In a particular city, the average annual salary for secretaries is $28,000. A sample of secretaries from Company A shows an average annual salary of $24,500 with a
Population standard deviation of $4500. Secretaries at Company A claim they are paid
Less than the city average. What is the test value for this claim?
A) 5.50
B) -5.50
C) -0.78
D) 0.78

Question

Quizplus · Accepted Answer

The test value (z-score) 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. Without the sample size, we assume it's for comparing means directly, thus simplifying to $z = \frac{24500 - 28000}{4500}$, which equals -5.50, indicating the sample mean is 5.50 standard deviations below the population mean.

In a Particular City, the Average Annual Salary for Secretaries