Reconstruct missing ranks

Question provides partial ranking information and the value of Spearman's coefficient, requiring reconstruction of the complete missing ranks.

2 questions · Challenging +1.5

5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank
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Edexcel FS2 2019 June Q8
11 marks Challenging +1.8
8 Nine athletes, \(A , B , C , D , E , F , G , H\) and \(I\), competed in both the 100 m sprint and the long jump. After the two events the positions of each athlete were recorded and Spearman's rank correlation coefficient was calculated and found to be 0.85
  1. Stating your hypotheses clearly, test whether or not there is evidence to suggest that the higher an athlete's position is in the 100 m sprint, the higher their position is in the long jump. Use a \(5 \%\) level of significance. The piece of paper the positions were recorded on was mislaid. Although some of the athletes agreed their positions, there was some disagreement between athletes \(B , C\) and \(D\) over their long jump results. The table shows the results that are agreed to be correct.
    Athlete\(A\)\(B\)\(C\)\(D\)\(E\)\(F\)\(G\)\(H\)\(I\)
    Position in 100 m sprint467928315
    Position in long jump549312
    Given that there were no tied ranks,
  2. find the correct positions of athletes \(B , C\) and \(D\) in the long jump. You must show your working clearly and give reasons for your answers.
  3. Without recalculating the coefficient, explain how Spearman's rank correlation coefficient would change if athlete \(H\) was disqualified from both the 100 m sprint and the long jump.
SPS SPS FM Statistics 2021 January Q7
7 marks Challenging +1.2
Nine athletes, \(A\), \(B\), \(C\), \(D\), \(E\), \(F\), \(G\), \(H\) and \(I\), competed in both the 100m sprint and the long jump. After the two events the positions of each athlete were recorded and Spearman's rank correlation coefficient was calculated and found to be 0.85 The piece of paper the positions were recorded on was mislaid. Although some of the athletes agreed their positions, there was some disagreement between athletes \(B\), \(C\) and \(D\) over their long jump results. The table shows the results that are agreed to be correct.
Athlete\(A\)\(B\)\(C\)\(D\)\(E\)\(F\)\(G\)\(H\)\(I\)
Position in 100m sprint467928315
Position in long jump549312
Given that there were no tied ranks,
  1. find the correct positions of athletes \(B\), \(C\) and \(D\) in the long jump. You must show your working clearly and give reasons for your answers. [5]
  2. Without recalculating the coefficient, explain how Spearman's rank correlation coefficient would change if athlete \(H\) was disqualified from both the 100m sprint and the long jump. [2]