The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the test statistic for this test?
A)±3.82
B)+0.204
C)-3.82
D)+3.82

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: $z = \frac{8745 - 8500}{1200/\sqrt{350}} \approx 3.82$. Since the administrator believes the average cost is higher, we are looking at a one-tailed test, and the positive value of the test statistic is used, making the correct answer +3.82.

The Average Cost of Tuition and Room and Board at a Small