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 $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-Students take a math test before and after tutoring. The data for a random sample of students is given below. $$\begin{array} { c | l l l l l l l l l } \text { Before } & 54 & 72 & 59 & 82 & 46 & 80 & 63 & 36 & 44 \\ \hline \text { After } & 68 & 70 & 67 & 78 & 55 & 90 & 63 & 52 & 40 \end{array}$$ At the 2.5% level of significance, do the data provide sufficient evidence to conclude that the mean score before the tutoring is lower than the mean score after the tutoring?

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Critical value Do not reject . At th...

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