Perform the Indicated Wilcoxon Test $$\alpha = 0.05 .$$

question 31

Essay

Perform the indicated Wilcoxon 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 their 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 Wilcoxon signed-rank test to test the claim that the vitamin E supplement is effective in increasing athletesʹ
strength. Use $$\alpha = 0.05 .$$ $$\begin{array} { l c c c c c c c c c } \hline \text { Athlete } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline \text { Before } & 185 & 241 & 251 & 187 & 216 & 210 & 204 & 219 & 183 \\\text { After } & 195 & 246 & 251 & 185 & 223 & 225 & 209 & 214 & 188 \\\hline\end{array}$$

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Definitions:

Probability

A measure of the likelihood of occurrence of an event, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Z Statistic

A statistic that tells us how many standard deviations an element is from the mean. It is used in hypothesis testing.

Probability

A measure quantifying the likelihood that events will occur, ranging from 0 (impossibility) to 1 (certainty).

α

Typically used to denote the level of significance in hypothesis testing, representing the probability of rejecting a true null hypothesis or the threshold of rareness.