Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in a data 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
$$\text{Unknown environment 'tabular'}$$
chest size can be used to predict the weight? Use a significance level of $\alpha =0.05$.

Determine the null and alternative hypotheses.
$$\begin{array}{ll}{H}_0:\rho & \mathrm{\nabla }\\ H_1:\rho & \mathrm{\nabla }\end{array}$$
(Type integers or decimals. Do not round.)

Step 1 ：Determine the null and alternative hypotheses for the claim that there is a linear correlation between the weights of bears and their chest sizes.

Step 2 ：The null hypothesis ($H_0$) states that there is no linear correlation between the two variables, which means the population correlation coefficient ($\rho$) is equal to zero.

Step 3 ：The alternative hypothesis ($H_1$) states that there is a linear correlation between the two variables, which means the population correlation coefficient ($\rho$) is not equal to zero.

Step 4 ：Given the correlation coefficient $r=0.967835$ and the critical $r=\pm 0.2680855$, we can see that $r$ is much greater than the critical $r$.

Step 5 ：The P-value is $0.000$, which is less than the significance level of $\alpha =0.05$, indicating that we reject the null hypothesis.

Step 6 ：Since we reject the null hypothesis, we accept the alternative hypothesis, which suggests that there is a linear correlation between the weights of bears and their chest sizes.

Step 7 ：$\boxed{{\displaystyle H_0:\rho =0}}$

Step 8 ：$\boxed{{\displaystyle H_1:\rho \ne 0}}$