Problem

Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient $r$, and find the P-value using $\alpha=0.05$. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities?
\begin{tabular}{|c|c|c|c|c|c|}
\hline Lemon Imports & 232 & 264 & 359 & 481 & 533 \\
\hline Crash Fatality Rate & 15.9 & 15.7 & 15.4 & 15.3 & 14.9 \\
\hline
\end{tabular}
Construct a scatterplot. Choose the correct graph below.
A.
B.
c.
D.

Answer

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Answer

Final Answer: The correlation coefficient is \(\boxed{-0.977}\), and the p-value is \(\boxed{0.005}\). There is sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rate. However, the results do not suggest that imported lemons cause car fatalities.

Steps

Step 1 :Construct a scatterplot by plotting the lemon imports on the x-axis and the crash fatality rate on the y-axis. The scatterplot shows a downward trend, indicating a negative correlation between lemon imports and crash fatality rate. This means as lemon imports increase, the crash fatality rate decreases.

Step 2 :Calculate the correlation coefficient, which is a measure of the strength and direction of the linear relationship between two variables. The correlation coefficient for lemon imports and crash fatality rate is negative, which confirms the observation from the scatterplot that there is a negative correlation between the two variables.

Step 3 :Calculate the p-value, which is a measure of the probability that the observed correlation occurred by chance. If the p-value is less than the significance level (0.05 in this case), then we reject the null hypothesis that there is no correlation and conclude that there is a statistically significant correlation.

Step 4 :Final Answer: The correlation coefficient is \(\boxed{-0.977}\), and the p-value is \(\boxed{0.005}\). There is sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rate. However, the results do not suggest that imported lemons cause car fatalities.

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