Use repeated random sampling data, for a variety of values of 𝑝 and a range of sample sizes, to examine the distribution of 𝑝̂ and the approximate standard normality of 𝑝̂−𝑝 √𝑝̂(1−𝑝̂)/𝑛, where the closeness of the approximation depends on both 𝑛 and 𝑝.

mm-u4-t4-s2-d3

Interactive

Does (p̂ − p)/√(p̂(1−p̂)/n) look standard normal?

manipulative

Sample from a Bernoulli population, standardise each sample proportion, and watch the z histogram settle on N(0,1) as n grows and p stays moderate.

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