Suppose the mean salary for full professors in the United States is believed to be $61,650. A sample of 36 full professors revealed a mean salary of $69,800. Assuming the standard deviation is $5,000,
a.) Can it be concluded that the average salary has changed or is it still the same (using a 0.05 level of significance)? (Please state the null hypothesis: H0: μ = $61,650 and provide two approaches, both the "T-test" and "P-value" approach.)
b. Create the 95% Confidence Interval for the population mean using the information above.