It has been suggested that people who reach top management positions (chief executive officers, chief financial officers, etc.) are, on average, taller than those people who stay at mid level positions or below. You take a simple random sample of 400 top level managers and 400 long time mid level managers, and find the average height for the top level sample to be 73.2 inches, with standard deviation of 1.8 inches. For the mid level managers, average height is 68.7 inches, with standard deviation of 2.7 inches. Construct and interpret the appropriate 99% confidence interval estimate of the difference in average heights for the two populations represented here.