A survey of full professors (highest ranking) in History found that the average income is $74,914. Because that survey is now over 8 years old, an institutional researcher wants to test this figure by taking a random sample of 112 History professors with full professorship status. The researcher finds a sample mean of $81,342. The population standard deviation is known to be $15,121.
-The test statistic is _____.
A)4.50
B)47.61
C)9.00
D)-47.61
E)-4.50

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula: $z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$, 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: $z = \frac{81342 - 74914}{15121 / \sqrt{112}} \approx 4.50$.

A Survey of Full Professors (Highest Ranking) in History Found