Question

At a university, the average cost of books per student has been $400 per student per semester. The Dean of Students believes that the costs are increasing and that the average is now greater than $400. He surveys a sample of 40 students and finds that for the most recent semester their average cost was $430 with a standard deviation of $80. What is the test value for this hypothesis test?

Answer 1

To find the test value we need to test the hypothesis

$$H _ {0}: \mu = 400$$ $$H _ {1}: \mu > 400$$

Test statistics is calculated using the formula:

$$t = \frac {\bar {x} - \mu_ {0}}{s / \sqrt {n}}$$

In this particular case we have such values:

$$\bar {x} = 430$$ $$\mu_ {0} = 400$$ $$n = 40$$ $$s = 80$$

Thus

$$t = \frac {\bar {x} - \mu_ {0}}{s / \sqrt {n}} = \frac {430 - 400}{80 / \sqrt {40}} = 2.372$$