Significance tests for means, paired data and two samples

Learning objectives

Identify the appropriate t-test for a population mean, a mean difference from paired data or a difference between two population means, define each parameter in context, and state the null and alternative hypotheses

Check the conditions for a t-test — random data, the 10% condition, and a normal population, a large sample or a graph showing no strong skew or outliers, applied to the differences when the data are paired — and justify each with evidence

Calculate the test statistic t = (x̄ − μ₀) ÷ (s/√n) with n − 1 degrees of freedom and its p-value, and state a conclusion in context by comparing the p-value with the significance level

Carry out a paired t-test on the differences from a matched pairs design, and explain why treating paired data as two independent samples is wrong

Carry out a two-sample t-test for a difference between two population means, stating the degrees of freedom used and the conclusion in context

Use a confidence interval to decide the outcome of a two-sided test at the matching significance level, and describe a Type I error or a Type II error for a test about means in context