Suppose the mean salary for full professors in the United States is believed to be $71,650. A sample of 15 full professors revealed a mean salary of $74,250 with a standard deviation of $5,000. Can it be concluded that the average salary has increased using a 1% level of significance?

Step 1: State the null and alternative hypothesis

Step 2: Calculate the test statistic

Step 3: Find the p-value.

Step 4: State your conclusion. (Do not just say "Reject H0" or "Do not reject H0", state the conclusion in the context of the problem.)