A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 8 children from her practice, measures their height and head circumference, and obtains the data shown in the table. Complete parts (a) through (e) below. E Click here to see the Table of Critical Values for Correlation Coefficient. Height (in.) Head Circumference (in.) O 17.5 27.25 25.25 16.9 26.5 17.3 25 17 28 17.6 17.2 26.25 Data Table 26.25 17.1 27.25 17.3 Critical Values for Correlation Coefficient n 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 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 ..... (1,1) More

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A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She
randomly selects 8 children from her practice, measures their height and head circumference, and obtains the data
shown in the table. Complete parts (a) through (e) below.
Height (in.) Head Circumference (in.) O
27.25
17.5
25.25
16.9
Click here to see the Table of Critical Values for Correlation Coefficient.
26.5
17.3
25
17
28
17.6
26.25
17.2
Data Table
26.25
17.1
27.25
17.3
Critical Values for Correlation Coefficient
n
3
0.997
4
0.950
0.878
0.811
7
0.754
8
0.707
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
.....
(1,1)
More
n
Transcribed Image Text:A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 8 children from her practice, measures their height and head circumference, and obtains the data shown in the table. Complete parts (a) through (e) below. Height (in.) Head Circumference (in.) O 27.25 17.5 25.25 16.9 Click here to see the Table of Critical Values for Correlation Coefficient. 26.5 17.3 25 17 28 17.6 26.25 17.2 Data Table 26.25 17.1 27.25 17.3 Critical Values for Correlation Coefficient n 3 0.997 4 0.950 0.878 0.811 7 0.754 8 0.707 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 ..... (1,1) More n
(b) Draw a scatter diagram. Choose the correct graph below.
A.
В.
C.
D.
17.6-
28-
17.6-
28-
16.9-
25
Circ. (in.)
254
16.9
Circ. (in.)
16.9
25
254
16.9
28
17.6
28
17.6
Height (in.)
Height (in.)
(c) Compute the linear correlation coefficient between the height and head circumference of a child.
r =
(Round to three decimal places as needed.)
(d) Does a linear relation exist between height and head circumference? Select the correct choice below and fill in the answer box to complete your choice.
(Round to three decimal places as needed.)
O A. No, the variables height and head circumference are not linearly related because r is negative and the absolute value of the correlation coefficient is less than the critical value,.
B. Yes, the variables height and head circumference are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value,
C. No, the variables height and head circumference are not linearly related because r is positive and the absolute value of the correlation coefficient is less than the critical value,
D. Yes, the variables height and head circumference are positively associated because r is negative and the absolute value of the correlation coefficient is greater than the critical value,
Height (in.)
Height (in.)
Circ. (in.)
Circ. (in.)
Transcribed Image Text:(b) Draw a scatter diagram. Choose the correct graph below. A. В. C. D. 17.6- 28- 17.6- 28- 16.9- 25 Circ. (in.) 254 16.9 Circ. (in.) 16.9 25 254 16.9 28 17.6 28 17.6 Height (in.) Height (in.) (c) Compute the linear correlation coefficient between the height and head circumference of a child. r = (Round to three decimal places as needed.) (d) Does a linear relation exist between height and head circumference? Select the correct choice below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. No, the variables height and head circumference are not linearly related because r is negative and the absolute value of the correlation coefficient is less than the critical value,. B. Yes, the variables height and head circumference are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value, C. No, the variables height and head circumference are not linearly related because r is positive and the absolute value of the correlation coefficient is less than the critical value, D. Yes, the variables height and head circumference are positively associated because r is negative and the absolute value of the correlation coefficient is greater than the critical value, Height (in.) Height (in.) Circ. (in.) Circ. (in.)
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