Use a pooled two-sample t-test to compare two population means when the samples are independent, the population variances are unknown but assumed equal, and the underlying populations are normally distributed. In IB Mathematics: Applications and Interpretation SL 4.11, perform the calculation using your GDC and interpret the result in context.
Method
| Research claim | Alternative hypothesis |
|---|---|
| The means are different | |
| Population 1 has a greater mean | |
| Population 1 has a smaller mean |
In every case, .
Before testing, check the assumptions: the two samples must be independent, each variable should come from an approximately normal population, and the population variances must be equal. “Equal variances” is the required wording; “similar variances” is not precise enough.
In the GDC, choose the two-sample t-test, enter both lists or the six summary statistics, select pooled, and choose the tail that matches . The calculator performs the test; do not replace the required setup and interpretation with hand calculation.
Worked example
Suppose two independent groups have , , and , , . For a two-tailed pooled t-test, the GDC gives approximately , , and .
Since , reject . There is sufficient evidence at the significance level that the two population means differ.
Exam technique
This SL content can appear on either GDC-active paper. Examiners expect hypotheses involving population means, the correct pooled test, an explicit comparison such as , and a contextual conclusion. A common misconception is to write “accept ” when ; instead, write “there is insufficient evidence to reject .”
