Solved: American Black Bears The American black bear (Ursus americanus) is one of eight

Chapter 14, Problem 18

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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 bears 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), y139.0 110138.0 60139.0 90120.5 60149.0 85141.0 100141.0 95150.0 85166.0 155151.5 140129.5 105150.0 110Source: fieldtripearth.orgUse the results from in Section 4.2 to answer thefollowing questions:(a) Treating total length as the explanatory variable, x, determinethe estimates of b0 and b1.(b) Assuming the residuals are normally distributed, test whethera linear relation exists between total length and weight at thea = 0.05 level of significance.(c) Assuming the residuals are normally distributed, constructa 95% confidence interval for the slope of the true leastsquaresregression line.(d) What is the mean weight of American black bears of length 146.0 cm?