Question

The following data represent the commute time​ (in minutes) x and a score on a​ well-being survey y. The equation of the​ least-squares regression line is ModifyingAbove y with caret equals negative 0.0522 x plus 69.3800 and the standard error of the estimate is 0.3295. Complete parts ​(a) through ​(e) below.    x 10 20 30 40 55 77 110    y 69.0 68.3 67.9 67.1 66.1 65.9 63.5 ​(a) Predict the mean​ well-being index composite score of all individuals whose commute time is 35 minutes. ModifyingAbove y with caret equals nothing ​(Round to two decimal places as​ needed.) ​(b) Construct a​ 90% confidence interval for the mean​ well-being index composite score of all individuals whose commute time is 35 minutes. Lower Bound equals nothing ​ (Round to two decimal places as​ needed.) Upper Bound equals nothing ​ (Round to two decimal places as​ needed.) ​(c) Predict the​ well-being index composite score of​ Jane, whose commute time is 35 minutes. ModifyingAbove y with caret equals nothing ​(Round to two decimal places as​ needed.) ​(d) Construct a​ 90% prediction interval for the​ well-being index composite score of​ Jane, whose commute time is 35 minutes. Lower Bound equals nothing ​ (Round to two decimal places as​ needed.) Upper Bound equals nothing ​ (Round to two decimal places as​ needed.) ​(e) What is the difference between the predictions made in parts​ (a) and​ (c)? A. The prediction made in part​ (a) is an estimate of the​ well-being score for the​ individual, Jane, whose commute is 35 ​minutes, and the prediction made in part​ (c) is an estimate of the mean​ well-being score for all individuals whose commute is 35 minutes. B. The prediction made in part​ (a) is an estimate of the mean​ well-being score for all individuals whose commute is 35 ​minutes, and the prediction made in part​ (c) is an estimate of the​ well-being score for the​ individual, Jane, whose commute is 35 minutes. C. The prediction made in part​ (a) is the average​ well-being score for all individuals whose commute is 67.55 ​minutes, and the prediction made in part​ (c) is an estimate of the​ well-being score for the​ individual, Jane, whose commute is 67.55 minutes.

Answer 1

(a) Predict the mean​ well-being index composite score of all individuals whose commute time is 35 minutes. ModifyingAbove y with caret equals nothing ​(Round to two decimal places as​ needed.)​

y= 67.55

​(b) Construct a​ 90% confidence interval for the mean​ well-being index composite score of all individuals whose commute time is 35 minutes. Lower Bound equals nothing ​ (Round to two decimal places as​ needed.) Upper Bound equals nothing ​ (Round to two decimal places as​ needed.)

lower	upper
67.28	67.83

​(c) Predict the​ well-being index composite score of​ Jane, whose commute time is 35 minutes. ModifyingAbove y with caret equals nothing ​(Round to two decimal places as​needed.)

y= 67.55

​(d) Construct a​ 90% prediction interval for the​well-being index composite score of​ Jane, whose commute time is 35 minutes. Lower Bound equals nothing ​ (Round to two decimal places as​ needed.) Upper Bound equals nothing ​ (Round to two decimal places as​ needed.)

lower	upper
66.83	68.27

​(e) What is the difference between the predictions made in parts​ (a) and​ (c)?

B. The prediction made in part​ (a) is an estimate of the mean​ well-being score for all individuals whose commute is 35 ​minutes, and the prediction made in part​ (c) is an estimate of the​ well-being score for the​individual, Jane, whose commute is 35 minutes.