3 A large college is holding a piano competition. Each student has played a particular piece of music and two judges have each awarded a mark out of 80 . The marks awarded to a random sample of 14 students are shown in the following table.

\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | c | c | c | c | c | }
\hline
Student & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ & $I$ & $J$ & $K$ & $L$ & $M$ & $N$ \\
\hline
Judge 1 & 79 & 54 & 63 & 74 & 69 & 52 & 50 & 57 & 55 & 42 & 63 & 55 & 56 & 48 \\
\hline
Judge 2 & 75 & 62 & 60 & 73 & 76 & 41 & 31 & 51 & 45 & 55 & 49 & 50 & 65 & 36 \\
\hline
\end{tabular}
\end{center}

(a) One of the students claims that on average Judge 1 is awarding higher marks than Judge 2. Carry out a Wilcoxon matched-pairs signed-rank test at the 5\% significance level to test whether the data supports the student's claim.\\

(b) Give a reason why it is preferable to use a Wilcoxon matched-pairs signed-rank test in this situation rather than a paired sample $t$-test.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2022 Q3}}