- The table below shows the number of televised tournaments won and the total number of tournaments won by the top 10 ranked darts players in 2020
| Player's rank | Televised tournaments won | Total tournaments won |
| 1 | 55 | 135 |
| 2 | 7 | 33 |
| 3 | 5 | 17 |
| 4 | 2 | 14 |
| 5 | 4 | 9 |
| 6 | 2 | 5 |
| 7 | 9 | 36 |
| 8 | 0 | 15 |
| 9 | 3 | 3 |
| 10 | 0 | 13 |
Michael did not want to calculate Spearman’s rank correlation coefficient between player's rank and the rank in televised tournaments won because there would be tied ranks.
- Explain how Michael could have dealt with these tied ranks.
Given that the largest number of total tournaments won is ranked number 1
- calculate the value of Spearman's rank correlation coefficient between player's rank and the rank in total tournaments won.
- Stating your hypotheses and critical value clearly, test at the \(5 \%\) level of significance, whether or not there is evidence of a positive correlation between player's rank and the rank in total tournaments won for these darts players.
Michael does not believe that there is a positive correlation between player's rank and the rank in total number of tournaments won.
- Find the largest level of significance, that is given in the tables provided, which could be used to support Michael's claim.
You must state your critical value.