5B) In Ontario we have a three-tiered graduation system for attaining a “Driver’s License”; G_{1}, G_{2} and the G license. In New Brunswick, my home province, there is only one; either you get it or you don’t.
I wanted to look at the efficacy of these two systems. Does having a three-tiered system result in fewer traffic mortalities? We did not consider accidents but mortalities since the latter was an easier number to attain; especially from a historical perspective. (After all, if we considered an accident, then we would have to consider the severity and all other definables.)
So we went back in history and randomly looked at 20,000 reported accidents. The data are as follows:
Did the Accident result in Death? |
|||||
Location |
Yes |
No |
Total |
||
New Brunswick |
65 |
7,935 |
8,000 |
||
Ontario |
35 |
11,965 |
12,000 |
||
Total |
100 |
19,900 |
20,000 |
From these data and using the Chi-squared test, test the claim at 95% confidence that there is a relationship between the type of driver’s license (location issued) and the number of accidents resulting in death.
(a)
The null hypothesis is:
H0: There is no relationship between the type of driver’s license (location issued) and the number of accidents resulting in death.
The alternative hypothesis is
Ha: There is a relationship between the type of driver’s license (location issued) and the number of accidents resulting in death.
(b)
Degree of freedom: df =( number of rows -1)*(number of columns-1) = (2-1)*(2-1)=1
The critical value of chi square using excel function "=CHIDIST(0.05,1)" is 0.8230.
Rejection region:
If , reject H0
(c)
Expected frequencies will be calculated as follows:
Following table shows the expected frequencies:
Expected Frequency (E) | |||
Location | Yes | No | Total |
New Brunswick | 40 | 7960 | 8,000 |
Ontario | 60 | 11940 | 12,000 |
Total | 100 | 19900 | 20,000 |
Following table shows the calculations for chi square test statistics:
O | E | (O-E)^2/E |
65 | 40 | 15.625 |
35 | 60 | 10.41666667 |
7,935 | 7960 | 0.078517588 |
11,965 | 11940 | 0.052345059 |
Total | 26.17252931 |
Following is the test statistics:
(d)
Since test statistics lies in the rejection region so we reject the null hypothesis. That is we can conclude that there is a relationship between the type of driver’s license (location issued) and the number of accidents resulting in death.
5B) In Ontario we have a three-tiered graduation system for attaining a “Driver’s License”; G1, G2...
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