Financial Risk Manager Part 1

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A survey is conducted to determine if the average starting salary of investment bankers is equal to or greater than $57,000 per year. Given a sample of 115 newly employed investment bankers with a mean starting salary of $65,000 and a standard deviation of $4,500, and assuming a normal distribution, what is the test statistic?

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Community

TTanishq

204.44

19.06

1.78

746

Explanation:

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).

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