The average cost of tuition plus 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 first set up the hypotheses:
Null hypothesis: The average cost per term is equal to $8,500
Alternative hypothesis: The average cost per term is greater than $8,500

We can use a one-sample t-test since we have the sample mean, population standard deviation, and sample size.

The test statistic is calculated as:

t = (sample mean - hypothesized mean) / (population standard deviation / sqrt(sample size))
t = (8745 - 8500) / (1200 / sqrt(350))
t = 4.02

Using a t-table or software, 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 evidence to support that the average cost per term at small liberal arts colleges is greater than $8,500. Therefore, the best choice is B.

The Average Cost of Tuition Plus Room and Board at Small