The average life span of American male professors is 75.6 years, but standard deviation is unknown. A random sample of n = 5 recently (last 10 years) deceased male college professors at John Jay College is obtained from the Human Resources Office's personnel files and the age of death is provided below.
i 1 2 3 4 5
Age of Death 72 85 77 84 69
Could you conclude that John Jay Professors live longer than average? Use the appropriate two-tailed test with an a = 0.05. Also, construct a 95% confidence interval. Do the statistical test and the confidence interval agree? Write up your results.