In a population of coffee drinkers, the average daily consumption is three cups of coffee per day. A manager wants to know if his colleagues tend to drink more than the national average of cups of coffee per day. He asked 50 colleagues to state how many cups of coffee they consumed each day and found an average of 3.8 cups per day with the standard deviation of 1.5 cups per day.

a. Does he have enough evidence that his colleagues drink more than the national average? Use alpha = 0.01 for the test.

b. Use the information provided in the question to determine the largest sample mean that would derive the conclusion that the manager’s colleagues do not drink more than the national average.