The following data were taken from teh 2012 General Social Survey regarding the
ID: 3133150 • Letter: T
Question
The following data were taken from teh 2012 General Social Survey regarding the political views and income of 3763 people:
Political views in 3 categories * Income in 3 categories Crosstabulation
Income in 3 categories
Total
0-$19999
$20000-$34999
$35000+
Political views in 3 categories
Liberal
Count
268
119
146
533
% within income3
25.8%
28.2%
28.5%
27.0%
Moderate
Count
402
150
161
713
% within income3
38.7%
35.5%
31.4%
36.1%
Conservative
Count
370
153
205
728
% within income3
35.6%
36.3%
40.0%
36.9%
Total
Count
1040
422
512
1974
% within income3
100.0%
100.0%
100.0%
100.0%
Answer the following based on the table and information provided:
What is the independent variable? What set of hypothesis is being tested here? Based on this crosstab, does there appear to be an association between political views and income in this sample and if so describe the association. If you were going to calculate a chi square statistic, what would be the expected frequency of income 0- $19999 among people who are liberal. If you calculated it out, you would find that the chi square test statistic for this sample = 8.14, with a p-value (significance) of 0.087. In plain English, with this information, what would you conclude about political views and income in the US population?
Political views in 3 categories * Income in 3 categories Crosstabulation
Income in 3 categories
Total
0-$19999
$20000-$34999
$35000+
Political views in 3 categories
Liberal
Count
268
119
146
533
% within income3
25.8%
28.2%
28.5%
27.0%
Moderate
Count
402
150
161
713
% within income3
38.7%
35.5%
31.4%
36.1%
Conservative
Count
370
153
205
728
% within income3
35.6%
36.3%
40.0%
36.9%
Total
Count
1040
422
512
1974
% within income3
100.0%
100.0%
100.0%
100.0%
Explanation / Answer
Chi square test for independence
What is the independent variable? What set of hypothesis is being tested here? Based on this crosstab, does there appear to be an association between political views and income in this sample and if so describe the association. If you were going to calculate a chi square statistic, what would be the expected frequency of income 0- $19999 among people who are liberal. If you calculated it out, you would find that the chi square test statistic for this sample = 8.14, with a p-value (significance) of 0.087. In plain English, with this information, what would you conclude about political views and income in the US population?
Solution:
Here, we have to use the chi square test for independence.
The independent variables are given as income in three categories and political views in three categories.
The null and alternative hypothesis for this chi square test for independence is given as below:
Null hypothesis: H0: The two variables income in three categories and political views in three categories are independent.
Alternative hypothesis: Ha: The two variables income in three categories and political views in three categories are not independent.
We assume the level of significance for this test as alpha = 0.05 or 5%.
The chi square test is given as below:
Chi square test of independence for checking the independence between the two variables income in three categories and political views in three categories
Observed Frequencies
Income in three categories
Political views in three categories
0-$19999
$20000-$34999
$35000+
Total
Liberal
268
119
146
533
Moderate
402
150
161
713
Conservative
370
153
205
728
Total
1040
422
512
1974
Expected Frequencies
Income in three categories
Political views in three categories
0-$19999
$20000-$34999
$35000+
Total
Liberal
280.810537
113.9442756
138.245187
533
Moderate
375.6433637
152.4245187
184.932118
713
Conservative
383.5460993
155.6312057
188.822695
728
Total
1040
422
512
1974
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
3
Degrees of Freedom
4
Results
Critical Value
9.487729037
Chi-Square Test Statistic
8.13754601
p-Value
0.086667681
Do not reject the null hypothesis
Expected frequency assumption
is met.
Here, we get the p-value as 0.087 which is greater than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis that the two variables income in three categories and political views in three categories are independent.
Chi square test of independence for checking the independence between the two variables income in three categories and political views in three categories
Observed Frequencies
Income in three categories
Political views in three categories
0-$19999
$20000-$34999
$35000+
Total
Liberal
268
119
146
533
Moderate
402
150
161
713
Conservative
370
153
205
728
Total
1040
422
512
1974
Expected Frequencies
Income in three categories
Political views in three categories
0-$19999
$20000-$34999
$35000+
Total
Liberal
280.810537
113.9442756
138.245187
533
Moderate
375.6433637
152.4245187
184.932118
713
Conservative
383.5460993
155.6312057
188.822695
728
Total
1040
422
512
1974
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
3
Degrees of Freedom
4
Results
Critical Value
9.487729037
Chi-Square Test Statistic
8.13754601
p-Value
0.086667681
Do not reject the null hypothesis
Expected frequency assumption
is met.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.