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A Professor of Economics Wants to Study the Relationship Between

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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.  Education 161115812101314 Income 5840553543415249\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:

Burned Over District

A term for Western New York in the early 19th century, highlighting the region's intense religious revivals and reform movements.

Second Great Awakening

A Protestant religious revival during the early 19th century in the United States, which led to the growth of new denominations and increased emphasis on personal piety and social reforms.

Religious Conversions

The act of adopting a new religious belief or changing one's religious affiliation, often involving a significant transformation of personal identity and worldview.

State and Religion

the relationship or arrangement between a government and religious institutions, varying from separation to integration.

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