Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in a dala set. Results are shown in the accompanying display, Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? Use a significance level of $\alpha=0,05$ \begin{tabular}{|c|c|} \hline \multicolumn{2}{|l|}{ Correlation Results } \\ \hline Correlation coeff, r: & 0.961086 \\ \hline Critical r: & $\neq 0.2680855$ \\ \hline P-value (two tailed): & 0.000 \\ \hline \end{tabular} Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? Choose the correct answer below and, if necessary, fill in the answer box within your choice. (Round to three decimal places as needed) A. No, because the correlation coelficient falls outside the critical value(s) B. Yes, because the correlation coefficient falls between the critical values. C. Yes, because the correlation coefficient $\square$ falls outside the critical value(s). D. No, because the correlation coefficient falls between the critical values. E. The answer cannot be determined from the given information.
Solution
Step 1 ：The question is asking whether there is a linear correlation between the weights of bears and their chest sizes. The correlation coefficient, r, is given as 0.961086, which is very close to 1. This indicates a strong positive linear correlation.
Step 2 ：The critical r value is not equal to 0.2680855.
Step 3 ：The p-value is 0, which is less than the significance level of 0.05. This means that the correlation is statistically significant.
Step 4 ：Therefore, there is sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes.
Step 5 ：The correct answer is C. Yes, because the correlation coefficient falls outside the critical value(s).
Step 6 ：However, we need to calculate the exact value of the correlation coefficient that falls outside the critical value(s).
Step 7 ：correlation_coefficient = 0.961086
Step 8 ：critical_value = 0.2680855
Step 9 ：Final Answer: The correlation coefficient that falls outside the critical value(s) is \(\boxed{0.961}\).
