Homework SourseIt is suspected that the tendency of an automobile to catch
It is suspected that the tendency of an automobile to catch fire in a rear-end collision is not independent of the make of the car. To support this contention, a random sample of 200 cars involved in rear end collisions is selected from past records. Each car is classified as to make and whether or not it is one of the cars suspected of being especially susceptible to fire under these circumstances. The data gathered is shown in table 15.15. Is there evidence of an association between this make of car and the presence of fire when involved in a rear-end collision? Explain.
Table 15.15
Suspect Make
Fire Yes No
Yes 9 31
No 16 144
Solution
It is suspected that the tendency of an automobile to catch fire in a rear-end collision is not independent of the make of the car. To support this contention, a random sample of 200 cars involved in rear end collisions is selected from past records. Each car is classified as to make and whether or not it is one of the cars suspected of being especially susceptible to fire under these circumstances. The data gathered is shown in table 15.15. Is there evidence of an association between this make of car and the presence of fire when involved in a rear-end collision? Explain.
Table 15.15
Suspect Make
Fire Yes No
Yes 9 31
No 16 144
Null hypothesis: There is no association between make of car and the presence of fire when involved in a rear-end collision
Alternate hypothesis: There is association between make of car and the presence of fire when involved in a rear-end collision
Chi square test used.
Chi-Square Test
Observed Frequencies
suspect make
Calculations
fire
yes
no
Total
fo-fe
yes
9
31
40
4
-4
no
16
144
160
-4
4
Total
25
175
200
Expected Frequencies
suspect make
fire
yes
no
Total
(fo-fe)^2/fe
yes
5
35
40
3.2000
0.4571
no
20
140
160
0.8000
0.1143
Total
25
175
200
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
2
Degrees of Freedom
1
Results
Critical Value
3.841
Chi-Square Test Statistic
4.5714
Chi square value at 0.05 level =3.841
Calculated chi square =4.5714 > 3.841 the table value.
The null hypothesis is rejected.
At the 5% level of significance, we conclude that there is an association between make of car and the presence of fire when involved in a rear-end collision.
| Chi-Square Test | ||||||
| Observed Frequencies | ||||||
| suspect make | Calculations | |||||
| fire | yes | no | Total | fo-fe | ||
| yes | 9 | 31 | 40 | 4 | -4 | |
| no | 16 | 144 | 160 | -4 | 4 | |
| Total | 25 | 175 | 200 | |||
| Expected Frequencies | ||||||
| suspect make | ||||||
| fire | yes | no | Total | (fo-fe)^2/fe | ||
| yes | 5 | 35 | 40 | 3.2000 | 0.4571 | |
| no | 20 | 140 | 160 | 0.8000 | 0.1143 | |
| Total | 25 | 175 | 200 | |||
| Data | ||||||
| Level of Significance | 0.05 | |||||
| Number of Rows | 2 | |||||
| Number of Columns | 2 | |||||
| Degrees of Freedom | 1 | |||||
| Results | ||||||
| Critical Value | 3.841 | |||||
| Chi-Square Test Statistic | 4.5714 |
