Please be as clear as possible and show work

[5 marks] A mid-distance running coach for the Olympic team claims that his 6-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 the coach's 6-month training program and their completion time of 1500-meter run was recorded (in minutes). After six months of training under the coach, the same five runners' 1500-meter run time was recorded. The results are given below. Assume that the difference in running times for given runner is normally distributed. Runner 1 2 3 4 5 Completion time before training 5.9 7.5 6.1 6.8 6.9 Completion time after training 5.4 7.1 6.2 6.5 6.6 At the 5% level of significance, can we conclude that the coach's 6-month training program significantly reduces the average time to complete a 1500-meter run