Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 12.3, Problem 18AYU
American Black Bears In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the American black bear (Ursus americanus) 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 |
Source: fieldtripearth.org
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 β0 and β1.
- b. Assuming the residuals are
normally distributed , test whether a linear relation exists between total length and weight at the α = 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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Chapter 12 Solutions
Fundamentals of Statistics (5th Edition)
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