Financial Risk Manager Part 1

Explanation

To calculate the test statistic for this hypothesis test, we use the formula for a one-sample t-test:

[\text{Test statistic} = \frac{(\text{Sample mean} - \text{Hypothesized value})}{\text{Standard error of the sample mean}}]

Step 1: Calculate the standard error [\text{Standard error} = \frac{\text{Standard deviation}}{\sqrt{\text{Sample size}}} = \frac{$4,500}{\sqrt{115}} = \frac{4,500}{10.7238} = 419.6272]

Step 2: Calculate the test statistic [\text{Test statistic} = \frac{(65,000 - 57,000)}{419.6272} = \frac{8,000}{419.6272} = 19.06]

This is a large test statistic, indicating strong evidence against the null hypothesis that the average starting salary is $57,000 or less. The test statistic follows a t-distribution with 114 degrees of freedom (n-1 = 115-1 = 114).