3. A doctor is interested in the relationship between a person's Body Mass Index (BMI) and their level of fitness. She believes that a lower BMI leads to a greater level of fitness. She randomly selects 10 female 18 year-olds and calculates each individual's BMI. The females then run a race and the doctor records their finishing positions. The results are shown in the table.
| Individual | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) |
| BMI | 17.4 | 21.4 | 18.9 | 24.4 | 19.4 | 20.1 | 22.6 | 18.4 | 25.8 | 28.1 |
| Finishing position | 3 | 5 | 1 | 9 | 6 | 4 | 10 | 2 | 7 | 8 |
- Calculate Spearman's rank correlation coefficient for these data.
- Stating your hypotheses clearly and using a one tailed test with a \(5 \%\) level of significance, interpret your rank correlation coefficient.
- Give a reason to support the use of the rank correlation coefficient rather than the product moment correlation coefficient with these data.