Using a sample to say something about a population, and being honest about the uncertainty. The t-distribution handles small samples where the normal would be over-confident.
Syllabus points covered
- Calculate unbiased estimates of the population mean and variance
- Formulate hypotheses and carry out tests for a population mean using a normal distribution
- Use the t-distribution for small samples from a normal population with unknown variance
- Determine and interpret confidence intervals for a population mean and for a difference of means
Common mistakes
- Using the normal distribution where the sample is small and the variance unknown.
- Dividing by n rather than n − 1 when estimating the population variance.
- Reading the t-table with the wrong number of degrees of freedom.
- Stating a conclusion without reference to the context of the question.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questions
- Mark scheme
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Further Mathematics past papers