From Don: Assume: Leukemia occurs at an incidence of 1 in 10,000.
Benzene is a known carcinogen which causes Leukemia and has been found in toxic levels in the homes of a community of 1200 people.
Question: How many cases of Leukemia would be necessary to reject the null hypothesis. That is, to suggest that statistically, the cases are more likely due to benzene exposure rather than chance.
From Donna Hall: A skeptic gives the following argument to show that there must be a flaw in the central limit theorem: We know that the sum of independent Poisson random variables follows a Poisson distribution with a parameter that is the sum of the parameters of the summands. In particular, if n independent Poisson random variables, each with parameter 1/n, are summed, the sum has a Poisson distribution with parameter 1. The central limit theoren says the sum tends to a normal distribution, but Poisson distribution with parameter 1 is not normal.
What do you think of this argument?
Answered by Neal Madras.
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