A civil engineer has been studying the frequency of vehicle accidents on a certa

Question

A civil engineer has been studying the frequency of vehicle accidents on a certain stretch of interstate
highway. Long-term history indicates that there has been an average of 1.78 accidents per day on this
section of the interstate. Let r be a random variable that represents number of accidents per day. Let 0
represent the number of observed accidents per day based on local highway patrol reports. A random
sample of 87 days gave the following information.

r I 0 , 1 , 2 , 3 , 4or more

o I 20, 24, 12, 16, 15

The civil engineer wants to use a Poisson distribution to represent the probability of r, the number of
accidents per day. The Poisson distribution is

e-X;1,r

P(r)=-,-

ri

where A = 1.78 is the average number of accidents per day. Compute the sample statistic.

2 J (0-E)2

X=k-I E

8.761

11.465

5.289

0.787

0.580

Explanation / Answer

here average number of accidents r =1.78

therefore applying chi square goodness of fit test on above:

therefore test statisitc is  11.465

observed Expected Chi square Type Probability O E=total*p =(O-E)^2/E 0 0.169 20.000 14.67 1.94 1 0.300 24.000 26.12 0.17 2 0.267 12.000 23.24 5.44 3 0.159 16.000 13.79 0.35 4 or more 0.106 15.000 9.18 3.69 1 87 87 11.5886

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