A Coach Uses a New Technique in Training Middle Distance

Essay

A coach uses a new technique in training middle distance runners.The times for 8 different athletes to run 800 metres before and after this training are shown below. $$\begin{array} { l | c c c c c c c c } \hline \text { Athlete } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } & \mathrm { F } & \mathrm { G } & \mathrm { H } \\\hline \begin{array} { l } \text { Time before trairing } \\\text { (seconds) }\end{array}& 109.2 & 110.6 & 109.3 & 108 & 114.3 & 118.1 & 111.9 & 110.1 \\\hline \begin{array} { l } \text { Time after training } \\\text { (seconds) }\end{array} & 109.8 & 109.3 & 106.9 & 108.8 & 112.5 & 118.2 & 108.3 & 106.2 \\\hline \text { Before - After } & - 0.6 & 1.3 & 2.4 & - 0.8 & 1.8 & - 0.1 & 3.6 & 3.9 \\\hline\end{array}$$ Do the data suggest that the training helps to improve the athletes' times for the 800 metres? Perform a Wilcoxon signed-rank test at the 5% significance level.