Hypothesis test of Spearman’s rank correlation coefficien
A junior judge is being trained by a senior judge to learn how to assess ice skaters. After the training, the judges each assess 6 ice skaters \(A , B , C , D , E\) and \(F\). They each list them in order of preference with the best ice skater first. The results are shown in the table below.
Rank
1
2
3
4
5
6
Senior Judge
\(A\)
\(B\)
\(D\)
\(C\)
\(F\)
\(E\)
Junior Judge
\(B\)
\(D\)
\(A\)
\(F\)
\(C\)
\(E\)
Calculate Spearman's rank correlation coefficient for these data.
Test, at the \(5 \%\) level of significance, whether or not there is evidence of a positive correlation between the rankings of the junior judge and the senior judge. State your hypotheses clearly.
Comment on the effectiveness of the training delivered by the senior judge.