Critical region or probability

Question asks to find the critical region for a test, or calculate probabilities related to obtaining specific values of Spearman's coefficient.

3 questions · Standard +0.5

5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank
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OCR Further Statistics 2018 March Q8
11 marks Challenging +1.2
8 At a wine-tasting competition, two judges give marks out of 100 to 7 wines as follows.
Wine\(A\)\(B\)\(C\)\(D\)\(E\)\(F\)\(G\)
Judge I86.387.587.688.889.489.990.5
Judge II85.388.182.787.789.089.491.5
  1. A spectator claims that there is a high level of agreement between the rank orders of the marks given by the two judges. Test the spectator's claim at the \(1 \%\) significance level.
  2. A competitor ranks the wines in a random order. The value of Spearman's rank correlation coefficient between the competitor and Judge I is \(r _ { s }\).
    1. Find the probability that \(r _ { s } = 1\).
    2. Show that \(r _ { s }\) cannot take the value \(\frac { 55 } { 56 }\).
OCR FS1 AS 2018 March Q8
8 marks Challenging +1.2
8 In a competition, entrants have to give ranks from 1 to 7 to each of seven resorts. The correct ranks for the resorts are decided by an expert.
  1. One competitor chooses his ranks randomly. By considering all the possible rankings, find the probability that the value of Spearman's rank correlation coefficient \(r _ { s }\) between the competitor's ranks and the expert's ranks is at least \(\frac { 27 } { 28 }\).
  2. Another competitor ranks the seven resorts. A significance test is carried out to test whether there is evidence that this competitor is merely guessing the rank order of the seven resorts. The critical region is \(r _ { s } \geqslant \frac { 27 } { 28 }\). State the significance level of the test. \section*{END OF QUESTION PAPER}
OCR S1 2010 June Q2
7 marks Moderate -0.8
Three skaters, \(A\), \(B\) and \(C\), are placed in rank order by four judges. Judge \(P\) ranks skater \(A\) in 1st place, skater \(B\) in 2nd place and skater \(C\) in 3rd place.
  1. Without carrying out any calculation, state the value of Spearman's rank correlation coefficient for the following ranks. Give a reason for your answer. [1]
    Skater\(A\)\(B\)\(C\)
    Judge \(P\)123
    Judge \(Q\)321
  2. Calculate the value of Spearman's rank correlation coefficient for the following ranks. [3]
    Skater\(A\)\(B\)\(C\)
    Judge \(P\)123
    Judge \(R\)312
  3. Judge \(S\) ranks the skaters at random. Find the probability that the value of Spearman's rank correlation coefficient between the ranks of judge \(P\) and judge \(S\) is 1. [3]