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Exam-Style Question on CorrelationA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 466. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.
The Farang Parkour Team hosted a Free Running event. The judges, Anan and Jason awarded 7 competitors a score out of 10. The scores are shown in the following table.
| Free Runners | A | B | C | D | E | F | G |
| Anan's Score (x) | 7.8 | 9.1 | 8.3 | 6.9 | 7.0 | 8.5 | 9.3 |
| Jason's Score (y) | 7.2 | 9.0 | 8.7 | 7.5 | 6.9 | 8.7 | 8.9 |
(a) Find the Pearson’s product–moment correlation coefficient, \(r\), of these scores.
(b) Using the value of \(r\), interpret the relationship between Anan’s scores and Jason’s score.
(c) Write down the equation of the regression line \(y\) on \(x\).
(d) Use your regression equation from part (c) to estimate Jason’s score to one decimal place when Anan awards a score of 5.
(e) State whether this estimate is reliable. Justify your answer.
(f) The adjudicator for the event would like to find the Spearman’s rank correlation coefficient of the scores. Copy and complete the information in the following table.
| Free Runners | A | B | C | D | E | F | G |
| Anan's Rank | 7 | 1 | |||||
| Jason's Rank | 1 | 7 |
(g) Find the value of the Spearman’s rank correlation coefficient, \(r_s\).
(h) Comment on the result obtained for \(r_s\).
The adjudicator believes Jason’s score for competitor E is too high and so decreases the score from 6.9 to 6.5.
(i) Explain why the value of the Spearman’s rank correlation coefficient \(r_s\) does not change.
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