### One of eight bear species in the world

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American Black Bears The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population in Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear's weight (since it is not practical to weigh bears in the field). One variable that is thought to be related to weight is the length of the bear. The following data represent the lengths and weights of 12 American black bears.

 Total Length (cm), x Weight (kg), y 139.0 110 138.0 60 139.0 90 120.5 60 149.0 85 141.0 100 141.0 95 150.0 85 166.0 155 151.5 140 129.5 105 150.0 110

Use the results from Problem 20 in Section 4.2 to answer the following questions:

(a) Treating total length as the explanatory variable, x, determine the estimates of ß0 and ß1.

(b) Assuming the residuals are normally distributed, test whether a linear relation exists between total length and weight at the a = 0.05 level of significance.

(c) Assuming the residuals are normally distributed, construct a 95% confidence interval for the slope of the true least squares regression line.

(d) What is the mean weight of American black bears of length 146.0 cm?

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