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 $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-In a study of the effectiveness of physical exercise in weight reduction, 12 subjects followed a program of physical exercise for two months. Their weights (in pounds)before and after this program are shown in the following table. $$\begin{array} { l l l l l l l l l l l l l } \text { Before } & 162 & 190 & 188 & 152 & 148 & 127 & 195 & 164 & 175 & 156 & 180 & 136 \\ \hline \text { After } & 157 & 194 & 179 & 149 & 135 & 130 & 183 & 168 & 168 & 148 & 170 & 138 \end{array}$$ At the 5% significance level, do the data provide sufficient evidence to conclude that the exercise program is effective in reducing weight?

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Critical value Reject ...

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