An Ardent Fan of Television Game Shows Has Observed That

question 67

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:

Final Choice

The ultimate decision made after considering all options and outcomes.

Routine Decisions

Decisions that are made frequently, following established policies or procedures with predictable outcomes.

Momentous Decisions

Decisions of great importance or significance, often having far-reaching consequences.

Technical Knowledge

The specific expertise and skills required to perform tasks related to technology, engineering, or specialized areas of a field.