The average cost of tuition plus room and board for a small private liberal arts college 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 can use a one-sample t-test to test if the average cost is significantly different from $8,500. The null hypothesis is:

H0: μ = $8,500

The alternative hypothesis is:

Ha: μ > $8,500

where μ is the population mean cost per term.

We can compute the test statistic as:

t = (x̄ - μ) / (s / sqrt(n))

where x̄ is the sample mean cost per term ($8,745), s is the population standard deviation ($1,200), and n is the sample size (350).

Plugging in the values, we get:

t = (8,745 - 8,500) / (1,200 / sqrt(350)) = 3.73

Using a t-distribution table (or calculator) with 349 degrees of freedom (df = n - 1), we can find the p-value for this test.

For a one-tailed test with α = 0.05, the critical t-value is tα,df = 1.645. Since our computed t-value (3.73) is greater than the critical t-value, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the average cost per term is greater than $8,500.

Therefore, the best choice is B.

The Average Cost of Tuition Plus Room and Board for a Small