5 Five runners, \(A , B , C , D\) and \(E\), take part in two different races.
Spearman’s rank correlation coefficient for the orders in which the runners finish is calculated and a test for positive agreement is carried out at the \(5 \%\) significance level.
- State suitable hypotheses for the test.
- Find the largest possible value of \(\sum d ^ { 2 }\) for which the result of the test is to reject the null hypothesis.
- In the first race, the order in which the five runners finished was: \(A , B , C , D , E\). In the second race, three of the runners finished in the same positions as in the first race. The result of the test is to reject the null hypothesis.
Find a possible order for the runners to finish in the second race.