For a sample of eight bears, researchers measured the distances around the bears

Question

For a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r= 0.809.Using = 0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

Click here to view a table of critical values for the correlation coefficient.

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a. Is there a linear correlation between chest size and weight?

(Selections)

A.No, because the absolute value of the test statistic exceeds the critical value of 0.707.

B. Yes, because the test statistic falls between the critical values of 0.707 and 0.707.

C.Yes, because the absolute value of the test statistic exceeds the critical value of 0.707.

D.The answer cannot be determined from the given information.

b. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

_____________

(Round to three decimal places as needed.)

Explanation / Answer

Ans: Given that r=0.809 and alpha=0.05

a) From the given information, we know that 80% of the variation in weight can be explained by the relationship between chest size and weight.

b) Based on the critical value of the correlation coefficient we can judge whether there exists a linear relation between the weight and chest size.

Here, the critical value is not mentioned but the rules are as below:

If the test statistic lies between the critical values, we accept the null hypothesis that there is no linear relation between the two fields. On the other hand, if the test statistic exceeds the critical value, the null can be rejected.

b) From the given data we know that 80% the variation in weight can be explained by the linear relationship between weight and chest size.

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