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. 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 number of bears O B. The length of the bear OC. The weight of the bear (b) Draw a scatter diagram of the data. Choose the correct graph below. O A. O B. OC. OD. O D. AWeight (kg) 180+ T ALength (cm) 180+ T AWeight (kg) 180- AWeight (kg) 180+ T t .. H 40T > 200 Length (cm) 40- 100 40H 100 Length (cm) 40- 100 Length (cm) 100 200 200 200 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 negatively associated because r is positive and the absolute value of the correlation coefficient,, is greater than the critical value, (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.
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 number of bears
O B. The length of the bear
OC. The weight of the bear
(b) Draw a scatter diagram of the data. Choose the correct graph below.
O A.
OB
Oc.
OD.
AWeight (kg)
180+ --
ALength (cm)
180+ TTT
AWeight (kg)
180-
Weight (kg)
180-
++++
+++++
Q
40
100
Length (cm)
40 M ..
100
Weight (kg)
404
100
Length (cm)
40-
100
Length (cm)
200
200
200
200
(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 negatively associated because r is positive and the absolute value of the correlation coefficient,, is greater 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. 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 number of bears O B. The length of the bear OC. The weight of the bear (b) Draw a scatter diagram of the data. Choose the correct graph below. O A. OB Oc. OD. AWeight (kg) 180+ -- ALength (cm) 180+ TTT AWeight (kg) 180- Weight (kg) 180- ++++ +++++ Q 40 100 Length (cm) 40 M .. 100 Weight (kg) 404 100 Length (cm) 40- 100 Length (cm) 200 200 200 200 (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 negatively associated because r is positive and the absolute value of the correlation coefficient,, is greater than the critical value, (Round to three decimal places as needed.)
Researchers initiated a long-term study of the population of American black bears. One aspect of the study
the field). One variable thought to be related to weight is the length of the bear. The accompanying data re
E Click the icon to view the data table.
Critical values for the correlation coefficient
þears i
.....
E Click the icon to view the critical values table.
Critical Values for Correlation Coefficient
- X
n
3 0,997
Data table
(a) Which variabl
4 0.950
5 0.878
6 0.811
O A. The num
6
7 0.754
O B. The lengt
8 0.707
9 0.666
Total Length (cm)
Weight (kg)
O C. The weigl
138.0
110
10 0.632
Lo 602
135.0
60
(b) Draw a scatte
11 0.602
12LO576
12 0.576
13 0.553
130.0
90
120.5
60
O A.
149.0
95
14 0.532
AWeight (kg)
180t TL
15 0.514
0.514
16 0.497
141.0
100
141.0
95
17 0.482
18 0.468
150.0
85
166.0
155
40 +---
100
19 0.456
20 0.444
151.5
140
Length (cm)
129.5
105
21 0.433
22 0.423
23 0.413
150.0
110
(c) Determine the
The linear correla
24 0.404
(Round to three d
25 0.396
26 0.388
(d) Does a linear
Print
Done
27 0.381
The variables we
(Round to three decimal places as needed.)
28 0.374
29 0.367
positive
Print
Done
Transcribed Image Text:Researchers initiated a long-term study of the population of American black bears. One aspect of the study the field). One variable thought to be related to weight is the length of the bear. The accompanying data re E Click the icon to view the data table. Critical values for the correlation coefficient þears i ..... E Click the icon to view the critical values table. Critical Values for Correlation Coefficient - X n 3 0,997 Data table (a) Which variabl 4 0.950 5 0.878 6 0.811 O A. The num 6 7 0.754 O B. The lengt 8 0.707 9 0.666 Total Length (cm) Weight (kg) O C. The weigl 138.0 110 10 0.632 Lo 602 135.0 60 (b) Draw a scatte 11 0.602 12LO576 12 0.576 13 0.553 130.0 90 120.5 60 O A. 149.0 95 14 0.532 AWeight (kg) 180t TL 15 0.514 0.514 16 0.497 141.0 100 141.0 95 17 0.482 18 0.468 150.0 85 166.0 155 40 +--- 100 19 0.456 20 0.444 151.5 140 Length (cm) 129.5 105 21 0.433 22 0.423 23 0.413 150.0 110 (c) Determine the The linear correla 24 0.404 (Round to three d 25 0.396 26 0.388 (d) Does a linear Print Done 27 0.381 The variables we (Round to three decimal places as needed.) 28 0.374 29 0.367 positive Print Done
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