A Weight-Lifting Coach Claims That a Weight-Lifter Can Increase Strength $\mathrm { E }$

Essay

A weight-lifting coach claims that a weight-lifter can increase strength by taking vitamin E. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed below. Thirty days later, after regular training supplemented by vitamin E, they are tested again. The new results are listed below. Use the Wilcoxon signed rank test to find the critical value to test the claim that the vitamin $\mathrm { E }$ supplement is effective in increasing the athletes' strength. Use $\alpha = .05$ .
$\begin{array}{lccccccccc}\hline \text { Athlete } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline \text { before } & 204 & 274 & 264 & 206 & 270 & 219 & 226 & 196 & 267 \\\text { After } & 214 & 279 & 264 & 204 & 277 & 234 & 231 & 191 & 272\end{array}$