Records pertaining to the monthly number of job-related injuries were being studied by a federal agency. The values of the past 100 months are:

Injuries per month      Frequency of occurrences

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 underlying distribution is Poisson. Use the level of significance ?= 0.05

(b) Apply the chi-square test to these data to test the hypothesis that the distribution is Poisson with mean 1.0.