Binomial & Poisson Tests

Hypothesis testing using Binomial and Poisson distributions.

Exercises

Key Skills

Binomial & Poisson Tests

Hypothesis testing using Binomial and Poisson distributions.

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Exercises

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Practice exam-style binomial & poisson tests problems

Key Skills

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);

for a two-tailed test, double the smaller tail probability.

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);

for a two-tailed test, double the smaller tail probability.

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);

for a two-tailed test, double the smaller tail probability.

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);

for a two-tailed test, double the smaller tail probability.