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Chapter 12: Q.27 (page 793)

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=footlength&y=heightwere recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Which of the following is a 95%confidence interval for the population slope 尾1?

a.3.0867卤0.4117

b. 3.0867卤0.8518

c.3.0867卤0.8069

d.3.0867卤0.8497

e.localid="1654193042763" 3.0867卤0.8481

Short Answer

Expert verified

The correct option is option (b)

3.0867卤0.8518

Step by step solution

01

Given Information

Given in the question that

n=25

c=0.95

we have to determine the correct option.

02

Explanation

The confidence interval is computed as

b卤t*脳SEb

where b1=3.0867and SEb1=0.4117which is given in the computer output.

The degree of difference is

df=n-2=25-2=23

The critical T value can be found in the Tdistribution table, so t*is2.069.

Therefore, the confidence interval is

localid="1654497378353" b卤t*SEb=3.0867卤2.069脳0.4117=3.0867卤0.8518

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Most popular questions from this chapter

How well do professional golfers putt from various distances to the hole? The scatterplot shows various distances to the hole (in feet) and the per cent of putts made at each distance for a sample of golfers.

The graphs show the results of two different transformations of the data. The first graph plots the natural logarithm of per cent made against distance. The second graph plots the natural logarithm of per cent made against the natural logarithm of distance.

a. Based on the scatterplots, would an exponential model or a power model provide a better description of the relationship between distance and per cent made? Justify your answer.

b. Here is computer output from a linear regression analysis of ln(per cent made) and distance. Give the equation of the least-squares regression line. Be sure to define any variables you use.

c. Use your model from part (b) to predict the per cent made for putts of 21 feet.

d. Here is a residual plot for the linear regression in part (b). Do you expect your prediction in part (c) to be too large, too small, or about right? Justify your answer.

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=footlength&y=heightere recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

26. Which of the following is the best interpretation of the value 0.4117in the computer output?

a. For each increase of 1cmin foot length, the average height increases by about0.4117cm

b. When using this model to predict height, the predictions will typically be off by about 0.4117cm.

c. The linear relationship between foot length and height accounts for 41.17%of the variation in height.

d. The linear relationship between foot length and height is moderate and positive.

e. In repeated samples of size 25the slope of the sample regression line for predicting height from foot length will typically vary from the population slope by about 0.4117.

Tattoos: What per cent of U.S. adults have one or more tattoos? The Harris Poll conducted an online survey of 2302adults and found 29% of respondents had at least 1 tattoo. According to the published report, 鈥淩espondents for this survey were selected from among those who have agreed to participate in Harris Interactive surveys.鈥� Explain why it would not be appropriate to use these data to construct a 95% confidence interval for the proportion of all U.S. adults who have tattoos.

Do beavers benefit beetles? Researchers laid out 23circular plots, each 4meters in diameter, at random in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth so beetles prefer them. If so, more stumps should produce more beetle larvae

Here is computer output for regression analysis of these data. Construct and interpret a99% confidence interval for the slope of the population regression line. Assume that the conditions for performing inference are met.

role="math" localid="1654159204144" PredictorCoefSECoefTPConstant鈭�1.2862.853鈭�0.450.657Stumps11.8941.13610.470.000S=6.41939R-Sq=83.9%R-Sq(adj)=83.1%

T12.12 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 20 Ponderosa pine trees that have been harvested. (Note that a board foot is defined as a piece of lumber 12 inches by 12 inches by 1 inch.) Here is a scatterplot of the data.

a. Here is some computer output and a residual plot from a least-squares regression on these data. Explain why a linear model may not be appropriate in this case.

The foresters are considering two possible transformations of the original data: (1) cubing the diameter values or (2) taking the natural logarithm of the yield measurements. After transforming the data, a least-squares regression analysis is performed. Here is some computer output and a residual plot for each of the two possible regression models:

b. Use both models to predict the amount of usable lumber from a Ponderosa pine with diameter 30 inches.
c. Which of the predictions in part (b) seems more reliable? Give appropriate evidence to support your choice.
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