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## For a sample of eight bears, researchers measured the distances around the bears' chests and weighed

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 = 0.982. Using alpha = 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?

a. To determine if there is a linear correlation, test the claim that the correlation coefficient is different from 0. The hypotheses for this test are shown below.

b. The proportion of the variation in weight explained by the linear relationship between chest size and weight is defined to be r^2 where r is the linear correlation coefficient.