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:

Routine, Positive Messages

Messages that are regularly communicated and convey affirmative or positive information.

Letters of Recommendation

Written endorsements that articulate an individual's qualifications, character, and abilities, typically for academic or job purposes.

Simple Requests

Basic petitions or appeals made with the expectation of an uncomplicated response or action.

Professional Tone

The formal or business-like manner of communication that reflects respect and appropriate conduct in professional settings.