2 The table below shows the heart rates, \(x\) beats per minute, and the systolic blood pressures, \(y\) milligrams of mercury, of a random sample of 10 patients undergoing kidney dialysis.
| Patient | \(\mathbf { 1 }\) | \(\mathbf { 2 }\) | \(\mathbf { 3 }\) | \(\mathbf { 4 }\) | \(\mathbf { 5 }\) | \(\mathbf { 6 }\) | \(\mathbf { 7 }\) | \(\mathbf { 8 }\) | \(\mathbf { 9 }\) | \(\mathbf { 1 0 }\) |
| \(\boldsymbol { x }\) | 83 | 86 | 88 | 92 | 94 | 98 | 101 | 111 | 115 | 121 |
| \(\boldsymbol { y }\) | 157 | 172 | 161 | 154 | 171 | 169 | 179 | 180 | 192 | 182 |
- Calculate the value of the product moment correlation coefficient for these data.
- Assuming that these data come from a bivariate normal distribution, investigate, at the \(1 \%\) level of significance, the claim that, for patients undergoing kidney dialysis, there is a positive correlation between heart rate and systolic blood pressure.