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.
| Student | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) | \(K\) | \(L\) | \(M\) | \(N\) |
| Judge 1 | 79 | 54 | 63 | 74 | 69 | 52 | 50 | 57 | 55 | 42 | 63 | 55 | 56 | 48 |
| Judge 2 | 75 | 62 | 60 | 73 | 76 | 41 | 31 | 51 | 45 | 55 | 49 | 50 | 65 | 36 |
- 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.
- 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.