Conduct a chi-square test of the hypotheses: H 0 : VOTE00 and REGION are indepen

Question

Conduct a chi-square test of the hypotheses:

H0: VOTE00 and REGION are independent
Ha: VOTE00 and REGION are dependent

the expected frequency table under H0 is ,

1172

Computation of chi-square....

2.075561

a. The value of the test statistic is:   
round your answer to two decimal places

b. The contribution to the chi-square statistic for "did vote" and "mountain region" is:  

f. The largest contribution to the chi-square statistic came from the cell count for which two categories?
(Note: one category will be from the row variable and one will be from the column variable.)

West south central

Middle Atlantic

Did not vote

Pacific

Voted

Mountain

East south central

East north central

Ineligible

West north central

New England

g. For which two categories did the expected and observed counts differ the least?
(Again, one category will be from the row variable and one will be from the column variable.)

Voted

Pacific

Ineligible

East north central

Middle Atlantic

New England

East south central

West south central

Did not vote

Mountain

West north central

South Atlantic

   1 2 3 4 5 6 7 8 9 207.7979 721.5908 928.7551 381.3851 1107.411 322.4668241 571.4442 382.6522 742.4973 91.04227 316.1498 406.9145 167.0959 485.1887 141.2820543 250.3662 167.651 325.3096 28.57898 99.24227 127.7341 52.45289 152.3051 44.34970484 78.59221 52.62715 102.1176 0.580874 2.017119 2.596222 1.066116 3.095632 0.901416765 1.597403 1.069658 2.075561 Total 328 1139 1466 602 1748 509 902 604

1172

Explanation / Answer

Conduct a chi-square test of the hypotheses:

For this chi square test we have the following null and alternative hypothesis.

Null hypothesis: H0: The variables Region and vote are independent.

Alternative hypothesis: Ha: The variables region and vote are not independent.

We consider the level of significance or alpha value for this test as 5% or 0.05.

The formula for test statistic is given as below:

Chi square = [(O – E)^2/E]

The test is given as below:

Chi-Square Test

Observed Frequencies

Region

Vote00

New England

Middle Atantic

E.Nor.Central

W.Nor.Central

South Atalantic

E.South central

W south central

Mountain

Pacific

Total

Voted

231

748

975

406

1030

314

539

395

728

5366

Did not vote

69

296

365

155

575

151

287

159

294

2351

Ineligible

27

91

122

40

141

42

76

49

150

738

Refused to answer

1

4

4

1

2

2

0

1

0

15

Total

328

1139

1466

602

1748

509

902

604

1172

8470

Expected Frequencies

Region

Vote00

New England

Middle Atantic

E.Nor.Central

W.Nor.Central

South Atalantic

E.South central

W south central

Mountain

Pacific

Total

Voted

207.7978749

721.590791

928.7551358

381.385124

1107.410626

322.4668241

571.4441558

382.6521842

742.497285

5366

Did not vote

91.04226682

316.1498229

406.9145218

167.0958678

485.1886659

141.2820543

250.3662338

167.6510035

325.309563

2351

Ineligible

28.57898465

99.24226682

127.7341204

52.45289256

152.3050767

44.34970484

78.59220779

52.62715466

102.117591

738

Refused to answer

0.580873672

2.017119244

2.59622196

1.066115702

3.095631641

0.901416765

1.597402597

1.069657615

2.0755608

15

Total

328

1139

1466

602

1748

509

902

604

1172

8470

Data

Level of Significance

0.05

Number of Rows

4

Number of Columns

9

Degrees of Freedom

24

Results

Critical Value

36.4150285

Chi-Square Test Statistic

89.68814519

p-Value

1.6234E-09

Reject the null hypothesis

Expected frequency assumption

The value for test statistic for this test is given as chi square = 89.6881.

The p-value for this test is given as 0.00 approximately.

Level of significance or alpha value = 0.05

For this test we get the p-value as the 0.00 approximately which is less than the alpha value or level of significance 0.05, so we reject the null hypothesis that the variables Region and vote are independent. This means we concluded that the variables region and vote are not independent.

Chi-Square Test

Observed Frequencies

Region

Vote00

New England

Middle Atantic

E.Nor.Central

W.Nor.Central

South Atalantic

E.South central

W south central

Mountain

Pacific

Total

Voted

231

748

975

406

1030

314

539

395

728

5366

Did not vote

69

296

365

155

575

151

287

159

294

2351

Ineligible

27

91

122

40

141

42

76

49

150

738

Refused to answer

1

4

4

1

2

2

0

1

0

15

Total

328

1139

1466

602

1748

509

902

604

1172

8470

Expected Frequencies

Region

Vote00

New England

Middle Atantic

E.Nor.Central

W.Nor.Central

South Atalantic

E.South central

W south central

Mountain

Pacific

Total

Voted

207.7978749

721.590791

928.7551358

381.385124

1107.410626

322.4668241

571.4441558

382.6521842

742.497285

5366

Did not vote

91.04226682

316.1498229

406.9145218

167.0958678

485.1886659

141.2820543

250.3662338

167.6510035

325.309563

2351

Ineligible

28.57898465

99.24226682

127.7341204

52.45289256

152.3050767

44.34970484

78.59220779

52.62715466

102.117591

738

Refused to answer

0.580873672

2.017119244

2.59622196

1.066115702

3.095631641

0.901416765

1.597402597

1.069657615

2.0755608

15

Total

328

1139

1466

602

1748

509

902

604

1172

8470

Data

Level of Significance

0.05

Number of Rows

4

Number of Columns

9

Degrees of Freedom

24

Results

Critical Value

36.4150285

Chi-Square Test Statistic

89.68814519

p-Value

1.6234E-09

Reject the null hypothesis

Expected frequency assumption

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