5 Each contestant in a talent competition is given a score out of 20 by a judge. The organisers suspect that the judge's scores are associated with the age of the contestant. Table 5.1 and the scatter diagram in Fig. 5.2 show the scores and ages of a random sample of 7 contestants.
\begin{table}[h]
| Contestant | A | B | C | D | E | F | G |
| Age | 66 | 51 | 39 | 29 | 9 | 22 | 14 |
| Score | 12 | 11 | 15 | 17 | 16 | 18 | 9 |
\captionsetup{labelformat=empty}
\caption{Table 5.1}
\end{table}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b4109d98-1009-4929-a0d2-2ba12234894b-4_638_1079_772_502}
\captionsetup{labelformat=empty}
\caption{Fig. 5.2}
\end{figure}
Contestant G did not finish her performance, so it is decided to remove her data.
- Spearman's rank correlation coefficient between age and score, including all 7 contestants, is - 0.25 . Explain why Spearman's rank correlation coefficient becomes more negative when the data for contestant G is removed.
- Calculate Spearman's rank correlation coefficient for the 6 remaining contestants.
- Using this value of Spearman's rank correlation coefficient, carry out a hypothesis test at the \(5 \%\) level to investigate whether there is any association between age and score.
- Briefly explain why it may be inappropriate to carry out a hypothesis test based on Pearson's product moment correlation coefficient using these data.