Is the composition of state legislatures in the House of Representative related
ID: 3435592 • Letter: I
Question
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
Explanation / Answer
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
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