A Researcher Wants to Determine the Efficacy of a Training

Multiple Choice

A researcher wants to determine the efficacy of a training program directed at improving concentration, focus, and memory on college students.She selects a random sample of 16 individuals and has them take an initial assessment test before the training program.Then the individuals complete the training program, and at the end they take a final test that's comparable to the initial test.The results are shown in the following table: $$\begin{array} { | c | c | c | } \hline \text { Individ. } & \text { Before } & \text { After } \\\hline 1 & 79 & 81 \\\hline 2 & 74 & 73 \\\hline 3 & 81 & 82.5 \\\hline 4 & 75 & 82.5 \\\hline 5 & 72.5 & 85 \\\hline 6 & 75 & 90 \\\hline 7 & 67.5 & 83.5 \\\hline 8 & 57.5 & 72.5 \\\hline 9 & 62.5 & 87.5 \\\hline 10 & 77.5 & 80 \\\hline 11 & 61.5 & 92.5 \\\hline 12 & 57.5 & 80 \\\hline 13 & 61.5 & 71 \\\hline 14 & 72.5 & 84 \\\hline 15 & 64 & 78.5 \\\hline 16 & 71 & 97.5 \\\hline\end{array}$$ The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level.The observed z score is ______.

A) -3.4645
B) -3.2157
C) -3.0178
D) -2.9857
E) -2.7978