I can find Hypothesis test for poisson distribution on the internet as below example, but seems JMP does not have such test (I can't find cumulative tables for poisson distribution in JMP)? And another question is when the distribution is gamma poisson, how do i modify test method?
Example:
An existing car model is known to break down on average 1.5 times/ per year. Now we want to test if new designed model is less likely to break down with ten randomly selected cars break down a total of 8 times within the first year.
Let X be the number of break downs of the new model of car in a year. X∼Poisson(λ) with λ=1.5. The null and alternative hypotheses will be
H0: λ=1.5
H1: λ <1.5.
We need to decide whether P[X≤8]<α, where α=0.05. Firstly, the expected number of breakdowns λ t =1.5×10=15. We use the cumulative tables with λ t =15 and x=8 to see P[X≤8]=0.0374
P[X≤8] = 0.0374 < 0.05
so we accept the alternative hypothesis. The average rate of breakdowns has decreased.