What you’ll learn8 learning objectivesChoose one objective for a focused lesson, or study the complete topic.6.4.1Samples and populations• understand the distinction between a sample and a population, and appreciate the necessity for randomness in choosing samplesSyllabus objective6.4.2Sampling methods• explain in simple terms why a given sampling method may be unsatisfactory Including an elementary understanding of the use of random numbers in producing random samples. Knowledge of particular sampling methods, such as quota or stratified sampling, is not required.Syllabus objective6.4.3Sample mean• recognise that a sample mean can be regarded as a random variable, and use the facts that E X = n_ i and that Var X n 2 = v_ iSyllabus objective6.4.4Normal distribution• use the fact that X_ i has a normal distribution if X has a normal distributionSyllabus objective6.4.5Sample mean• use the Central Limit Theorem where appropriate Only an informal understanding of the Central Limit Theorem (CLT) is required; for large sample sizes, the distribution of a sample mean is approximately normal.Syllabus objective6.4.6Unbiased estimates• calculate unbiased estimates of the population mean and variance from a sample, using either raw or summarised data Only a simple understanding of the term 'unbiased' is required, e.g. that although individual estimates will vary the process gives an accurate result 'on average'.Syllabus objective6.4.7Mean confidence intervals• 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 usedSyllabus objective6.4.8Proportion confidence intervals• determine, from a large sample, an approximate confidence interval for a population proportion.Syllabus objective