It is known that the average tuition per semester at colleges in Virginia is $3712. Suppose we take a sample of 15 colleges and find that the average tuition per semester is $4512 with a sample standard deviation of $595. We are interested in testing if the average amount of tuition is increasing.

Using the sample of 15 people, what would the 95% confidence interval be for the population mean?

What are the null and alternative hypotheses?

What is the critical value at 95% confidence?

Calculate the test statistic.

Find the p-value

What conclusion would be made here at the 95% confidence level?

Would my conclusion change if I changed alpha to .01?