QuestionGood 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 50 people had a mean FICO score of 707 with a standard deviation of 79 . Can the economist conclude that the mean FICO score is less than 720? Use the level of significance and the -value method with the TI-84 Plus calculator.
Part:
Part 1 of 5
(a) State the appropriate null and alternate hypotheses.
This hypothesis test is a (Choose one) test.
Studdy Solution
STEP 1
1. The sample size is 50, which is sufficiently large for the Central Limit Theorem to apply.
2. The sample mean FICO score is 707, with a standard deviation of 79.
3. The level of significance is 0.10.
4. We are using the P-value method to determine statistical significance.
STEP 2
1. State the null and alternate hypotheses.
2. Identify the type of hypothesis test.
3. Calculate the test statistic.
4. Determine the P-value using the TI-84 Plus calculator.
5. Make a conclusion based on the P-value and .
STEP 3
State the null and alternate hypotheses.
The null hypothesis () is that the mean FICO score is equal to 720. The alternate hypothesis () is that the mean FICO score is less than 720.
STEP 4
Identify the type of hypothesis test.
This is a one-tailed test because we are testing if the mean is less than a specific value.
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