Over a lifetime, about 1.5% of people in the US will develop cancer of the blood

Question

Over a lifetime, about 1.5% of people in the US will develop cancer of the blood (leukemia, lymphoma, and myeloma, LLM If you want to abbreviate). Villestadt is a town with a population of 2700 people. We can treat this as a random sample of people in the US. If there are 135 towns of similar size of Villestadt in the US, would it be considered unusual to see one of them with a rate this high just by random chance? In Villestadt, 60 of the 2700 residents have come down with cancer of the blood. A manufacturing plant near the town has been blamed for the elevated rate of blood Cancers

Explanation / Answer

p = 60/2700 = 1/45, P = 0.015, n = 2700
= sqrt(P*(1-P)/n) = 0.002339278

z = (p-P)/ = 3.087
significance level 0.05, p-value = 0.001(right tailed)

0.001*135 = 0.135 is the expected frequency for 135 towns and therefore it would be considered unusual to see one of them with a rate this high just by random chance

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