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Binomial and Poisson Tests
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Hypothesis testing using Binomial and Poisson distributions.
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Binomial test for proportion
AHL AI 4.18
A binomial test for proportion checks whether the number of “successes” in a sample is consistent with a hypothesized population proportion p.
To find the p-value, calculate the probability of observing results at least as extreme as your sample using the binomial distribution. On the calculator, use
bimomcdf(n,p,k−1) for P(X≤k) and
1−bimomcdf(n,p,k−1) for P(X≥k);
Warning: it's easy to mix up the p value and the binomial probability p.
Note: The syllabus guide explicitly notes that only one-tailed Binomial tests will be required.
Poisson test for mean
AHL AI 4.18
A Poisson test for rate checks whether the number of observed events in a sample is consistent with a hypothesized mean rate λ.
To find the p-value, calculate the probability of observing results at least as extreme as your sample using the Poisson distribution. On the calculator, use
poissoncdf(λ,k) for P(X≤k) and
1−poissoncdf(λ,k−1) for P(X≥k);
Note: The syllabus guide explicitly notes that only one-tailed Poisson tests will be required.
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