7. For one of the activities at a gymnastics competition, 8 gymnasts were awarded marks out of 10 for each of artistic performance and technical ability. The results were as follows.
| Gymnast | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
| Technical ability | 8.5 | 8.6 | 9.5 | 7.5 | 6.8 | 9.1 | 9.4 | 9.2 |
| Artistic performance | 6.2 | 7.5 | 8.2 | 6.7 | 6.0 | 7.2 | 8.0 | 9.1 |
The value of the product moment correlation coefficient for these data is 0.774 .
- Stating your hypotheses clearly and using a \(1 \%\) level of significance, interpret this value.
- Calculate the value of the rank correlation coefficient for these data.
- Stating your hypotheses clearly and using a \(1 \%\) level of significance, interpret this coefficient.
- Explain why the rank correlation coefficient might be the better one to use with these data.
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