step 3 ：Calculate the t-statistic and p-value. The calculated t-statistic is -1.85 and the p-value is 0.0338.
Step 4 ：Compare the p-value with the significance level. The p-value is greater than the significance level of 0.01, so we fail to reject the null hypothesis.
Step 5 ：Final Answer: The economist cannot conclude that the mean FICO score is less than 720. \(\boxed{Fail \ to \ reject \ H_{0}}\).
