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The Poisson Distribution

Simulation Solution

Calculate the mean: 21 points / 25 regions = 0.84

Graphical evidence:

H0: The observed frequencies agree with the expected frequencies

H1: The observed frequencies do not agree with the expected frequencies

Test statistic: (using Excel)

Observed Expected (Observed - Expected)^2/Expected
11 10.79276309 0.003979253
9 9.065920992 0.000479331
3 3.807686817 0.171326589
2 1.066152309 0.817961471
     
    0.993746644

Note: the Expected values are calculated using =25*POISSON(ROW()-2,0.84,FALSE)

p-value: =CHIDIST(0.9937,3) = 0.8028

Conclusion: Since 0.8028 > 0.05, fail to reject the null hypothesis. The observed values follow a Poisson distribution.

Note: The animation on the Overview page should have the Poisson distribution skewed more to the right. Apparently, the author chose a different model for aesthetic reasons.