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Chapter 12: Q.26 (page 764)
A confidence interval for the population slope is
(a) .
(b) .
(c) .
(d) .
(e) .
The slope of the true regression line is . Therefore, option (b) is the correct option.
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Inference about the slope of a least-squares regression line is based on which of the following distributions?
(a) The t distribution with degrees of freedom
(b) The standard Normal distribution
(c) The chi-square distribution with degrees of freedom
(d) The t distribution with degrees of freedom
(e) The Normal distribution with mean and standard deviation
A company has been running television commercials for a new children’s product on five different
family programs during the evening hours in a large city over a one-month period. A random sample of families is taken, and they are asked to indicate the one program they viewed most often and their rating of the advertised product. The results are summarized in the following table.
The advertiser decided to use a chi-square test to see if there is a relationship between the family program viewed and the product’s rating. What would be the degrees of freedom for this test?
(a) 3 (c) 12 (e) 19
(b) 4 (d) 18
A large machine is filled with thousands of small
pieces of candy, of which are orange. When money
is deposited, the machine dispenses randomly selected
pieces of candy. The machine will be recalibrated if a
group of candies contains fewer than that are
orange. What is the approximate probability that this will
happen?
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The body’s natural electrical field helps wounds heal. If diabetes changes this field, it might explain why people with diabetes heal more slowly. A study of this idea compared randomly selected normal mice and randomly selected mice bred to spontaneously develop diabetes. The investigators attached sensors to the right hip and front feet of the mice and measured the difference in electrical potential (in millivolts) between these locations. Graphs of the data for each group reveal no outliers or strong skewness. The computer output below provides numerical summaries of the .
The researchers want to know if there is evidence of a significant difference in mean electrical potentials between normal mice and mice with diabetes. Carry out a test using a level of significance and report your conclusion.
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.
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