To investigate whether there is an association between happiness and income leve
ID: 3351368 • Letter: T
Question
To investigate whether there is an association between happiness and income level, we will use data from the 2002 General Social Survey (GSS), cross-classifying a person’s perceived happiness with their family income level. The GSS is a survey of randomly selected U.S. adults who are not institutionalized. Here are the data:
a. Identify the explanatory variable. Is it a categorical variable or a quantitative variable?
b. Identify the response variable. Is it a categorical variable or a quantitative variable?
c. Among above-average-income individuals 0.379 are very happy (110/290); among average income individuals 0.342 are very happy (221/646); and, among below-average- income individuals 0.195 are very happy (83/426). Do the data provide any indication of an association between happiness and income level? Why or why not?
d. Is it okay to conclude that income affects happiness? If yes, explain why. If no, then identify a confounding variable that provides an alternative explanation for the associa- tion between happiness and income level.
Income Above Average average Below Total average 83414 Happy? Pretty happy 159372 249780 94 168 290 646426 1,362 Very happy 110221 Not too happy 21 53 TotalExplanation / Answer
Answer:
a. Identify the explanatory variable. Is it a categorical variable or a quantitative variable?
Income and categorical variable
b. Identify the response variable. Is it a categorical variable or a quantitative variable?
Happy and categorical variable.
c. Among above-average-income individuals 0.379 are very happy (110/290); among average income individuals 0.342 are very happy (221/646); and, among below-average- income individuals 0.195 are very happy (83/426). Do the data provide any indication of an association between happiness and income level? Why or why not?
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
Total
fo-fe
R1
110
221
83
414
21.8502
24.6388
-46.4890
R2
159
372
249
780
-7.0793
2.0441
5.0352
R3
21
53
94
168
-14.7709
-26.6828
41.4537
Total
290
646
426
1362
Expected Frequencies
Column variable
Row variable
C1
C2
C3
Total
(fo-fe)^2/fe
R1
88.14978
196.3612
129.489
414
5.4161
3.0916
16.6904
R2
166.0793
369.9559
243.9648
780
0.3018
0.0113
0.1039
R3
35.77093
79.68282
52.54626
168
6.0994
8.9351
32.7029
Total
290
646
426
1362
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
3
Degrees of Freedom
4
Results
Critical Value
9.488
Chi-Square Test Statistic
73.3525
p-Value
0.0000
Reject the null hypothesis
Calculated chi square = 73.35 which is > 9.488, chi square critical value at 0.05 level. Ho is rejected.
Yes, the data provide enough evidence that there is an association between happiness and income level.
d. Is it okay to conclude that income affects happiness? If yes, explain why. If no, then identify a confounding variable that provides an alternative explanation for the association between happiness and income level.
No, it is not appropriate to conclude that income affects happiness. confounding variables may be job satisfaction , quality of life etc.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
Total
fo-fe
R1
110
221
83
414
21.8502
24.6388
-46.4890
R2
159
372
249
780
-7.0793
2.0441
5.0352
R3
21
53
94
168
-14.7709
-26.6828
41.4537
Total
290
646
426
1362
Expected Frequencies
Column variable
Row variable
C1
C2
C3
Total
(fo-fe)^2/fe
R1
88.14978
196.3612
129.489
414
5.4161
3.0916
16.6904
R2
166.0793
369.9559
243.9648
780
0.3018
0.0113
0.1039
R3
35.77093
79.68282
52.54626
168
6.0994
8.9351
32.7029
Total
290
646
426
1362
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
3
Degrees of Freedom
4
Results
Critical Value
9.488
Chi-Square Test Statistic
73.3525
p-Value
0.0000
Reject the null hypothesis
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