Mathematical Methods Β· Unit 4 Β· Sampling and proportions Β· Sample proportions

Understand the concept of the sample proportion 𝑝̂ as a random variable whose value varies between samples, and the formulas for the mean 𝑝 and standard deviation βˆšπ‘(1 βˆ’ 𝑝)/𝑛 of the sample proportion 𝑝̂, where 𝑛 is the sample size.

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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 π‘Μ‚βˆ’π‘ βˆšπ‘Μ‚(1βˆ’π‘Μ‚)/𝑛, where the closeness of the approximation depends on both 𝑛 and 𝑝.
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