Question

An analysis of the time headways resulted in a model for the time elapsed between the arrival of consecutive vehicles on urban roads. Following are 137 arrival times (in seconds) along with the values expected from the theoretical model Observed Expected Time 0-2 2-4 4-6 6-8 8-10 10-12 12-18 18-22 < 22 18 28 14 7 23 18 16 13 10 20 30 19 Can you conclude that the theoretical model does not explain the observed val well? Test using -5%
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Answer #1

Test statistic

chi^2 = sum rac{(O_i-E_i)^2}{Ei}

(30 19) 19 2 (18 23)2 (28 18) 18

X-21.475

Degrees of freedom = 9 - 1 = 8

Hence,

p - Value = P(chi^2_8 > 21.475) = 0.0060

Since this p - value is less than 0.05, we reject Ho. Hence,

We have sufficient evidence to conclude that the theoratical model doesnot explain the observed values.

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