Question

In 2017, the average credit score for loans that were purchased by a government-sponsored mortgage loan company was 744. A random sample of 35 mortgages recently purchased by the company was selected, and it was found that the average credit score was 753 with a sample standard deviation of 19. Complete the following:

a. Using α = 0.05, is there enough evidence from this sample to conclude that the average credit score for mortgages purchased by the company has increased since 2017? Determine the null and alternative hypotheses.
Null Hypothesis (H0): μ = 744
Alternative Hypothesis (H1): μ > 744

b. Determine the appropriate critical value. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.)
OA. -tα
B. tα = 1.691
OC. tα/2 =

c. Calculate the appropriate test statistic.
Test Statistic (t) = 2.80 (Round to two decimal places as needed)

Answer 1

The hypothesis test for the average credit score involves setting up the correct null and alternative hypotheses, determining the critical value using a t-distribution for a right-tailed test with an alpha of 0.05, and comparing the calculated test statistic of t = 2.80 to this critical value.

Step-by-step explanation:

To address the question, we must perform a hypothesis test for the mean credit score for mortgages purchased by the company.

Step 1: Null and Alternative Hypotheses

Null Hypothesis (H0): μ = 744
Alternative Hypothesis (H1): μ > 744

Step 2: Critical Value

With an alpha level of α = 0.05 and a right-tailed test, the critical value using a t-distribution with 34 degrees of freedom (n-1 for sample size of 35) can be found on a t-distribution table or using statistical software. It would not be -tα (option A), as this would be for a left-tailed test.

Step 3: Test Statistic

The calculated test statistic is t = 2.80.

We compare the calculated test statistic against the critical t-value. If t > tα, we reject the null hypothesis, indicating that there is enough evidence to support the alternative hypothesis that the average credit score has increased.