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Records pertaining to the monthly number of jobs-related injuries at an underground coal mine were being studied by a federal agency. The values for the past 100 months were as follows:

Injuries per month Frequency of Occurrence
0 35
1 40
2 13
3 6
4 4
5 1
6 1

a) Apply the chi-square test to these data to test the hypothesis that the underlying distribution is Poisson. Use the level of significance α = 0.05

b) Apply the chi-square test to these data to test the hypothesis that the distribution is Poisson with mean 1.0. Again let α = 0.05

c) What are the differences between parts (a) and (b) and when might each case arise?

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