Question

Here is the interval of time, in seconds, between two white trains passing through the road
major in a city. Whether the time interval can be modeled by the distribution
Exponent? Test at significance level of 0.05.

time lapse 0- 20- 40- 60- 90- 120-180

frequency 41 19 16 13 9 2

Answer 1

lower	upper	mid	f	p	mid * p
0	20	10	41	0.41	4.1
20	40	30	19	0.19	5.7
40	60	50	16	0.16	8
60	90	75	13	0.13	9.75
90	120	105	9	0.09	9.45
120	180	150	2	0.02	3
			100	1	40

hence mean = 40 min

lower	upper	p under null
0	20	0.39346934
20	40	0.23865122
40	60	0.14474928
60	90	0.11773094
90	120	0.05561216
120	180	0.04978707
		1

p theoretical = P(X < x2) - P(X < x1) for each class x1-x2

now

P(X <x) = 1 -e^(-x/mean)

p	Oi	Ei	(Oi-Ei)^2/Ei
0.3935	41	39.3469	0.0694
0.2387	19	23.8651	0.9918
0.1447	16	14.4749	0.1607
0.1177	13	11.7731	0.1279
0.0556	9	5.5612	2.1264
0.0498	2	4.9787	1.7821
1	100	100
		TS	5.2583
	0.0500	critical value	11.0705
		p-value	0.3852

p-value = 0.3852

p-value > 0.05

hence we fail to reject the null hypothesis

we conclude that there is no evidence to reject the hypothesis that does not come from exponential distribution

Exponential distribution is valid