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Chapter 12: Q. 2 (page 799)
If and events
are independent, what is )?
result is:
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Foresters are interested in predicting the amount of usable lumber they can harvest from various tree species. They collect data on the diameter at breast height (DBH) in inches and the yield in board feet of a random sample of Ponderosa pine trees that have been harvested. (Note that a board foot is defined as a piece of lumber inches by inches by inch.) A scatterplot of the data is shown below
(a) Some computer output and a residual plot from a least squares regression on these data appear below. Explain why a linear model may not be appropriate in this case.
(B) Use both models to predict the amount of usable lumber from a Ponderosa pine with diameter inches. Show your work.
(c) Which of the predictions in part (b) seems more reliable? Give appropriate evidence to support your choice.
The professor swims Here are data on the time (in minutes) Professor Moore takes to swim 2000 yards and his pulse rate (beats per minute) after swimming for a random sample of 23 days:
(a) Is there statistically significant evidence of a negative linear relationship between Professor Moore's swim time and his pulse rate in the population of days on which he swims 2000 yards?
Carry out an appropriate significance test at the level.
(b) Calculate and interpret a confidence interval for the slope of the population regression line.
Two six-sided dice are rolled and the sum of the faces showing is recorded after each roll. Let the number of rolls required until a sum greater than is obtained. If trials are conducted, which of the following is most likely to be part of the probability distribution of ?
Color words Explain why it is not safe to use paired t procedures to do inference about the difference in the mean time to complete the two tasks.
Paired tires Exercise 69 in Chapter 8 (page 519 ) compared two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained. Both methods were used to estimate the total distance traveled by each tire. The scatterplot below displays the two estimates (in thousands of miles) for each tire.
Computer output from a least-squares regression analysis of these data is shown below. Assume that the conditions for regression inference are met.
(a) Verify that the 99% confidence interval for the slope of the population regression line is (0.5785,1.001).
(b) Researchers want to test whether there is a difference between the two methods of estimating tire wear.
Explain why an appropriate pair of hypotheses for this test is
(c) What conclusion would you draw for this significance test based on your interval in part (a)? Justify your answer.
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