3 Samples of water are taken from 10 randomly chosen wells in an area of a country. A researcher is investigating whether there is any relationship between the levels of dissolved oxygen, \(x\), and the amounts of radium, \(y\), in the water from the wells. Both quantities are measured in suitable units. The table and the scatter diagram in Fig. 3 show the values of \(x\) and \(y\) for the ten wells.
| \(x\) | 45.9 | 48.3 | 52.2 | 64.6 | 66.6 | 67.6 | 69.3 | 75.0 | 77.4 | 82.8 |
| \(y\) | 25.4 | 23.9 | 26.6 | 18.8 | 18.9 | 19.0 | 16.8 | 16.3 | 17.8 | 17.2 |
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e3ac0ba0-9692-4018-894e-2b04b07eaf32-3_865_786_657_635}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{figure}
- Explain why it may not be appropriate to carry out a hypothesis test based on the product moment correlation coefficient.
- Calculate Spearman's rank correlation coefficient for these data.
- Using this value of Spearman's rank correlation coefficient, carry out a hypothesis test at the 1\% significance level to investigate whether there is any association between \(x\) and \(y\).
- Explain the meaning of the term 'significance level' in the context of the test carried out in part (iii).