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The Poisson Distribution

Sample Extension Solution

Calculate the mean: 1000 patrons / 100 minutes = 10

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
2   1.89166374 0.006204456
3   3.78332748 0.162185786
6   6.3055458 0.014805734
9   9.007922572 6.96799E-06
10   11.25990321 0.140974223
15   12.51100357 0.495172364
15   12.51100357 0.495172364
11   11.37363961 0.012274572
10   9.478033009 0.028745367
8   7.290794622 0.068987304
4   5.207710445 0.280077883
3   3.471806963 0.064116989
2   2.169879352 0.013299815
1   1.276399619 0.059853316
1   0.709110899 0.119327554
       
    Sum 1.961204697

Note: the Expected values are calculated using =100*POISSON(ROW()+2,10,FALSE)

p-value: =CHIDIST(1.96,14) = 0.99993

Conclusion: Since 0.99993 > 0.05, fail to reject the null hypothesis. The observed values follow a Poisson distribution.