- A random sample of 9 footballers is chosen to participate in an obstacle course. The time taken, \(y\) seconds, for each footballer to complete the obstacle course is recorded, together with the footballer's Body Mass Index, \(x\). The results are shown in the table below.
| Footballer | Body Mass Index, \(\boldsymbol { x }\) | Time taken to complete the obstacle course, \(y\) seconds |
| A | 18.7 | 690 |
| B | 19.5 | 801 |
| C | 20.2 | 723 |
| D | 20.4 | 633 |
| E | 20.8 | 660 |
| F | 21.9 | 655 |
| G | 23.2 | 711 |
| H | 24.3 | 642 |
| I | 24.8 | 607 |
Russell claims, that for footballers, as Body Mass Index increases the time taken to complete the obstacle course tends to decrease.
- Find, to 3 decimal places, Spearman's rank correlation coefficient between \(x\) and \(y\).
- Use your value of Spearman's rank correlation coefficient to test Russell's claim. Use a 5\% significance level and state your hypotheses clearly.
The product moment correlation coefficient for these data is - 0.5594
- Use the value of the product moment correlation coefficient to test for evidence of a negative correlation between Body Mass Index and the time taken to complete the obstacle course. Use a 5\% significance level.
- Using your conclusions to part (b) and part (c), describe the relationship between Body Mass Index and the time taken to complete the obstacle course.