Hypothesis testing: chi-squared tests and the t-test

Learning objectives

State a null and an alternative hypothesis in words and in symbols, choose a significance level, and state the decision rule that a p-value below the significance level leads to rejection of the null hypothesis

Carry out a chi-squared test for independence on a contingency table, calculating expected frequencies as (row total × column total)/grand total, finding the degrees of freedom as (rows − 1)(columns − 1), and comparing the statistic with the critical value or the p-value with the significance level

Carry out a chi-squared goodness of fit test by calculating the expected frequencies from the proposed model, and state the degrees of freedom for the test

Explain that the chi-squared approximation requires each expected frequency to be greater than 5, and describe what should be done when a cell does not meet this

Carry out a t-test to compare the means of two populations using technology, choose between a one-tailed and a two-tailed alternative from the wording of the question, and state the assumption that the populations are normally distributed

Write a conclusion in the context of the data, saying whether there is sufficient evidence at the stated level to support the alternative hypothesis, and avoid claiming that the null hypothesis has been proved