The average cost of tuition and 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. The population standard deviation is $1,200. Let α = 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-sample t-test to test whether the sample mean of $8,745 is significantly different from the population mean of $8,500. The null and alternative hypotheses are:

H0: μ = $8,500
Ha: μ > $8,500

We use a one-tailed test because we want to know whether the average cost is higher than $8,500. The significance level is α=0.05.

To conduct the test, we calculate the t-statistic:

t = (x̄ - μ) / (s / √n) = (8,745 - 8,500) / (1,200 / √350) = 5.62

where x̄ is the sample mean, s is the population standard deviation, and n is the sample size.

The degrees of freedom are df = n - 1 = 349. Using a t-distribution table or a calculator, we find the p-value to be less than 0.0001.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. This means we have sufficient evidence to 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 and Room and Board at Small