- Bara is investigating whether or not the two judges of a skating competition are in agreement. The two judges gave a score to each of the 8 skaters in the competition as shown in the table below.
| \cline { 2 - 9 }
\multicolumn{1}{c|}{} | Skater |
| \cline { 2 - 9 } | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
| Judge 1 | 71 | 70 | 72 | 62 | 63 | 61 | 57 | 53 |
| Judge 2 | 73 | 71 | 67 | 64 | 62 | 56 | 52 | 53 |
Bara decided to calculate Spearman's rank correlation coefficient for these data.
- Calculate Spearman's rank correlation coefficient between the ranks of the two judges.
- Test, at the \(1 \%\) level of significance, whether or not the two judges are in agreement.
Judge 1 accidentally swapped the scores for skaters \(D\) and \(E\). The score for skater \(D\) should be 63 and the score for skater \(E\) should be 62
- Without carrying out any further calculations, explain how Spearman's rank correlation coefficient will change. Give a reason for your answer.