Q1) Does happiness depend on one's marital status? Please consider the following set of data collected from a random sample:
|
|
Married
|
Widowed
|
Divorced/Separated
|
Never Married
|
|
Very Happy
|
600
|
63
|
112
|
144
|
|
Somewhat Happy
|
720
|
142
|
355
|
459
|
|
Not Too Happy
|
93
|
51
|
119
|
127
|
Required:
(a) Please write the hypotheses that correspond to the above scenario.
(b) Please conduct a chi square test at an alpha = 0.05 level of significance. Provide your chi square table and output resulting from this analysis.
Q2) The 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 this index can be found at http://www.well-beingindex.com/ (Links to an external site.)
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:
|
Commute Time (in minutes)
|
Gallup-Healthways Well-Being Index Composite Score
|
|
5
|
69.2
|
|
15
|
68.3
|
|
25
|
67.5
|
|
35
|
67.1
|
|
50
|
66.4
|
|
72
|
66.1
|
|
105
|
63.9
|
Source: The Gallup Organization
Required:
(a) Please generate or sketch a scatterplot of these data. Please also briefly explain what conclusions you can draw from this scatterplot.
(b) Please compute the Pearson correlation coefficient (Pearson's r) between commute time and well-being index score.
(c) What can you conclude based on the value of your correlation coefficient and the associated scatterplot? Does a linear relationship exist between commute time and well-being index score? Why or why not?
Q3) An economist was interested in modeling the relationship among annual income, level of education, and work experience. The level of education is the number of years of education beyond eighth grade, so 1 represents completing 1 year of high school, 8 means completing 4 years of college, and so on. Work experience is the number of years employed in the current profession.
From a random sample of 12 individuals, this economist obtained the following data:
|
Work Experience (years)
|
Level of Education
|
Annual Income ($ thousands)
|
|
12
|
6
|
34.7
|
|
14
|
3
|
17.9
|
|
4
|
8
|
22.7
|
|
16
|
8
|
63.1
|
|
12
|
4
|
33.0
|
|
20
|
4
|
41.4
|
|
25
|
1
|
20.7
|
|
8
|
3
|
14.6
|
|
24
|
12
|
97.3
|
|
28
|
9
|
72.1
|
|
4
|
11
|
49.1
|
|
15
|
4
|
52.0
|
Required:
(a) Please state the regression equation corresponding to the above scenario.
(b) Please conduct a regression analysis of these data. Be sure to include (e.g., copy and paste) your relevant regression output as part of your response.
(c) What can you conclude regarding the relationship among annual income, level of education and work experience based on your regression analysis results in part (b)? Be sure to cite relevant numeric indices or results of your regression analysis as part of your response.