Question

for a data set of chest sizes (distance around chest in inches) and weights (pounds) of seven anesthetized bears that were measured, the linear correlation coefficient is r = 0.208. use the table available below to find the critical values of r. based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation? click the icon to view the table of critical values of r. the critical values are - 0.754,0.754. (type integers or decimals. do not round. use a comma to separate answers as needed.) since the correlation coefficient r is , there sufficient evidence to support the claim of a linear correlation.

Explanation:

Step1: Recall correlation - decision rule

If \(|r|\lt\) critical - value, there is not sufficient evidence for linear correlation. If \(|r|\geq\) critical - value, there is sufficient evidence for linear correlation.

Step2: Calculate the absolute value of \(r\)

Given \(r = 0.208\), then \(|r|=|0.208| = 0.208\).

Step3: Compare \(|r|\) with the critical value

The critical values are \(- 0.754\) and \(0.754\), so the critical value for comparison is \(0.754\). Since \(0.208\lt0.754\).

Answer:

Since the correlation coefficient \(r\) is between \(- 0.754\) and \(0.754\), there is not sufficient evidence to support the claim of a linear correlation.