Question

The average cost of tuition, room and board at small private liberal arts colleges 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 ? = 0.05
What is the test statistic for this test?

Answer 1

Answer:

The test statistic for this test is 3.82.

Step-by-step explanation:

The null hypothesis is:

$H_{0} = 8500$

The alternate hypotesis is:

$H_{1} > 8500$

Our test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation of the population and n is the size of the sample.

In this question:

$X = 8745, \mu = 8500, \sigma = 1200, n = 350$

So

$t = \frac{8745 - 8500}{\frac{1200}{\sqrt{350}}} = 3.82$

The test statistic for this test is 3.82.