Homework SourseAragon Equipment Inc is a tractor manufacturer that is begin
Aragon Equipment, Inc. is a tractor manufacturer that is beginning to realize the importance of sales data in marketing its products. Its two main products are The Incisor, a tractor used in large agricultural settings, and The Caddy, a smaller tractor primarily used in landscape. The company divides its market into four geographic regions: Great Lakes, Ohio Valley, Mid-Atlantic, and Corn Belt. With the aim of maximally allocating its resources, Aragon decides to investigate whether there is a relationship between geographic location and the type of tractor sold.
Table 1 (below), a contingency table, summarizes sales data from 500 Aragon tractor sales. Each cell of Table 1 contains three numbers: the first number is the observed cell frequency (f0); the second number is the expected cell frequency (fE) under the assumption that there is no relationship between the type of tractor sold and the geographic region of the sale; and the third number is the value
(f0
| (f0 |
Solution
Type of tractor
Great Lakes
Ohio Valley
Mid-Atlantic
Corn belt
Total
The Incisor
153
85
61
89
388
147.44
79.15
55.87
105.54
0.209
0.432
0.47
2.592
The Caddy
37
17
11
47
112
42.56
22.85
16.12
30.46
0.726
1.498
1.626
8.981
Total
190
102
72
136
500
Table 2: Summary of the Hypothesis Test
The type of test statistic
Z, t, Chi Square, F
The value of the test statistic:
(Round your answer to at least two decimal places.)
16.53
The critical value for a test at the 0.05 level of significance:
(Round your answer to at least two decimal places.)
7.82
Can we conclude that there is a relationship between the type of Argon tractor sold and the geographic region of the sale? Use the 0.05 level of significance.
Yes
Comment
| Type of tractor | Great Lakes | Ohio Valley | Mid-Atlantic | Corn belt | Total | |
| The Incisor | 153 | 85 | 61 | 89 | 388 | |
| 147.44 | 79.15 | 55.87 | 105.54 | |||
| 0.209 | 0.432 | 0.47 | 2.592 | |||
| The Caddy | 37 | 17 | 11 | 47 | 112 | |
| 42.56 | 22.85 | 16.12 | 30.46 | |||
| 0.726 | 1.498 | 1.626 | 8.981 | |||
| Total | 190 | 102 | 72 | 136 | 500 |
