Researchers initiated a long-term study of the population of American black bears. 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 t thought to be related to weight is the length of the bear. The accompanying data represent the lengths and weights of 12 American black bears. Complete parts (a) through (d) below. | Click the icon to view the data table. E Click the icon to view the critical values table. (a) Which variable is the explanatory variable based on the goals of the research? O A. The weight of the bear O B. The number of bears OC. The length of the bear (b) Draw a scatter diagram of the data. Choose the correct graph below. O A. OB. Oc. OD. AWeight (kg) 180- AWeight (kg) 180- Q AWeight (kg) 180- ALength (cm) 180- .... - -- .. 40+ 100 200 Length (cm) 40+ 100 200 Length (cm) 40- 100 Length (cm) 40+ 100 200 200 Weight (kg) (c) Determine the linear correlation coefficient between weight and length. The linear correlation coefficient between weight and length is r=D: (Round to three decimal places as needed.)

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Researchers initiated a long-term study of the population of American black bears. 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
thought to be related to weight is the length of the bear. The accompanying data represent the lengths and weights of 12 American black bears. Complete parts (a) through (d) below.
Click the icon to view the data table.
Click the icon to view the critical values table.
(a) Which variable is the explanatory variable based on the goals of the research?
A. The weight of the bear
B. The number of bears
C. The length of the bear
(b) Draw a scatter diagram of the data. Choose the correct graph below.
O A.
В.
С.
D.
AWeight (kg)
180-
A Weight (kg)
180-
AWeight (kg)
180-
ALength (cm)
180-
40-
100
40-
100
40-
100
40-
100
200
200
200
200
Length (cm)
Length (cm)
Length (cm)
Weight (kg)
(c) Determine the linear correlation coefficient between weight and length.
The linear correlation coefficient between weight and length is r=
(Round to three decimal places as needed.)
(d) Does a linear relation exist between the weight of the bear and its length?
The variables weight of the bear and length of the bear are
associated because r is
and the absolute value of the correlation coefficient,
is
than the critical value,
(Round to three decimal places as needed.)
Transcribed Image Text:Researchers initiated a long-term study of the population of American black bears. 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 thought to be related to weight is the length of the bear. The accompanying data represent the lengths and weights of 12 American black bears. Complete parts (a) through (d) below. Click the icon to view the data table. Click the icon to view the critical values table. (a) Which variable is the explanatory variable based on the goals of the research? A. The weight of the bear B. The number of bears C. The length of the bear (b) Draw a scatter diagram of the data. Choose the correct graph below. O A. В. С. D. AWeight (kg) 180- A Weight (kg) 180- AWeight (kg) 180- ALength (cm) 180- 40- 100 40- 100 40- 100 40- 100 200 200 200 200 Length (cm) Length (cm) Length (cm) Weight (kg) (c) Determine the linear correlation coefficient between weight and length. The linear correlation coefficient between weight and length is r= (Round to three decimal places as needed.) (d) Does a linear relation exist between the weight of the bear and its length? The variables weight of the bear and length of the bear are associated because r is and the absolute value of the correlation coefficient, is than the critical value, (Round to three decimal places as needed.)
Data table
critical values for the correlation coefficient
Critical Values for Correlation Coefficient
Total Length (cm)
Weight (kg)
138.0
110
3
0.997
135.0
60
4
0.950
0.878
139.0
90
0.811
120.5
60
7
0.754
149.0
85
8.
0.707
141.0
105
9.
0.666
10 0.632
11 0.602
12 0.576
13 0.553
14 0.532
15 0.514
16 0.497
17 0.482
18 0.468
19 0.456
20 0.444
21 0.433
22 0.423
23 0.413
24 0.404
25 0.396
26 0.388
27 0.381
28 0.374
29 0.367
30 0.361
141.0
95
150.0
85
166.0
155
151.5
140
129.5
105
150.0
110
Print
Done
The linear correlation coefficient between weight and
(Round to three decimal places as needed.)
(d) Does a linear relation exist between the weight o
The variables weight of the bear and length of the b
(Round to three decimal places as needed.)
Click to select your answer(s).
Print
Done
Transcribed Image Text:Data table critical values for the correlation coefficient Critical Values for Correlation Coefficient Total Length (cm) Weight (kg) 138.0 110 3 0.997 135.0 60 4 0.950 0.878 139.0 90 0.811 120.5 60 7 0.754 149.0 85 8. 0.707 141.0 105 9. 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 141.0 95 150.0 85 166.0 155 151.5 140 129.5 105 150.0 110 Print Done The linear correlation coefficient between weight and (Round to three decimal places as needed.) (d) Does a linear relation exist between the weight o The variables weight of the bear and length of the b (Round to three decimal places as needed.) Click to select your answer(s). Print Done
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