An Ardent Fan of Television Game Shows Has Observed That

question 43

Essay

An ardent fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief, she gathers data about the last eight winners of her favourite game show. She records their winnings in dollars and their years of education. The results are as follows. $$\begin{array} { | c | c | c | } \hline \text { Contestant } & \begin{array} { c } \text { Years of } \\\text { education }\end{array} & \text { Winnings } \\\hline 1 & 11 & 750 \\\hline 2 & 15 & 400 \\\hline 3 & 12 & 600 \\\hline 4 & 16 & 350 \\\hline 5 & 11 & 800 \\\hline 6 & 16 & 300 \\\hline 7 & 13 & 650 \\\hline 8 & 14 & 400 \\\hline\end{array}$$ Calculate the Pearson correlation coefficient. What sign does it have? Why?

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Definitions:

American Children

Pertains to children living in or originating from the United States, focusing on their lifestyle, culture, or development.

Project Head Start

A scheme in the US offering extensive early childhood education, health care, nutritional support, and engagement opportunities for parents of families with low income.

Harold Stevenson

A psychologist known for his cross-cultural research in academic achievement and intelligence, particularly comparing the educational performances of children in the United States, China, and Japan.

Math Performance

The ability and efficiency in solving mathematical problems, reflecting one's proficiency in mathematics.