Use the Wilcoxon Signed -Ranks Test to Test the Claim

Essay

Use the Wilcoxon signed -ranks test to test the claim that the matched pairs have differences that come from a
population with a median equal to zero. Eleven runners are timed at the 100-meter dash and are timed again
one month later after following a new training program. The times (in seconds) are shown in the table. Use
Wilcoxon's signed-ranks test and a significance level of 0.05 to test the claim that the training has no effect on the times. $$\begin{array} { | l l l l l l l l l l l l | } \hline \text { Before } & 12.1 & 12.4 & 11.7 & 11.5 & 11.0 & 11.8 & 12.3 & 10.8 & 12.6 & 12.7 & 10.7 \\\hline \text { After } & 11.9 & 12.4 & 11.8 & 11.4 & 11.2 & 11.5 & 12.0 & 10.9 & 12.0 & 12.2 & 11.1 \\\hline\end{array}$$