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

question 32

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 $\alpha = 0.05$
$\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Weight } & 0.3 & 0.4 & 0.5 & 0.5 & 1.0 & 0.7 \\\hline \text { Price } & 510 & 1151 & 1343 & 1410 & 5669 & 2277 \\\hline\end{array}$

---

Definitions:

Purely Competitive Firm

A business that operates in a market with many buyers and sellers, where each has a negligible impact on price and product homogeneity prevails.

Unimpeded Entry

A situation in a market where there are no obstacles preventing new competitors from entering and competing.

MR = MC Rule

A principle in economics stating that profit maximization occurs when marginal revenue equals marginal cost.

Short Run

A period in economics where at least one input is fixed and cannot be changed.