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

question 21

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

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Definitions:

Bretton Woods Meeting

An international conference held in 1944 in Bretton Woods, New Hampshire, where the foundations for the modern international monetary system and major global financial institutions were established.

Economic System

A framework that defines how a society allocates, produces, and distributes resources and goods.

Native Americans

Indigenous peoples of the United States, including their history, culture, and present-day issues, often referring to the many diverse tribes, nations, and ethnic groups who originally inhabited the land now known as the United States.

Mainstream

Dominant trends, norms, or values that are widely accepted and practiced within a society or culture.