8 A swimming coach is investigating whether there is correlation between the times taken by teenage swimmers to swim 50 m Butterfly and 50 m Freestyle. The coach selects a random sample of 11 teenage swimmers and records the times that each of them take for each event. The spreadsheet shows the data, together with a scatter diagram to illustrate the data.
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- In the scatter diagram, Butterfly times have been plotted on the horizontal axis and Freestyle times on the vertical axis. A student states that the variables should have been plotted the other way around.
Explain whether the student is correct.
The student decides to carry out a hypothesis test to investigate whether there is any correlation between the times taken for the two events.
- Explain why the student decides to carry out a test based on Spearman's rank correlation coefficient.
- In this question you must show detailed reasoning.
Carry out the test at the 5\% significance level.
- The student concludes that there is definitely no correlation between the times.
Comment on the student's conclusion.