Preliminary Data Analyses Indicates That Use of a Paired Wilcoxon $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$

Preliminary data analyses indicates that use of a paired Wilcoxon signed-rank test is reasonable. Perform the hypothesistest by using a paired Wilcoxon signed-rank test. Assume that the null hypothesis is $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-Eleven runners are timed in 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 following table. $$\begin{array} { l l l l l l l l l l l l } \text { Before } & 12.1 & 12.4 & 11.7 & 11.5 & 11.0 & 11.8 & 12.3 & 10.8 & 12.6 & 12.7 & 10.7 \\ \hline \text { After } & 11.9 & 12.4 & 11.8 & 11.4 & 11.2 & 11.5 & 12.0 & 10.9 & 12.0 & 12.2 & 11.1 \end{array}$$ At the 10% significance level, do the data provide sufficient evidence to conclude that the training is effective in reducing times in the 100-meter dash?

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