Use the Traditional Method of Hypothesis Testing to Test the Given

Essay

Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that
two dependent samples have been randomly selected from normally distributed populations.
-A coach uses a new technique in training middle distance runners. The times for 8 different athletes to run 800 meters before and after this training are shown below. $\begin{array} { c | c c c c c c c c } \text{Athlete} & A&B&C&D&E&F&G&H\\\hline\text{ Time before} &116&115.9&118.6&109.7&111.5&113&119&116 \\\text{training (seconds)}\\\hline\text{ Time AFTER} &116.6&114.6&116.2&110.5&109.7&113.1&115.4&112.1\\\text{training (seconds)}\\\end{array}$
Using a $0.05$ level of significance, test the claim that the training helps to improve the athletes' times for the $800 \mathrm { n }$