Question

Interpreting r. In Exercises 5–8, use a significance level of A = 0.05 and refer to the accompanying displays.

5. Bear Weight and Chest Size Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in Data Set 9 “Bear Measurements” in Appendix B; results are shown in the accompanying Statdisk 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?

Short answer

There is enough evidence to support the claim that there is a linear correlation between weights and chest sizes.

The chest sizes are easier to be recorded than weights.

As weights and chest sizes are highly correlated, chest sizes can be used to predict weights.

Step-by-step solution

Given information

The level of significance is 0.05.

The output for the hypothesis test for correlation between weights of bears and chest sizes are known.

Hypothesis test for correlation between weights and chest size

Let\(\rho \)be the true correlation measure between the two variables; weights and chest sizes.

The hypotheses be formulated as follows:

\(\begin{array}{l}{H_o}:\rho = 0\\{H_a}:\rho \ne 0\end{array}\)

From the output the following measures are known,

\(\begin{array}{c}r = 0.963\\p{\rm{ - value}} = 0.000\end{array}\)

As the p-value is lesser than 0.05, the null hypothesis is rejected.

Thus, there is enough evidence at 0.05 level of significance to conclude that there is a significant correlation between the two variables; weight and chest sizeof bears.

Measurement of variables

Of the two measures, it is not easy to weigh the bears on a scale as they are too heavy to be lifted. On the other hand, the chest sizes are comparatively easier to be recorded for the bears in anethesized state.

Predict the measure of weight from chest size

The weight is highly correlated with the chest sizes, and hence the variable can be used to predict the weights.