A Professor of Economics Wants to Study the Relationship Between

question 146

Essay

A professor of economics wants to study the relationship between income y (in $1000s) and education x (in years). A random sample of eight individuals is taken and the results are shown below. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } \hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \\\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \\\hline\end{array}$$ Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a linear relationship exists between years of education and income.

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Definitions:

Sampling Error

The discrepancy between the estimated population parameter and the actual population parameter due to the sample not being a perfect representation of the population.

Probability Distribution

A mathematical representation that outlines all possible outcomes and their probabilities for a random variable within a specified scope.

Sample

A subset of individuals, items, or events from a larger population used to draw conclusions about that population.

Population Mean

The average of all the values in a population. It is a parameter that describes the central tendency of the entire population.