One-tailed binomial tests for a population proportion and Poisson tests for a mean rate, using the observed count and the relevant cumulative distribution to find the p-value and compare against a hypothesized value such as p or λ.
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.
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.
Nice work completing Binomial and Poisson Tests, here's a quick recap of what we covered:
Exercises checked off
One-tailed binomial tests for a population proportion and Poisson tests for a mean rate, using the observed count and the relevant cumulative distribution to find the p-value and compare against a hypothesized value such as p or λ.
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.
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.
Nice work completing Binomial and Poisson Tests, here's a quick recap of what we covered:
Exercises checked off