A researcher wishes to test the claim that the average cost of tuition and fees at a four-year public college is greater than $5700. She selects a random sample of 25 four year public colleges and finds the mean to be $5950. The population standard deviation is $659. Is there evidence to support the claim at 5% level of significance?

Step 1- Hypothesis

H0: μ = 5700 (null)

H1: μ > 5700 (alternative)

Step 2 – T or Z test

T test due to n=25 is less than 30 sample. With a 95% or 0.95 significance level and degrees of freedom of 24 as 25-1 (n-1). From the t-table we find the critical value is 2.064.

Step 3 – Calculated value

Step 4 – Reject or do not reject the null hypothesis

As calculated value is less than critical value we do not reject the null hypothesis.