An Ardent Fan of Television Game Shows Has Observed That

question 156

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:

Punctual

The quality of being on time to appointments or obligations, reflecting a respect for other people's time as well as one's own.

Five-Factor Model

A theory identifying five primary dimensions of personality: openness, conscientiousness, extraversion, agreeableness, and neuroticism.

Conscientiousness

A personality trait characterized by thoroughness, carefulness, and the desire to do a task well.

Dependable

Capable of being relied on; trustworthy and consistent in performance or behavior.