An Ardent Fan of Television Game Shows Has Observed That

question 38

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. $$\begin{array} { | c | c | c | } \hline \text { Contestant } & \begin{array} { c } \text { Years of } \\\text { education }\end{array} & \text { Winnings } \\\hline 1 & 11 & 750 \\\hline 2 & 15 & 400 \\\hline 3 & 12 & 600 \\\hline 4 & 16 & 350 \\\hline 5 & 11 & 800 \\\hline 6 & 16 & 300 \\\hline 7 & 13 & 650 \\\hline 8 & 14 & 400 \\\hline\end{array}$$ Predict with 95% the winnings of all contestants who have 15 years of education.

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Definitions:

Standard Deviation

A measure of the amount of variation or dispersion of a set of values; a low standard deviation indicates that the values are close to the mean of the set.

Exam Grades

Scores or marks received by students on academic tests, indicating their performance level.

Probability

An assessment of the probability that a certain event will happen.

Function

A relationship or rule that defines how one variable's values are determined by another variable or other variables.