Is the composition of state legislatures in the House of Rep

Is the composition of state legislatures in the House of Representative related to the specific state? Use  

? = 0.01.

Democrat

Republican

Pennsylvania

100

103

Ohio

39

59

West Virginia

75

25

Maryland

106

35

Show the table of observed and expected values and complete the output to include the following steps: the null and alternative hypothesis, the chi-square value, the p-value, and make a decision whether to reject H0 or not to reject H0 and write a valid conclusion based on the claim.

	Democrat	Republican
Pennsylvania	100	103
Ohio	39	59
West Virginia	75	25
Maryland	106	35

Solution

Is the composition of state legislatures in the House of Representative related to the specific state? Use  ? = 0.01.

Null hypothesis: The composition of state legislatures in the House of Representative not related to the specific state

Alternate hypothesis: The composition of state legislatures in the House of Representative related to the specific state

Chi-Square Test

Observed Frequencies

Column variable

Calculations

Democrat

Republican

Total

fo-fe

Pennsylvania

100

103

203

-19.8524

19.8524

Ohio

39

59

98

-18.8598

18.8598

West Virginia

75

25

100

15.9594

-15.9594

Maryland

106

35

141

22.7528

-22.7528

Total

320

222

542

Expected Frequencies

Column variable

Democrat

Republican

Total

(fo-fe)^2/fe

Pennsylvania

119.8524

83.1476

203

3.2884

4.7400

Ohio

57.8598

40.1402

98

6.1475

8.8612

West Virginia

59.0406

40.9594

100

4.3140

6.2184

Maryland

83.2472

57.7528

141

6.2187

8.9639

Total

320

222

542

Data

Level of Significance

0.01

Number of Rows

4

Number of Columns

2

Degrees of Freedom

3

Results

Critical Value

11.345

Chi-Square Test Statistic

48.7520

p-Value

<0.001

Calculate chi square value =48.752, which is > 11.345, the table value at n0.01 level

P<0.001 which is less than 0.01, the level of significance.

The null hypothesis is rejected.

We conclude that the composition of state legislatures in the House of Representative related to the specific state.

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
	Democrat	Republican	Total		fo-fe
Pennsylvania	100	103	203		-19.8524	19.8524
Ohio	39	59	98		-18.8598	18.8598
West Virginia	75	25	100		15.9594	-15.9594
Maryland	106	35	141		22.7528	-22.7528
Total	320	222	542
Expected Frequencies
	Column variable
	Democrat	Republican	Total		(fo-fe)^2/fe
Pennsylvania	119.8524	83.1476	203		3.2884	4.7400
Ohio	57.8598	40.1402	98		6.1475	8.8612
West Virginia	59.0406	40.9594	100		4.3140	6.2184
Maryland	83.2472	57.7528	141		6.2187	8.9639
Total	320	222	542
Data
Level of Significance	0.01
Number of Rows	4
Number of Columns	2
Degrees of Freedom	3
Results
Critical Value	11.345
Chi-Square Test Statistic	48.7520
p-Value	<0.001