A-Level Maths · Statistics · Hypothesis testing · last updated 21 October 2026

Hypothesis testing practice questions (A-Level Maths)

This statistics topic covers null and alternative hypotheses, significance levels, one- and two-tailed tests, critical regions and actual significance levels, binomial tests for a proportion, tests for the mean of a normal distribution, and tests for zero correlation. There are no free sample questions on it yet, so this page gives 7 key terms with the formulas typeset, and a door to make an A-Level Maths-style paper on this topic from your own notes. The free exams are typeset PDFs with an answer key; the exam downloads without a signup.

Make a practice exam from your notes →Upload your notesA-Level Maths style preselected; tick "Statistics · Hypothesis testing" on the next screen. Free to try, no card.

Sample questions

No free sample questions on hypothesis testing yet. The key terms below cover what A-Level Maths expects you to know for this topic; to practise it, make a paper from your notes or from the A-Level outline with the unit ticked.

Make a practice exam from your notes →Upload your notes

Key terms

The definitions and formulas A-Level Maths expects for hypothesis testing, typeset as they appear on the paper.

Null and alternative hypotheses: $H_0$ states the parameter has its claimed value; $H_1$ states the direction of the suspected change (one-tailed) or that it has changed (two-tailed). Write them in symbols with the parameter defined in context.
$H_0: p = p_0, \qquad H_1: p > p_0 \;\text{(or } p < p_0, \; p \ne p_0)$
Significance level and critical region: The significance level is the probability of rejecting $H_0$ when it is true. The critical region is the set of values of the test statistic that lead to rejection; for a two-tailed test, split the level between the tails.
Actual significance level: The probability of the critical region under $H_0$ , which for a discrete distribution is smaller than the nominal level because the region cannot match it exactly.
$P(X \in \text{critical region} \mid H_0)$
Binomial hypothesis test: Model the number of successes as $B(n, p_0)$ under $H_0$ , find the probability of the observed value or more extreme, compare with the significance level, and conclude in context without claiming certainty.
$X \sim B(n, p_0), \qquad \text{reject } H_0 \text{ if } P(X \ge x) < \alpha$
Test for the mean of a normal distribution: With known population variance, the sample mean is normal with the same mean and variance divided by $n$ . Standardise the observed sample mean and compare with the critical $z$ value, or find the probability directly.
$\bar{X} \sim N\left(\mu, \frac{\sigma^2}{n}\right), \qquad z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}}$
Test for zero correlation: Tests whether a sample PMCC is evidence of correlation in the population, by comparing $r$ with the critical value from the table for that sample size and significance level.
$H_0: \rho = 0, \qquad H_1: \rho > 0 \;\text{(or } \rho < 0, \; \rho \ne 0)$
Conclusion in context: Say whether the result is significant, whether $H_0$ is rejected, and what that means about the original claim, with hedged language: "there is evidence that..." rather than "it is proved that...".

Frequently asked questions

Are there free hypothesis testing practice questions for A-Level Maths?

Not as a ready-made sample yet. The key terms on this page cover what A-Level Maths expects for hypothesis testing. To practise it, open the generator with the A-Level Maths style, tick "Statistics · Hypothesis testing" and the questions are written from the A-Level outline for that topic; or upload your own notes on it.

How do I make an A-Level Maths practice paper on hypothesis testing from my notes?

Open the create page with the A-Level Maths style preselected, tick "Statistics · Hypothesis testing" under the units to cover (or upload your notes and slides on it), choose the question mix and time limit, and generate. You get a typeset PDF in the A-Level format with a separate answer key, in about a minute. It is free to try, no card needed.

What does A-Level Maths expect you to know about hypothesis testing?

This statistics topic covers null and alternative hypotheses, significance levels, one- and two-tailed tests, critical regions and actual significance levels, binomial tests for a proportion, tests for the mean of a normal distribution, and tests for zero correlation. The terms to have cold: Null and alternative hypotheses, Significance level and critical region, Actual significance level, Binomial hypothesis test, Test for the mean of a normal distribution. Each is defined below with its formula typeset where one applies.

What is the A-Level Maths exam format?

The A-Level Maths guide explains the papers, their timing and mark allocation, with a sample question and mark scheme and the common mistakes, and links to the generator with the A-Level Maths style preselected.

Make an A-Level Maths paper on hypothesis testing from your notes

Open "Pick your exam" with the A-Level Maths style preselected and tick "Statistics · Hypothesis testing", or upload your notes on it. You get a typeset paper in the A-Level format with a separate answer key.