An Ardent Fan of Television Game Shows Has Observed That

question 125

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 slope 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:

Disposable Income

This is the amount of money that households have available for spending and saving after income taxes have been accounted for.

Consumption

refers to the total amount of goods and services bought and used by households and individuals.

Savings Rate

The portion of disposable income not spent on consumption of goods and services but saved or invested, usually expressed as a percentage of disposable income.

Consumption

Consumption refers to the use of goods and services by households for personal satisfaction or living standards.