*Please use excel when anwsering. We don\'t use formulas, just excel. The truste
ID: 3300846 • Letter: #
Question
*Please use excel when anwsering. We don't use formulas, just excel.
The trustee of a firm's pension plan has solicited the opinions of a sample of the firm's employees about a proposed revision of the plan. Is there sufficient evidence at the 5% level to infer that the responses differ among the three groups of employees?
Actual Responses Responses Blue-collar workers White-collar workers Managers For 58 31 13 Against 72 19 7 Expected Responses Responses Blue-collar workers White-collar workers Managers For Against p =Explanation / Answer
Solution:
Here, we have to use chi square test to check the hypothesis or claim whether there is sufficient evidence that the responses differ among the three groups of employees or not. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: There is sufficient evidence to infer that responses differ among three groups of employees.
Alternative hypothesis: Ha: There is insufficient evidence to infer that responses differ among three groups of employees.
The level of significance or alpha value is given as 0.05 or 5%.
The test statistic formula is given as below:
Chi square = [(O – E)^2/E]
Where, O is observed or actual responses and E is expected responses.
E is calculated as below:
E = (Row total * Column total)/Grand total
Calculations for this test are summarises as below:
Actual Responses (O)
Responses
Blue-collar workers
White-collar workers
Managers
Total
For
58
31
13
102
Against
72
19
7
98
Total
130
50
20
200
Expected Responses (E)
Responses
Blue-collar workers
White-collar workers
Managers
Total
For
66.3
25.5
10.2
102
Against
63.7
24.5
9.8
98
Total
130
50
20
200
p =
0.04711951
O
E
(O - E)
(O - E)^2
(O - E)^2/E
58
66.3
-8.3
68.89
1.039064857
72
63.7
8.3
68.89
1.081475667
31
25.5
5.5
30.25
1.18627451
19
24.5
-5.5
30.25
1.234693878
13
10.2
2.8
7.84
0.768627451
7
9.8
-2.8
7.84
0.8
Chi square test statistic
6.110136362
P-value
0.047119508
P-value is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that there is sufficient evidence to infer that responses differ among three groups of employees.
There is insufficient evidence to conclude that responses differ among three groups of employees.
Actual Responses (O)
Responses
Blue-collar workers
White-collar workers
Managers
Total
For
58
31
13
102
Against
72
19
7
98
Total
130
50
20
200
Expected Responses (E)
Responses
Blue-collar workers
White-collar workers
Managers
Total
For
66.3
25.5
10.2
102
Against
63.7
24.5
9.8
98
Total
130
50
20
200
p =
0.04711951
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