2 In a study on speeding and road safety the government coll

2. In a study on speeding and road safety, the government collects the following data on speeding tickets and accidents from 10,000 drivers over a 1-year period: (a) Test the hypothesis that there is an association between number of speeding tickets and number of accidents. (b) Does this data show that driving faster increases the risk of accidents? If not, give an alternative possible explanation for the result.

Solution

H0: There is no association between number of speeding tickets and no of accidents.

Ha: There is association

Chi square two tailed test.

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Prepare chi square table as follows:

?² Calculations

Two-way Contingency Table

?² = 741.038,     df = 4,     ?²/df = 185.26 ,         P(?² > 741.038) = 0.0000

expected values are displayed in italics
individual ?²values are displayed in (parentheses)

As p value =0 < 0.01, reject null hypothesis at 0.01 significance level.

There is an association and it is statistically evident.

b) Actually for speeding ticket =1 no of accidents is the maximum.

Hence no is the answer.

no accident	1 accident	2 accidents
No ticketc	4852 4575.48 ( 16.71)	832 1019.07 ( 34.34)	54 143.45 ( 55.78)	5738
1 ticket	2844 2943.20 ( 3.34)	746 655.52 ( 12.49)	101 92.28 ( 0.82)	3691
2 ticket	278 455.32 ( 69.05)	198 101.41 ( 92.00)	95 14.28 ( 456.50)	571
	7974	1776	250	10000