IB Maths AI: Chi-Squared & Hypothesis Testing FAQ

Chi-squared and hypothesis testing is the statistical inference content in IB Maths AI's Statistics and Probability topic — covering the chi-squared test for independence and the goodness of fit test. It's examined on Paper 2 (GDC required), usually as one structured question worth 6-12 marks, testing setup, calculation and interpretation.

The independence test checks whether two categorical variables are related, using a contingency table with rows and columns. The goodness of fit test checks whether observed data matches an expected distribution, like a fair die. Both compare a calculated χ² statistic to a critical value or p-value at a stated significance level.

Chi-squared and hypothesis testing appears only in Mathematics: Applications and Interpretation (AI), not in Analysis and Approaches (AA). It sits in Topic 4 (Statistics and Probability), assessed at both SL and HL, with HL adding further hypothesis tests such as the t-test for a population mean.

No — the chi-squared formula is given in the Mathematics AI formula booklet, so you don't need to memorise it. What you do need cold is how to set up expected values, state your hypotheses correctly, choose the right degrees of freedom, and read your GDC's output accurately.

For a contingency table, degrees of freedom equal (rows − 1) × (columns − 1). For a goodness of fit test, it's the number of categories minus 1, minus any extra parameters estimated from the data. Get this step wrong and your critical value — and your entire conclusion — falls apart.

A typical exam question gives a contingency table and asks you to test for association at the 5% significance level. You state H0 (no association), find expected frequencies, calculate χ², compare it to the critical value or p-value, then write a conclusion in context — that last step is where most marks are lost.

The most common mistake is rounding expected frequencies too early, which throws off the whole statistic — keep at least three decimal places until the final step. A close second: writing conclusions in calculator language ('reject H0') instead of context, which is exactly what the mark scheme is looking for.

At SL, you're tested on the chi-squared tests for independence and goodness of fit only. At HL, that content carries over, but you also meet the t-test for a population mean and hypothesis testing for a single parameter — both examined with the same significance-level, p-value logic you first learn at SL.

Your GDC does the heavy calculating — entering the observed values as a matrix and running a χ²-test gives you the test statistic, degrees of freedom and p-value directly. Examiners still expect the hypotheses, degrees of freedom and a written conclusion shown by hand; a bare calculator readout alone won't earn full marks.

Chi-squared and hypothesis testing questions typically appear as one structured question on Paper 2, worth between 6 and 12 marks depending on whether it's SL or HL and how many sub-parts are asked. It's rarely the whole paper — expect it alongside probability distributions or regression in the same statistics question.

Expect 'state' for hypotheses, 'calculate' for the test statistic or p-value, 'determine' for degrees of freedom, and 'interpret' or 'comment on' for your conclusion. 'Interpret' is the term students most often answer too briefly — it wants a full sentence linking your result back to the original context, not a symbol.

Chi-squared and hypothesis testing isn't conceptually hard — the real difficulty is procedural: several dependent steps, so one small slip compounds through the whole answer. Compared with calculus-heavy Maths AI topics like optimisation, most students find statistics topics like this one more accessible, provided they're methodical with each step.

If your child is stronger with real-world data and calculator-based statistics than with algebraic proof, Maths AI — which includes chi-squared and hypothesis testing — usually suits them better than Analysis and Approaches. AA has no equivalent statistical-inference content and leans more heavily on calculus and algebraic rigour throughout.

Past-paper practice matters more here than in almost any other topic, because the question format barely changes year to year. Look for topical worksheets that isolate chi-squared and hypothesis testing specifically, paired with full timed mock papers — that combination of targeted repetition and exam-condition rehearsal is what shifts a 5 to a 7.