Question

At a certain university, the average cost of books per student was $400 per student last semester. In a sample of 40 students this semesterm their average cost was $430 with a standard deviation of $80. The dean of students believes that the costs are greater this semester. What is the p value for a one sided test of the data provided? At alpha 0.05, the null hypothesis would be rejected (true or false), At alpha 0.01, the Null hypothesis would be rejected (rue or false)

Answer 1

First the test statistic here is computed as:

Now as this is a one tailed test, The p-value here is computed as:

Therefore 0.0089 is the required p-value here.

As the p-value here is less than 0.05, we see that the test is significant at that level of significance, and the null hypothesis would be rejected here.

Also it is less than 0.01, therefore we can conclude here that the test is significant at the 1% level of significance as well and we can reject the null hypothesis at that level also.