3 A large number of students took two test papers in mathematics. The teacher believes that the marks obtained in Paper 1 will be higher than the marks obtained in Paper 2. She chooses a random sample of 9 students and compares their marks. The marks are shown in the table.
| Student | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) |
| Paper 1 | 46 | 73 | 55 | 64 | 86 | 42 | 66 | 68 | 60 |
| Paper 2 | 41 | 66 | 61 | 63 | 90 | 40 | 58 | 42 | 70 |
- Carry out a Wilcoxon matched-pairs signed-rank test, at the \(5 \%\) significance level, to test whether the data supports the teacher’s belief.
- State an assumption that you have made in carrying out the test in part (a).