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.AoS4.8
the concept of confidence intervals for proportions, variation in confidence intervals between samples and confidence intervals for estimates
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
U34.AoS4.13
calculate sample proportions and approximate confidence intervals for population proportions
