Critical Values for Correlation Coefficient n 3 0.997 4 0.950 5 0.878 6 0.811 0.754 8 0.707 co 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 0.361The 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 Commute lei parts (a) through (d) below. 11ml (In mlnutu) Well-Balng Soon 5 Click the icon to view the critical values for the correlation coefcient. 5 69.5 1 6 68.3 27 67.3 36 51 66 1 02 63.2 (3) Which variable is likely the explanatory variable and which is the response variable? (9 O B. The explanatory variable is commute time and the response variable is the well-being score because commute time affects the well-being score. The explanatory variable is the well rig score and the response variable is commute time because well-being score affects the commute time 0 C. The explanatory variable is commute time and the response variable is the well-being score because well-being score affects the commute time score, 0 D. The explanatory variable is the well-being score and the response variable is commute time because commute time affects the well-being score. (b) Draw a scatter diagram of the data. Which of the following represents the data? O A. O B. O c. O D. 70 Q 11 Q 70 7 a Q 2 Q 9 s c c o c :2 8 8 8 l'Z'i E\": 60 o 60 6 0 110 60 70 0 110 0 110 Commute Time (min) Commute Time (min) Commute Time (min) Commute Time (min) (c) Determine the linear correlation coefcient between commute time and well-being score. r = (Round to three decimal places as needed.) (d) Does a linear relation exist between the commute time and well-being index score? 0 A. Yes, there appears to be a positive linear association because r is positive and is greater than the critical value. 0 B. Yes, there appears to be a negative linear association because r is negative and is less than the negative of the critical value. 0 C. No, there is no linear association since r is positive and is less than the critical value, 0 D. Yes, there appears to be a positive linear association because r is positive and is less than the critical value