Hypothesis testing — t-test and chi-squared (IB Math AI HL)
Updated October 2026
One-sample and two-sample t-tests when the population variance is unknown. HL AI expects the null, alternative, test statistic, and p-value each stated explicitly.
Practise Hypothesis testing — t-test and chi-squared with AI marking
Open the full HL AI engine — every question in this unit is worked through with instant AI-graded feedback on your handwritten workings.
Write both hypotheses before any numbers: the null hypothesis H₀ (no difference, no association, or the stated value of the parameter) and the alternative hypothesis H₁.
Decide whether H₁ is one-tailed (greater than, or less than) or two-tailed (not equal to): it changes the p-value your GDC reports.
Use the significance level the question gives, for example 5%.
Find the test statistic and the p-value on your GDC, and write both down.
If the p-value is less than the significance level, reject H₀; otherwise do not reject it. Not rejecting H₀ does not prove it true.
End with a sentence in the context of the question, saying whether there is evidence for H₁.
Worked example
A test of H₀: μ = 50 against H₁: μ > 50 at the 5% significance level gives a p-value of 0.031. State the conclusion.
Compare the p-value with the significance level: 0.031 < 0.05.
So reject H₀.
In context: there is evidence at the 5% level that the population mean is greater than 50.
Answer: Reject H₀: at the 5% level there is evidence that the mean is greater than 50. At the 1% level the same result would not be enough, since 0.031 > 0.01.
Where can I practise hypothesis testing questions?
On the Chi-Square Goodness of Fit, Independence and Error Types questions page: 20 exam-style HL AI questions with full mark schemes, plus free step-by-step worked examples.
Can I use my calculator for hypothesis testing?
Yes: a GDC is allowed on every HL AI paper, so practise the calculator method as well as the working. The t-tests and χ² tests and Confidence intervals guides give the keystrokes for the TI-84 Plus CE, TI-Nspire CX II and Casio fx-CG50.