An Instructor Gives a Test Before and After a Lesson

Essay

An instructor gives a test before and after a lesson and results from randomly selected students are given below.
Use Wilcoxon's signed-ranks test and a 0.05 significance level to test the claim that the lesson has no effect on
the grade. $$\begin{array} { l l l l l l l l l l l l l l l l } \text { Before } & 54 & 61 & 56 & 41 & 38 & 57 & 42 & 71 & 88 & 42 & 36 & 23 & 22 & 46 & 51 \\\hline \text { After } & 82 & 87 & 84 & 76 & 79 & 87 & 42 & 97 & 99 & 74 & 85 & 96 & 67 & 84 & 79\end{array}$$