4. Over a period of time, researchers took 10 blood samples from one patient with a blood disease. For each sample, they measured the levels of serum magnesium, \(s \mathrm { mg } / \mathrm { dl }\), in the blood and the corresponding level of the disease protein, \(d \mathrm { mg } / \mathrm { dl }\). The results are shown in the table.
| \(s\) | 1.2 | 1.9 | 3.2 | 3.9 | 2.5 | 4.5 | 5.7 | 4.0 | 1.1 | 5.9 |
| \(d\) | 3.8 | 7.0 | 11.0 | 12.0 | 9.0 | 12.0 | 13.5 | 12.2 | 2.0 | 13.9 |
$$\text { [Use } \sum s ^ { 2 } = 141.51 , \sum d ^ { 2 } = 1081.74 \text { and } \sum s d = 386.32 \text { ] }$$
- Draw a scatter diagram to represent these data.
- State what is measured by the product moment correlation coefficient.
- Calculate \(S _ { x x } , S _ { d d }\) and \(S _ { s d }\).
- Calculate the value of the product moment correlation coefficient \(r\) between \(s\) and \(d\).
- Stating your hypotheses clearly, test, at the \(1 \%\) significance level, whether or not the correlation coefficient is greater than zero.
- With reference to your scatter diagram, comment on your result in part (e).