The Table Below Lists Weights (Carats) and Prices (Dollars) for Randomly

Essay

The table below lists weights (carats) and prices (dollars) for randomly selected diamonds. Is there sufficient evidence to suggest that there is a linear correlation between weights and prices? Construct a scatterplot, and find the value of the linear correlation coefficient $r$ . Also find the $P$ -value or the critical values of $r$ using $\alpha = 0.05$ .
$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Weight } & 0.3 & 0.4 & 0.5 & 0.5 & 1.0 & 0.7 \\\hline \text { Price } & 510 & 1151 & 1343 & 1410 & 5669 & 2277 \\\hline\end{array}$