Perform the Indicated Sign Test $$\alpha = 0.05$$

Perform the indicated sign test. Be sure to do the following: Identify the claim mathematically and state the null and
alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject
the null hypothesis and interpret the decision in the context of the original claim.
-A weight-lifting coach claims that weight-lifters 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. Thirty days later, after
regular training supplemented by vitamin E, they are tested again. The results are listed below. Use the sign
test to test the claim that the vitamin E supplement is effective in increasing the athletesʹ strength. Use $$\alpha = 0.05$$ $$\begin{array} { l c c c c c c c c c } \hline \text { Athlete } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline \text { Before } & 217 & 264 & 273 & 202 & 180 & 237 & 242 & 268 & 274 \\\text { After } & 227 & 269 & 273 & 200 & 187 & 252 & 247 & 263 & 279 \\\hline\end{array}$$