A Level Maths: Binomial Hypothesis Testing Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
- Binomial Hypothesis Testing (OCR)
- Binomial Hypothesis Testing (Edexcel)
- Binomial Hypothesis Testing Problems (OCR)
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Discrete Distributions (inc. Binomial Distribution) — the binomial distribution is the engine of the test
- Probability — foundational understanding of probability is essential
- Statistical Sampling — provides the context for why we test
A Level Maths binomial hypothesis testing is your first encounter with statistical inference — using sample data to draw conclusions about a population. You set up null and alternative hypotheses about a probability $p$, then use the binomial distribution to decide whether your observed data is sufficiently unlikely to reject the null. This is the foundation for all later hypothesis testing in the course.
You state hypotheses in terms of the population proportion $p$, with the null hypothesis typically $H_0: p = p_0$ for some specified value, and the alternative hypothesis $H_1$ either one-tailed ($p > p_0$ or $p < p_0$) or two-tailed ($p \ne p_0$). You calculate the $p$-value — the probability under the null hypothesis of observing data as extreme as what you actually got. You compare the $p$-value to the significance level (often $5\%$ or $10\%$), and reject the null if the $p$-value is smaller. Equivalently, you find the critical region — the set of values for which you would reject the null — and check whether your observed value falls in it. You write conclusions clearly in the context of the original problem, distinguishing between 'reject $H_0$' and 'sufficient evidence to suggest…'
Binomial hypothesis testing is part of the Statistics strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: for a two-tailed test at significance level $\alpha$, you compare the $p$-value to $\alpha/2$ on each side, not the full $\alpha$; never write 'accept $H_0$' — say 'do not reject $H_0$' or 'insufficient evidence to reject $H_0$', since failing to reject is not proof of truth; check whether the test is one-tailed or two-tailed BEFORE calculating; and write conclusions in CONTEXT — 'there is sufficient evidence that the proportion of left-handed students exceeds $10\%$', not just 'reject $H_0$'.