Two way table and inference for categorical data (10 points) A random sample of
ID: 3059116 • Letter: T
Question
Two way table and inference for categorical data
(10 points) A random sample of 710 United States citizens 18 years and older was asked, “What is your primary concern about this country?” In addition, they were asked to define themselves as a Democrat, Republican, or Independent. The results of this survey are seen in the table below.
Political Affiliation
Concerns
Democrat
Republican
Independent
Total
War
45
95
18
158
Economy
102
89
31
222
Environment
50
31
19
100
Health Care
88
53
48
189
Other
17
15
9
41
Total
302
283
125
710
This is an r × c table. What is the value of the number c?
What is the proportion of all people that considered themselves Independent?
What is the proportion of Democrats who believe that health care is the primary concern facing the United States?
Suppose we wish to test the null hypothesis that there is no association between a person’s political affiliation and their primary concern about the United States.
Under the null hypothesis, what is the expected number of Republicans that believe war is the primary concern for the United States is?
Under the null hypothesis, the expected number Democrats who believe the environment is the primary concern for the United States is 42.54. What is the chi-square component of this cell?
Under the null hypothesis, what are the degrees of freedom for the chi-square test statistic?
Excel calculates the P-value for this test to be 0.000. What is your conclusion from the test?
Political Affiliation
Concerns
Democrat
Republican
Independent
Total
War
45
95
18
158
Economy
102
89
31
222
Environment
50
31
19
100
Health Care
88
53
48
189
Other
17
15
9
41
Total
302
283
125
710
Explanation / Answer
Two way table and inference for categorical data
(10 points) A random sample of 710 United States citizens 18 years and older was asked, “What is your primary concern about this country?” In addition, they were asked to define themselves as a Democrat, Republican, or Independent. The results of this survey are seen in the table below.
Political Affiliation
Concerns
Democrat
Republican
Independent
Total
War
45
95
18
158
Economy
102
89
31
222
Environment
50
31
19
100
Health Care
88
53
48
189
Other
17
15
9
41
Total
302
283
125
710
This is an r × c table. What is the value of the number c?
What is the proportion of all people that considered themselves Independent?
What is the proportion of Democrats who believe that health care is the primary concern facing the United States?
Suppose we wish to test the null hypothesis that there is no association between a person’s political affiliation and their primary concern about the United States.
Under the null hypothesis, what is the expected number of Republicans that believe war is the primary concern for the United States is?
Under the null hypothesis, the expected number Democrats who believe the environment is the primary concern for the United States is 42.54. What is the chi-square component of this cell?
Under the null hypothesis, what are the degrees of freedom for the chi-square test statistic?
Excel calculates the P-value for this test to be 0.000. What is your conclusion from the test?
Political Affiliation
Concerns
Democrat
Republican
Independent
Total
War
45
95
18
158
Economy
102
89
31
222
Environment
50
31
19
100
Health Care
88
53
48
189
Other
17
15
9
41
Total
302
283
125
710
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