5. To qualify as a music examiner, a trainee must listen to a series of performances by 8 randomly chosen students. An experienced examiner and the trainee both award scores for each of the 8 performances. In order for the trainee to qualify, there must not be a significant difference between the average scores given by the experienced examiner and the trainee.
- Explain why the Wilcoxon signed rank test is appropriate.
The scores awarded are shown below.
| Student | A | B | C | D | E | F | G | H |
| Experienced Examiner | 108 | 109 | 92 | 95 | 145 | 148 | 134 | 120 |
| Trainee | 114 | 116 | 95 | 93 | 137 | 144 | 133 | 110 |
- Carry out an appropriate Wilcoxon signed rank test on this dataset, using a \(5 \%\) significance level.
- What conclusion should be reached about the suitability of the trainee to qualify?