Decide, at the Given Significance Level, Whether the Data Provide

question 20

Essay

Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful forpredicting y.
-The sample data below are the index of exposure (x)to radioactive waste for nine different Oregon counties and cancer mortality rate (y)(deaths per 100,000). $$\begin{array}{l} \begin{array} { l l l l l l l l l l } \hline \mathrm { x } & 2.49 & 2.57 & 3.41 & 1.25 & 1.62 & 3.83 & 11.64 & 6.41 & 8.34 \\ \hline \mathrm { y } & 147.1 & 130.1 & 129.9 & 113.5 & 137.5 & 162.3 & 207.5 & 177.9 & 210.3 \\ \hline \end{array}\\ \hat { y } = 114.72 + 9.23 x \end{array}$$ The standard error of the estimate is approximately 14.0099. At the 5% level of significance, do the data provide sufficient evidence to conclude that the slope of the population regression line is not 0 and hence that index of exposure is useful as a predictor of cancer mortality rate?

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Definitions:

Correlation

A statistical measure that indicates the extent to which two or more variables fluctuate together. A positive correlation indicates that variables move in the same direction, while a negative correlation indicates they move in opposite directions.

Risk-Free Rate

The hypothesized return on an investment that carries no risk, often linked with government bonds.

Minimum Required Return

The lowest acceptable return on an investment, considering the risk and the cost of capital.

Expected Return

The anticipated return on an investment, taking into account the probabilities of each potential outcome.