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For a sample of eight bears, researchers measured the distances around the bear’s chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r = 0.894. Using a= 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? Critical Values for the Correlation Coefficient n alpha = .05 alpha = .01 4 0.95 0.99 5 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 9 0.666 0.798 10 0.632 0.765 11 0.602 0.735 12 0.576 0.708 13 0.553 0.684 14 0.532 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482 0.606 18 0.468 0.59 19 0.456 0.575 20 0.444 0.561 25 0.396 0.505 30 0.361 0.463 35 0.335 0.43 40 0.312 0.402 45 0.294 0.378 50 0.279 0.361 60 0.254 0.33 70 0.236 0.305 80 0.22 0.286 90 0.207 0.269 100 0.196 0.256 Note: To test H subscript 0: rho equals 0 against H subscript 1: rho not equal to 0, reject H subscript 0 if the absolute value of r is greater than the critical value in the table.

Linear Algebra
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