Homework SourseThe table below shows the group and favorite category of 668
The table below shows the group and favorite category of 668 randomly selected people. Cat. A Cat. B Cat. C Group 1. 50 85 73 Group 2. 68 91 60 Group 3. 90 74 77 Use a 5 percent level of significance to test the null hypothesis that group and preferred category type are independent. Test Statistic: ________________ P-value: _________________ Critical Value: ________________ Conclusion about H0: ____________________
Comment
| Cat A Cat B Cat C | |
|---|---|
| Group1 | 50 85 73 |
| Group 2 | 68 91 60 |
| Group3 | 90 74 77 |
Solution
The table below shows the group and favorite category of 668 randomly selected people. Cat. A Cat. B Cat. C Group 1. 50 85 73 Group 2. 68 91 60 Group 3. 90 74 77 Use a 5 percent level of significance to test the null hypothesis that group and preferred category type are independent.
Null hypothesis: Group and preferred category type are independent
Alternate hypothesis: Group and preferred category type are not independent
Test Statistic: 12.9542
P-value: 0.0115
Critical Value: 9.4877
Conclusion about H0: Reject Ho
Comment : we conclude that Group and preferred category type are not independent
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
Total
fo-fe
R1
50
85
73
208
-14.7665
7.1557
7.6108
R2
68
91
60
219
-0.1916
9.0389
-8.8473
R3
90
74
77
241
14.9581
-16.1946
1.2365
Total
208
250
210
668
Expected Frequencies
Column variable
Row variable
C1
C2
C3
Total
(fo-fe)^2/fe
R1
64.7665
77.8443
65.3892
208
3.3667
0.6578
0.8858
R2
68.1916
81.9611
68.8473
219
0.0005
0.9968
1.1369
R3
75.0419
90.1946
75.7635
241
2.9816
2.9078
0.0202
Total
208
250
210
668
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
3
Degrees of Freedom
4
Results
Critical Value
9.4877
Chi-Square Test Statistic
12.9542
p-Value
0.0115
| Chi-Square Test | ||||||||
| Observed Frequencies | ||||||||
| Column variable | Calculations | |||||||
| Row variable | C1 | C2 | C3 | Total | fo-fe | |||
| R1 | 50 | 85 | 73 | 208 | -14.7665 | 7.1557 | 7.6108 | |
| R2 | 68 | 91 | 60 | 219 | -0.1916 | 9.0389 | -8.8473 | |
| R3 | 90 | 74 | 77 | 241 | 14.9581 | -16.1946 | 1.2365 | |
| Total | 208 | 250 | 210 | 668 | ||||
| Expected Frequencies | ||||||||
| Column variable | ||||||||
| Row variable | C1 | C2 | C3 | Total | (fo-fe)^2/fe | |||
| R1 | 64.7665 | 77.8443 | 65.3892 | 208 | 3.3667 | 0.6578 | 0.8858 | |
| R2 | 68.1916 | 81.9611 | 68.8473 | 219 | 0.0005 | 0.9968 | 1.1369 | |
| R3 | 75.0419 | 90.1946 | 75.7635 | 241 | 2.9816 | 2.9078 | 0.0202 | |
| Total | 208 | 250 | 210 | 668 | ||||
| Data | ||||||||
| Level of Significance | 0.05 | |||||||
| Number of Rows | 3 | |||||||
| Number of Columns | 3 | |||||||
| Degrees of Freedom | 4 | |||||||
| Results | ||||||||
| Critical Value | 9.4877 | |||||||
| Chi-Square Test Statistic | 12.9542 | |||||||
| p-Value | 0.0115 |
