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 with a standard deviation of $1,200. Let = 0.05. Based on the computed test statistic or p-value, what is our decision about the average cost?
A) Equal to $8,500
B) Greater than $8,500
C) Less than $8,500
D) Not equal to $8,500

Question

Quizplus · Accepted Answer

We need to conduct a one-tailed hypothesis test with the null hypothesis H0: µ = $8,500 and the alternative hypothesis Ha: µ > $8,500.

We can use a t-test since we are given the sample size (n = 350) and standard deviation (s = $1,200) of the population.

The test statistic is calculated as:

t = (x̄ - µ) / (s / √n)
t = (8,745 - 8,500) / (1,200 / √350)
t = 3.01

Using a t-table with 349 degrees of freedom (n-1), the critical value for a one-tailed test at α = 0.05 is 1.646.

Since our calculated t-value (3.01) is greater than the critical value (1.646), we reject the null hypothesis and conclude that the average cost per term at small private liberal arts colleges is greater than $8,500. Therefore, the best choice is B.

The Average Cost of Tuition, Room and Board at Small