Homework Sourse102 Do men and women select different breakfasts The breakfa
102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance.
| French toast | Pancakes | Waffles | Omelettes | |
| Men | 47 | 35 | 28 | 53 |
| Women | 65 | 39 | 55 | 60 |
Solution
102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance.
Null hypothesis: men and women select same breakfasts
Alternate hypothesis: men and women select different breakfasts
Chi-Square Test
Observed Frequencies
Column variable
Calculations
French toast
Pancakes
Waffles
Omelettes
Total
fo-fe
Men
47
35
28
53
163
-0.7906
3.4241
-7.4162
4.7827
Women
65
39
55
60
219
0.7906
-3.4241
7.4162
-4.7827
Total
112
74
83
113
382
Expected Frequencies
Column variable
French toast
Pancakes
Waffles
Omelettes
Total
(fo-fe)^2/fe
Men
47.7906
31.5759
35.4162
48.2173
163
0.0131
0.3713
1.5530
0.4744
Women
64.2094
42.4241
47.5838
64.7827
219
0.0097
0.2764
1.1559
0.3531
Total
112
74
83
113
382
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
4
Degrees of Freedom
3
Results
Critical Value
7.815
Chi-Square Test Statistic
4.2068
At 5% level, 3 Df table value =7.815
Calculated chi square =4.2068 < table value
The null hypothesis is not rejected
We conclude that men and women select same breakfasts.
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
C4
Total
fo-fe
R1
47
35
28
53
163
1.587065
-3.11443
-5.65423
7.181592
R2
65
59
55
60
239
-1.58706
3.114428
5.654229
-7.18159
Total
112
94
83
113
402
Expected Frequencies
Column variable
Row variable
C1
C2
C3
C4
Total
(fo-fe)^2/fe
R1
45.41294
38.11443
33.65423
45.81841
163
0.055464
0.254488
0.949964
1.125645
R2
66.58706
55.88557
49.34577
67.18159
239
0.037827
0.173563
0.647883
0.767699
Total
112
94
83
113
402
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
4
Degrees of Freedom
3
Results
Critical Value
7.814728
Chi-Square Test Statistic
4.012533
p-Value
0.260114
Do not reject the null hypothesis
| Chi-Square Test | ||||||||||
| Observed Frequencies | ||||||||||
| Column variable | Calculations | |||||||||
| French toast | Pancakes | Waffles | Omelettes | Total | fo-fe | |||||
| Men | 47 | 35 | 28 | 53 | 163 | -0.7906 | 3.4241 | -7.4162 | 4.7827 | |
| Women | 65 | 39 | 55 | 60 | 219 | 0.7906 | -3.4241 | 7.4162 | -4.7827 | |
| Total | 112 | 74 | 83 | 113 | 382 | |||||
| Expected Frequencies | ||||||||||
| Column variable | ||||||||||
| French toast | Pancakes | Waffles | Omelettes | Total | (fo-fe)^2/fe | |||||
| Men | 47.7906 | 31.5759 | 35.4162 | 48.2173 | 163 | 0.0131 | 0.3713 | 1.5530 | 0.4744 | |
| Women | 64.2094 | 42.4241 | 47.5838 | 64.7827 | 219 | 0.0097 | 0.2764 | 1.1559 | 0.3531 | |
| Total | 112 | 74 | 83 | 113 | 382 | |||||
| Data | ||||||||||
| Level of Significance | 0.05 | |||||||||
| Number of Rows | 2 | |||||||||
| Number of Columns | 4 | |||||||||
| Degrees of Freedom | 3 | |||||||||
| Results | ||||||||||
| Critical Value | 7.815 | |||||||||
| Chi-Square Test Statistic | 4.2068 |
