al Values

Values for Correlation Coefficient

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n

3

0.997

4 0.950

5 0.878

6

0.811

7 0.754

8 0.707

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

Done

X

The data in the table to the right are based on the results of a survey comparing the commute

time of adults to their score on a well-being test. Complete parts (a) through (d) below.

Click the icon to view the table of critical values of the correlation coefficient.

(a) Which variable is likely the explanatory variable and which is the response variable?

Score

A. The explanatory variable is the well-being score and the response variable is commute time because commute time affects the well-being score.

B. The explanatory variable is commute time and the response variable is the well-being score because commute time affects the well-being score.

C. The explanatory variable is the well-being score and the response variable is commute time because well-being score affects the commute time.

D. The explanatory variable is commute time and the response variable is the well-being score because well-being score affects the commute time score.

(b) Draw a scatter diagram of the data. Which of the following represents the data?

A.

r=

70-

60+

110

Time (min)

Time (min)

B.

70+

60-

0

Score

C

110

O C.

Time (min)

Commute Time

(in minutes)

5

13

26

37

54

66

98

110-

0-

60

Score

Well-Being

Score

69.3

68.8

67.5

67.1

66.5

65.2

63.4

70

Score

D.

110-

0-

60

Time (min)

70

(c) Determine the linear correlation coefficient between commute time and well-being score.

(Round to three decimal places as needed.)

(d) Does a linear relation exist between the commute time and well-being index score? Select the correct choice below and fill in the answer box to complete your choice.

(Round to three decimal places as needed.)

A. Yes, the variables commute time and well-being score are negatively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value

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