Inferential Statistics
Applied Mathematics, Unit VI. Covers Population and sample; Parameter, statistic and inference; t-test.
About this unit
Inferential statistics is about drawing conclusions about a large group from a small part of it. It is usually impossible or too costly to study every member of a population, so we study a sample and use it to estimate population values and to test claims about them. This unit explains the difference between a population and a sample, how to choose representative samples by simple random and systematic sampling, and the difference between a parameter and a statistic. It introduces sampling distributions, the standard error and the central limit theorem, which justifies using normal-based reasoning for sample means. Finally you apply these ideas in the one-sample t-test for small samples.
How to prepare
- Learn precise definitions: population, sample, parameter, statistic, sampling distribution, standard error, null and alternative hypotheses, level of significance, degrees of freedom.
- Memorise SE = σ/√n and t = (x̄ − μ)/(s/√n) with n − 1 degrees of freedom.
- Practise the full five-step t-test procedure, including the decision rule.
- Expect statement-based questions on the central limit theorem and on sampling methods.
Topics in this chapter
Population and sample
Representative samples, simple random and systematic sampling.
5 questionsParameter, statistic and inference
Statistical significance, sampling distributions and the central limit theorem.
5 questionst-test
One-sample t-test for small samples: hypotheses, degrees of freedom and inference.
5 questions