MathematicsCode 9709
Sampling and estimation
What this topic asks you to be able to do
- understand how a sample differs from a population, and appreciate why samples have to be picked at random
- account for, in plain language, why a particular sampling method might not be suitable
- recognise that the mean of a sample can be thought of as a random variable in its own right, and apply the results E_X i = n and Var X n 2 = v _ i
- apply the result that _X i follows a normal distribution whenever X is normally distributed
- apply the Central Limit Theorem in situations where it is suitable to do so
- work out unbiased estimates of a population's mean and variance from a sample, whether the data are raw or summarised
- work out a confidence interval for the mean of a population, and say what it tells you, in two cases: the population is normal with known variance, or the sample is large
- work out an approximate confidence interval for the proportion in a population, based on a large sample