An Ardent Fan of Television Game Shows Has Observed That

question 161

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. $$\begin{array} { | c | c | c | } \hline \text { Contestant } & \begin{array} { c } \text { Years of } \\\text { education }\end{array} & \text { Winnings } \\\hline 1 & 11 & 750 \\\hline 2 & 15 & 400 \\\hline 3 & 12 & 600 \\\hline 4 & 16 & 350 \\\hline 5 & 11 & 800 \\\hline 6 & 16 & 300 \\\hline 7 & 13 & 650 \\\hline 8 & 14 & 400 \\\hline\end{array}$$ Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a linear relationship exists between TV game show contestants' years of education and their winnings.

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Definitions:

Common Mistakes

Frequently occurring errors or oversights that people tend to make in various contexts.

Persuasive Message

A communication designed to convince or influence the audience to adopt a particular viewpoint or take a specific action.

Persuasion

The act or process of influencing someone's beliefs, attitudes, or actions through argument, reasoning, or appeal.

Best Interest

A principle that emphasizes acting in the most beneficial manner for the well-being or advantage of a person or entity.