Sampling and estimation

Sampling: Populations, Samples and RandomnessSign up

understand the purpose of sampling and recognise common sampling methods (simple random, stratified, systematic, quota, cluster, opportunity), including their advantages and disadvantages

The Sample Mean as a Random Variable and the Central Limit TheoremSign up

understand and use the result that if X has mean μ and variance σ^2, then the sample mean of n independent observations has mean μ and variance σ^2 / n, and is normally distributed when X is normal or n is large (central limit theorem)

Unbiased Estimates and Confidence Intervals for a MeanSign up

be able to construct and interpret confidence intervals for a population mean when σ is known (using the normal distribution) and when σ must be estimated (using the t distribution)

Confidence Interval for a Population ProportionSign up

determine, from a large sample, an approximate confidence interval for a population proportion (p-hat +/- z*sqrt(p-hat(1-p-hat)/n)) · interpret the proportion confidence interval in context and recognise the large-sample (normal approximation) validity conditions