Discussion:
Q: The mid-distance running coach, Zdravko Popovich, for the Olympic team of an eastern European country claims that his six-month training program significantly reduces the average time to complete a 1500-meter run. Five mid-distance runners were randomly selected before they were trained with coach Popovich's six-month training program and their completion time of 1500-meter run was recorded (in minutes). After six months of training under coach Popovich, the same five runners' 1500 meter run time was recorded again the results are given below.
Runner Completion time Before Training Completion time After Training
1 5.9 5.4
2 7.5 7.1
3 6.1 6.2
4 6.8 6.5
5 8.1 7.8
At an alpha level of .01, can we conclude that there has been a significant decrease in the mean time per mile?