8 Nine athletes, \(A , B , C , D , E , F , G , H\) and \(I\), competed in both the 100 m sprint and the long jump. After the two events the positions of each athlete were recorded and Spearman's rank correlation coefficient was calculated and found to be 0.85
- Stating your hypotheses clearly, test whether or not there is evidence to suggest that the higher an athlete's position is in the 100 m sprint, the higher their position is in the long jump. Use a \(5 \%\) level of significance.
The piece of paper the positions were recorded on was mislaid. Although some of the athletes agreed their positions, there was some disagreement between athletes \(B , C\) and \(D\) over their long jump results.
The table shows the results that are agreed to be correct.
| Athlete | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) |
| Position in 100 m sprint | 4 | 6 | 7 | 9 | 2 | 8 | 3 | 1 | 5 |
| Position in long jump | 5 | | | | 4 | 9 | 3 | 1 | 2 |
- find the correct positions of athletes \(B , C\) and \(D\) in the long jump. You must show your working clearly and give reasons for your answers.
- Without recalculating the coefficient, explain how Spearman's rank correlation coefficient would change if athlete \(H\) was disqualified from both the 100 m sprint and the long jump.