the definition of sample proportion as a random variable and key features of the distribution of sample proportions
U34.AoS4.4
statistical inference, including definition and distribution of sample proportions, simulations and confidence intervals:
- distinction between a population parameter and a sample statistic and the use of the sample statistic to estimate the population parameter
- simulation of random sampling, for a variety of values of 𝑝 and a range of sample sizes, to illustrate the distribution of 𝑃^ and variations in confidence intervals between samples
- concept of the sample proportion as a random variable whose value varies between samples, where 𝑋 is a binomial random variable which is associated with the number of items that have a particular characteristic and 𝑛 is the sample size
- approximate normality of the distribution of P^ for large samples and, for such a situation, the mean 𝑝 (the population proportion) and standard deviation
- determination and interpretation of, from a large sample, an approximate confidence interval for a population proportion where 𝑧 is the appropriate quantile for the standard normal distribution, in particular the 95% confidence interval as an example of such an interval where 𝑧 ≈ 1.96 (the term standard error may be used but is not required).
U34.AoS4.12
simulate repeated random sampling and interpret the results, for a variety of population proportions and a range of sample sizes, to illustrate the distribution of sample proportions and variations in confidence intervals
