Question: Suppose I independently choose six forwards and ten guards of NBA basketball players, obtaining an average weight for the six forwards of 220 pounds, with a standard deviation (for those six) of 30 pounds, an average weight for the ten guards of 170 pounds, with a standard deviation (for those ten) of 25 pounds.

Find a 99% confidence interval for the difference between the average weight of all forwards and the average weight, of all guards of NBA basketball players. Assume normality of weights, with approximately equal population standard deviations.