At a certain university, the average cost of books was $320 per student last semester and the population standard deviation was $85. This semester a sample of 55 students revealed an average cost of books of $355 per student. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis?
A) 0.41
B) 0.64
C) 3.05
D) 22.65

Question

Quizplus · Accepted Answer

To test the hypothesis, we need to calculate the test value, which is given by:
test value = (sample mean - population mean) / (population standard deviation /sqrt(sample size))
Substituting the values in the formula, we get:
test value = (355 - 320) / (85/sqrt(55)) = 3.05
Since this test value is greater than the critical value at the 5% level of significance (1.96 for a two-tailed test), we can reject the null hypothesis and conclude that there is evidence to suggest that the costs are indeed greater this semester. Hence, the best choice is C.

At a Certain University, the Average Cost of Books Was