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 = 0.877 Using α= 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. a. Is there a linear correlation between chest size and weight? O A. Yes, because the test statistic falls between the critical values of 0.707 and 0.707 O B. No, because the absolute value of the test statistic exceeds the critical value of 0.707 O C. Yes. because the absolute value of the test statistic exceeds the critical value of 0.707 O 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)

Answer 1

Solution:- Given that r = 0.877, using α = 0.05, n = 8

a. t = r*(sqrt(n-2))/sqrt(1-r^2)
= 0.877*(sqrt(8-2))/sqrt(1-0.877^2)
= 4.471

The critical value of t at 0.05 the level if significance

=>option A. Yes,because the absolute value of the test statistic exceeds the critical values of 0.707.

b. r = 0.877

r^2 = 0.877^2 = 0.769