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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