The dean of a business school claims that the average starting salary of its graduates is more than $50,000. It is known that the population standard deviation is $10,000. Sample data on the starting salaries of 20 randomly selected recent graduates yielded a mean of $55,000. What is the value of the sample test statistic?
A) z = 2.24
B) t = 7.2
C) t = 5.04
D) t = 2.24

Question

Quizplus · Accepted Answer

The sample test statistic is calculated using the formula for a z-test because the population standard deviation is known. The formula is $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{55000 - 50000}{10000/\sqrt{20}} = 2.24$.

The Dean of a Business School Claims That the Average