Sampling and estimation

What the syllabus asks of you

• understand the distinction between a sample and a population, and appreciate the necessity for randomness in choosing samples
• explain in simple terms why a given sampling method may be unsatisfactory
• recognise that a sample mean can be regarded as a random variable, and use the facts that E(X̄) = μ and that Var(X̄) = σ²/n
• use the fact that X̄ has a normal distribution if X has a normal distribution
• use the Central Limit Theorem where appropriate
• calculate unbiased estimates of the population mean and variance from a sample, using either raw or summarised data
• determine and interpret a confidence interval for a population mean in cases where the population is normally distributed with known variance or where a large sample is used
• determine, from a large sample, an approximate confidence interval for a population proportion.