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
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
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...
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