Solution Found!
An Unhealthy CommuteUse the results of Section to answer
Chapter 5, Problem 7AYU(choose chapter or problem)
Problem 7AYU
An Unhealthy CommuteUse the results of Problem from Section to answer the following questions:
(a) Predict the mean well-being index composite score of all individuals whose commute time is 20 minutes.
(b) Construct a 90% confidence interval for the mean wellbeing index composite score of all individuals whose commute time is 20 minutes.
(c) Predict the well-being index composite score of Jane, whose commute time is 20 minutes.
(d) Construct a 90% prediction interval for the well-being index composite score of Jane, whose commute time is 20 minutes.
(e) Explain the difference between the predictions made in parts (a) and (c).
Problem
An Unhealthy Commute The following data represent commute times (in minutes) and a score on a well-being survey.
Use the results from Problem in Section to answer the following questions:
(a) Treating commute time as the explanatory variable, x, determine the estimates of β0 and β1.
(b) Compute the standard error of the estimate, Se.
(c) A normal probability plot of the residuals indicates it is reasonable to conclude the residuals are normally distributed. Determine Sb1
(d) Test whether a linear relation exists between commute time and well-being index composite score at the α = 0.05 level of significance.
(e) Construct a 95% confidence interval about the slope of the true least-squares regression line.
Problem
Use the results from Problems
An Unhealthy Commute The following data represent commute times (in minutes) and score on a well-being survey.
(a)Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable.
(b)Interpret the slope and y-intercept, if appropriate.
(c) Predict the well-being index of a person whose commute is 30 minutes.
(d) Suppose Barbara has a 20-minute commute and scores 67.3 on the survey. Is Barbara more “well-off” than the typical individual who has a 20-minute commute?
problem
An Unhealthy CommuteThe Gallup Organization regularly surveys adult Americans regarding their commute time to work. In addition, they administer a Well-Being Survey. According to the Gallup Organization, “The Gallup-Healthways Well-Being Index Composite Score is comprised of six sub-indices: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment and Basic Access.” A complete description of the index can be found athttp://www.well-beingindex.com/. The data in the following table are based on the results of the survey, which represent commute time to work (in minutes) and well-being index score
(a) Which variable do you believe is likely the explanatory variable and which is the response variable?
(b) Draw a scatter diagram of the data.
(c) Determine the linear correlation coefficient between commute time and well-being index score.
(d) Does a linear relation exist between the commute time and well-being index score?
Questions & Answers
QUESTION:
Problem 7AYU
An Unhealthy CommuteUse the results of Problem from Section to answer the following questions:
(a) Predict the mean well-being index composite score of all individuals whose commute time is 20 minutes.
(b) Construct a 90% confidence interval for the mean wellbeing index composite score of all individuals whose commute time is 20 minutes.
(c) Predict the well-being index composite score of Jane, whose commute time is 20 minutes.
(d) Construct a 90% prediction interval for the well-being index composite score of Jane, whose commute time is 20 minutes.
(e) Explain the difference between the predictions made in parts (a) and (c).
Problem
An Unhealthy Commute The following data represent commute times (in minutes) and a score on a well-being survey.
Use the results from Problem in Section to answer the following questions:
(a) Treating commute time as the explanatory variable, x, determine the estimates of β0 and β1.
(b) Compute the standard error of the estimate, Se.
(c) A normal probability plot of the residuals indicates it is reasonable to conclude the residuals are normally distributed. Determine Sb1
(d) Test whether a linear relation exists between commute time and well-being index composite score at the α = 0.05 level of significance.
(e) Construct a 95% confidence interval about the slope of the true least-squares regression line.
Problem
Use the results from Problems
An Unhealthy Commute The following data represent commute times (in minutes) and score on a well-being survey.
(a)Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable.
(b)Interpret the slope and y-intercept, if appropriate.
(c) Predict the well-being index of a person whose commute is 30 minutes.
(d) Suppose Barbara has a 20-minute commute and scores 67.3 on the survey. Is Barbara more “well-off” than the typical individual who has a 20-minute commute?
problem
An Unhealthy CommuteThe Gallup Organization regularly surveys adult Americans regarding their commute time to work. In addition, they administer a Well-Being Survey. According to the Gallup Organization, “The Gallup-Healthways Well-Being Index Composite Score is comprised of six sub-indices: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment and Basic Access.” A complete description of the index can be found athttp://www.well-beingindex.com/. The data in the following table are based on the results of the survey, which represent commute time to work (in minutes) and well-being index score
(a) Which variable do you believe is likely the explanatory variable and which is the response variable?
(b) Draw a scatter diagram of the data.
(c) Determine the linear correlation coefficient between commute time and well-being index score.
(d) Does a linear relation exist between the commute time and well-being index score?
ANSWER:Answer:
Step 1
(a) Predict the mean well-being index composite score of all individuals whose commute time is 20 minutes.
The regression equation is a linear equation of the form
x |
y |
xy |
|
5 |
69.2 |
346 |
25 |
15 |
68.3 |
1024.5 |
225 |
15 |
67.5 |
1012.5 |
225 |
35 |
67.1 |
2348.5 |
1225 |
50 |
66.4 |
3320 |
2500 |
72 |
66.1 |
4759.2 |
5184 |
105 |
63.9 |
6709.5 |
11025 |
,
n = 7 , ,
,
= -0.0457
= 68.8674
Therefore,
Now, we need to predict the mean well-being index composite score of all individuals whose commute time is 20 minutes.
= 68.0674
(b)A simple random sample of size n = 7 is drawn from a population. The sample mean is found to be and the sample standard deviation is found to be s = 1.7094.
The Z-score corresponding to 90% confidence level is 1.645
( ,
(66.9285 - 1.0628, 66.9285 + 1.0628)
(65.8657, 67.9913)
(c) Now, we need to predict the mean well-being index composite score of Jane, whose commute time is 20 minutes.
= 68.0674
(d) The 90% confidence interval for the mean wellbeing index composite score of Jane, whose commute time is 20 minutes.
A simple random sample of size n = 7 is drawn from a population. The sample mean is found to be and the sample standard deviation is found to be s = 1.7094.
The Z-score corresponding to 90% confidence level is 1.645
( ,
(68.3 - 1.0628, 68.3 + 1.0628)
(67.2372, 69.3628)
(e) The prediction made in part (a) is an estimate of the mean wellbeing index composite score for all individuals whose commute time is 20 minutes. The prediction made in part (c) is an estimate of the well being index composite score of one individual, Jane, whose commute time is 20 minutes.