5. A marathon runner believes that she is more likely to win a medal at her national championships the higher the temperature is on the day of the race.
She records the temperature at the start of each of eight races against fields of a similar standard and her finishing position in each race. Her results are shown in the table below.
| Temperature \(\left( { } ^ { \circ } \mathrm { C } \right)\) | 16 | 9 | 11 | 5 | 7 | 21 | 12 | 15 |
| Finishing position | 2 | 15 | 5 | 19 | 10 | 4 | 6 | 11 |
- Calculate Spearman's rank correlation coefficient for these data.
- Using a 5\% level of significance and stating your hypotheses clearly, interpret your result.
Another runner suggests that she should use her time in each race instead of her finishing position and calculate the product moment correlation coefficient for the data.
- Comment on this suggestion.