HYPOTHESIS TESTING;T-Test for a Mean

Step 1: State the hypothesis and identify the claim.
I claim that the average cost of college tuition is less than $5836 per year as
concluded from “The College Board”. At a=.025, can it be concluded that the
average is less than $5836 based on a sample of 15 colleges?
H0: mu>/= $5836
H1: mu<$5836 (claim)
Step 2: Find the critical value
At a=.025 and d.f. = 14, the critical value is -2.145.
Step 3: Compute the sample test value.
m= 5069.73, s=787.80
t= (5069.73-5836)/(787.80/sqrt(15)) = -3.767
Step 4: Make the decision to reject or not reject the null hypothesis.
Reject the null hypotheses since -3.767 falls in the critical region.
Step 5: Summarize the results.