Homework SourseSamples of the members of five different labor unions were a
Samples of the members of five different labor unions were asked whether they are for or against a
certain piece of legislation: please show all work
Union 1 Union 2 Union 3 Union 4 Union 5 Total
For 74 81 69 75 91
Against 26 19 31 25 9
a)Use the 1% level of significance to test the null hypothesis that the corresponding true proportions are all
equal.
b)Find the matrix of expected values:
c)What test is appropriate for this problem?
Solution
Samples of the members of five different labor unions were asked whether they are for or against a
certain piece of legislation: please show all work
Union 1 Union 2 Union 3 Union 4 Union 5 Total
For 74 81 69 75 91
Against 26 19 31 25 9
a)Use the 1% level of significance to test the null hypothesis that the corresponding true proportions are all
equal.
Calculations
fo-fe
-4
3
-9
-3
13
4
-3
9
3
-13
(fo-fe)^2/fe
0.2051
0.1154
1.0385
0.1154
2.1667
0.7273
0.4091
3.6818
0.4091
7.6818
Data
Level of Significance
0.01
Number of Rows
2
Number of Columns
5
Degrees of Freedom
4
Results
Critical Value
13.277
Chi-Square Test Statistic
16.5501
p-Value
0.0024
Reject the null hypothesis
Calculate d chi square =16.5501 > 13.277 the table value
The null hypothesis is rejected
We conclude that corresponding true proportions are not equal.
b)Find the matrix of expected values:
Expected Frequencies
Column variable
Row variable
union1
union2
union3
union4
union5
Total
for
78
78
78
78
78
390
against
22
22
22
22
22
110
Total
100
100
100
100
100
500
c)What test is appropriate for this problem?
Chi square test is appropriate for the problem
| Calculations | ||||
| fo-fe | ||||
| -4 | 3 | -9 | -3 | 13 |
| 4 | -3 | 9 | 3 | -13 |
| (fo-fe)^2/fe | ||||
| 0.2051 | 0.1154 | 1.0385 | 0.1154 | 2.1667 |
| 0.7273 | 0.4091 | 3.6818 | 0.4091 | 7.6818 |
