A coach employs a new method in training middle distance runners. The times for eight different athletes to run 800 meters before and after this training are shown below.
Athlete A B C D E F G H
Time before training (seconds) 116 115.9 118.6 109.7 111.5 113 119 116
Time after training (seconds) 116.6 114.6 116.2 110.5 109.7 113.1 115.4 112.1
Using a 0.05 level of significance, test the claim that training aids to enhance the athletes' times for the 800 meters. (Suppose that two dependent samples have been randomly chosen from normally distributed populations. You can employ either the p-value or the traditional techniques of hypothesis testing to test the given claim regarding the means of two populations.)