Question

The data in the table to the right are based on the results of a...

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​ (c) through​ (d) below.


DATA

Commute Time Score

7 69.1

16 68.3

24 67.4

37 67.1

51 66.6

74 65.6

104 63.7



Image transcription text

(c) Determine the linear correlation coefficient between commute time and well-being score. E (Round to three decimal places as needed.) (d) Does a linear relation exist between the commute time and well-being index score? O A. Yes, there appears to be a negative linear association because r is negative and is less than the negative of the critical value. O B. No, there is no linear association since r is positive and is less than the critical value. O C. Yes, there appears to be a positive linear association because r is positive and is greater than the critical value. O D. Yes, there appears to be a positive linear association because r is positive and is less than the critical value.

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Answer & Explanation
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Required answers are

(c) r = -0.988

(d) option A

Step-by-step explanation

(c) By TI plus calculator

  • 2nd button —> CATALOG —> Diagnostic On
  • STAT —> EDIT —> commute time in L1 and score in L2
  • STAT —> CALC —> LinReg(ax + b)
  • Xlist : L1
  • Ylist : L2
  • FreqList:
  • ENTER

Result

 Correlation coefficient r = -0.988


(d) Sample size n = 7

By critical table, critical correlation = -0.754

Since calculated correlation coefficient r (-0.988) < critical value (-0.754), indicating a significant linear association between variable

Hence, option A is correct explanation