A Professor of Economics Wants to Study the Relationship Between

question 89

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } \hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \\\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \\\hline\end{array}$$ Predict with 95% confidence the income of an individual with 10 years of education.

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Definitions:

Alpha Level

Alpha level, often denoted as α, is a threshold value used in statistics to determine the significance of a result, especially in hypothesis testing; it represents the probability of erroneously rejecting the null hypothesis.

Rejection Region

In hypothesis testing, the range of values for which the null hypothesis is not considered plausible and is therefore rejected.

Null Hypothesis

A statement positing that no statistical significance exists in a set of observations, serving as the default assumption in hypothesis testing.

Rejection Region

The area in the probability distribution that, if the test statistic falls within, leads to the rejection of the null hypothesis.