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Chapter 10: Q11BSC (page 468)

Interpreting a Computer Display. In Exercises 9–12, refer to the display obtained by using the paired data consisting of Florida registered boats (tens of thousands) and numbers of manatee deaths from encounters with boats in Florida for different recent years (from Data Set 10 in Appendix B). Along with the paired boat, manatee sample data, StatCrunch was also given the value of 85 (tens of thousands) boats to be used for predicting manatee fatalities.

Predicting Manatee Fatalities Using x = 85 (for 850,000 registered boats), what is the single value that is the best predicted number of manatee fatalities resulting from encounters with boats?

Short Answer

Expert verified

The single value that is the best-predicted number of manatee fatalities when there are 850,000 registered boats is 70.5.

Step by step solution

01

Given information

Results are obtained for the linear relation between the variables “number of registered boats” and “number of manatee deaths” using StatCrunch.

02

Step 2:Single predicted value

It can be observed in the results table that the single predicted value of Y(number of manatee fatalities) for the given value of X(registered boats) at 850,000 is obtained as 70.481772 (approximately 70.5).

Thus, the predicted value of Y (number of manatee fatalities) is 70.5.

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Most popular questions from this chapter

Cigarette Nicotine and Carbon Monoxide Refer to the table of data given in Exercise 1 and use the amounts of nicotine and carbon monoxide (CO).

a. Construct a scatterplot using nicotine for the xscale, or horizontal axis. What does the scatterplot suggest about a linear correlation between amounts of nicotine and carbon monoxide?

b. Find the value of the linear correlation coefficient and determine whether there is sufficient evidence to support a claim of a linear correlation between amounts of nicotine and carbon monoxide.

c. Letting yrepresent the amount of carbon monoxide and letting xrepresent the amount of nicotine, find the regression equation.

d. The Raleigh brand king size cigarette is not included in the table, and it has 1.3 mg of nicotine. What is the best predicted amount of carbon monoxide?

Tar

25

27

20

24

20

20

21

24

CO

18

16

16

16

16

16

14

17

Nicotine

1.5

1.7

1.1

1.6

1.1

1.0

1.2

1.4

Interpreting r. In Exercises 5–8, use a significance level of A = 0.05 and refer to the accompanying displays.

5. Bear Weight and Chest Size Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in Data Set 9 “Bear Measurements” in Appendix B; results are shown in the accompanying Statdisk display. Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight?

Explore! Exercises 9 and 10 provide two data sets from “Graphs in Statistical Analysis,” by F. J. Anscombe, the American Statistician, Vol. 27. For each exercise,

a. Construct a scatterplot.

b. Find the value of the linear correlation coefficient r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot.

x

10

8

13

9

11

14

6

4

12

7

5

y

9.14

8.14

8.74

8.77

9.26

8.10

6.13

3.10

9.13

7.26

4.74

In Exercises 9–12, refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 20 “Car Measurements” in Appendix B. The response (y) variable is CITY (fuel consumption in mi, gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi, gal).

A Honda Civic weighs 2740 lb, it has an engine displacement of 1.8 L, and its highway fuel consumption is 36 mi/gal. What is the best predicted value of the city fuel consumption? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate?

Testing for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of A = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.)

CSI Statistics Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print lengths, foot lengths, and heights of males (from Data Set 2 “Foot and Height” in Appendix B). Is there sufficient evidence to conclude that there is a linear correlation between shoe print lengths and heights of males? Based on these results, does it appear that police can use a shoe print length to estimate the height of a male?

Shoe print(cm)

29.7

29.7

31.4

31.8

27.6

Foot length(cm)

25.7

25.4

27.9

26.7

25.1

Height (cm)

175.3

177.8

185.4

175.3

172.7
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