Sample proportions

Mathematical Methods · Unit 4 — Further calculus, trigonometry and statistics · Sampling and proportions

Learning objectives (2)

LO-1Understand 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 √𝑝(1 − 𝑝)/𝑛 of the sample proportion 𝑝̂, where 𝑛 is the sample size.LO-2Use 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.

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