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. At the 0.05 level of significance, test the claim that the lesson has no effect on the grade. Use Wilcoxon's signed-ranks test. $$\begin{array} { l l l l l l l l l l l l l l l l } \text { Before } & 54 & 61 & 56 & 41 & 38 & 57 & 42 & 71 & 88 & 42 & 36 & 23 & 22 & 46 & 51 \\\hline \text { After } & 82 & 87 & 84 & 76 & 79 & 87 & 42 & 97 & 99 & 74 & 85 & 96 & 67 & 84 & 79\end{array}$$