Problem 11.6 16 professional marathon runners participated in a 3month training program which included one hour of swimming three times a week. The best personal time (BPT) in minutes for a 5 km run of these athletes was recorded, before and after the training program. The data is summarized in the following table: I BPT Before BPT After Difference (a?) (y) (d = a? - 31) Mean 30.8 29.1 1.7 Standard Deviation 5.2 4.1 1.6 Using this data, can we say that integrating swimming into the training practice of professional runners improves their BPT? Use a test of hypotheses of level a = 0.005. Assume that variables X, Y and D are normally distributed, and the variables X and Y have the same variances