3. Each of 7 athletes competed in a 200 metre race and a 400 metre race.
The table shows the time, in seconds, taken by each athlete to complete the 200 metre race.
| Athlete | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) |
| 200 metre race (seconds) | 23.4 | 23.1 | 22.9 | 23.7 | 27.6 | 24.4 | 24.1 |
The finishing order in the 400 metre race is shown below, with athlete \(A\) finishing in the fastest time.
\(\begin{array} { l l l l l l l } A & B & G & C & D & F & E \end{array}\)
- Calculate the Spearman's rank correlation coefficient between the finishing order in the 200 metre race and the finishing order in the 400 metre race.
- Stating your hypotheses clearly, test whether or not there is evidence of a positive correlation between the finishing order in the 200 metre race and the finishing order in the 400 metre race. Use a \(5 \%\) level of significance.
The 7 athletes also competed in a long jump competition with the following results.
| Athlete | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) |
| Long jump (metres) | 6.50 | 6.47 | 6.12 | 6.12 | 6.48 | 6.38 | 6.47 |
Yuliya wants to calculate the Spearman's rank correlation coefficient between the finishing order in the 200 metre race and the finishing order in the long jump for these athletes. - Without carrying out any further calculations, explain how Yuliya should do this.