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. What is the test statistic for this test?
A) $\pm$3.82
B) 0.204
C) -3.82
D) +3.82

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 with a standard deviation of $1,200. Let = 0.05. What is the test statistic for this test?
A)  $\pm$3.82
B) 0.204
C) -3.82
D) +3.82

Quizplus · Accepted Answer

To find the test statistic, we need to use the formula:

t = (x̄ - μ) / (s / √n)

where x̄ is the sample mean (8,745), μ is the hypothesized population mean (8,500), s is the sample standard deviation (1,200), and n is the sample size (350).

Plugging in the values, we get:

t = (8,745 - 8,500) / (1,200 / √350) ≈ 3.82

Since we are testing if the average cost is higher than $8,500 (i.e. a one-tailed test), we need to look at the positive end of the t-distribution. Checking a t-table with 349 degrees of freedom (df = n-1), we find that the critical value for α = 0.05 is 1.647. Since our calculated t-value (3.82) is greater than the critical value, we reject the null hypothesis and conclude that the average cost is indeed higher than $8,500.

The correct answer is D, +3.82.

The Average Cost of Tuition, Room and Board at Small ±\pm±

The Average Cost of Tuition, Room and Board at Small $\pm$