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.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | c | }
\hline
Patient & $\mathbf { 1 }$ & $\mathbf { 2 }$ & $\mathbf { 3 }$ & $\mathbf { 4 }$ & $\mathbf { 5 }$ & $\mathbf { 6 }$ & $\mathbf { 7 }$ & $\mathbf { 8 }$ & $\mathbf { 9 }$ & $\mathbf { 1 0 }$ \\
\hline
$\boldsymbol { x }$ & 83 & 86 & 88 & 92 & 94 & 98 & 101 & 111 & 115 & 121 \\
\hline
$\boldsymbol { y }$ & 157 & 172 & 161 & 154 & 171 & 169 & 179 & 180 & 192 & 182 \\
\hline
\end{tabular}
\end{center}

(a) Calculate the value of the product moment correlation coefficient for these data.\\
(b) 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.

\hfill \mbox{\textit{AQA S3  Q2}}