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

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?