Question

5B) In Ontario we have a three-tiered graduation system for attaining a “Driver’s License”; G₁, G₂ 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.

1. State the Null and Alternative Hypotheses (1)
2. Prepare the appropriate PDF and state the Decision Rule (1,1)
3. Determine the test value. (5)
4. What is the decision? (1)
5. What are the odds of having an accident resulting in death with the driver having the New Brunswick license versus the driver with the Ontario license? In other words, determine the Unadjusted Odds Ratio (4)
6. Now we want to determine whether the Unadjusted Odds Ratio is significant.
   1. State the Hypothesis (1)
   2. If appropriate, prepare the PDF and state the Decision Rule (1)
   3. Perform the test (3)
   4. Is this a significant result? In other words, what is your Decision? (1)
   5. Is your Decision the same at 99% confidence? Why or why not? (1)
7. What is your Interpretation of the entire question? (looking for two or three statements) (1)

Answer 1

(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.