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Topic 4: Sampling and proportions

Random sampling

3 hours

• Understand the concept of a random sample.
• Understand sources of bias in samples, and procedures to ensure randomness. 1 interactive
• Identify and use procedures to ensure randomness.
• Recognise and use graphical displays of real and simulated data of random samples from various types of distributions, including uniform, Bernoulli, binomial and normal.

Sample proportions

8 hours

• 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 √𝑝(1 − 𝑝)/𝑛 of the sample proportion 𝑝̂, where 𝑛 is the sample size. 1 interactive
• Recognise and use the approximate normality of the distribution of 𝑝̂ for large samples.
• 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. 1 interactive