Knowledge organisers

Hypothesis testing: A Level Maths knowledge organiser

Everything to know about hypothesis testing on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Null hypothesis: H₀: the parameter has the value assumed so far, such as p = 0.3.
Alternative hypothesis: H₁: what you suspect instead, such as p > 0.3 (one-tailed) or p ≠ 0.3 (two-tailed).
Significance level: The probability threshold, such as 5%, below which you reject H₀.
Critical region: The values of the test statistic that would lead you to reject H₀.

Key formulas

Formulas marked with a label are given in the exam (we only say so where our formula sheet confirms it). Learn the rest.

Sample meanIn the formula booklet: Edexcel, AQA	\(\bar X\sim N\!\left(\mu,\tfrac{\sigma^2}n\right),\) \(Z=\frac{\bar X-\mu}{\sigma/\sqrt n}\)
Tests: reject \(H_0\) if \(p\)-value \(<\alpha\); two-tailed: \(\alpha/2\) each tail; PMCC test \(H_0\!:\rho=0\)

Worked example

X ~ B(20, p). Test H₀: p = 0.3 against H₁: p > 0.3 at the 5% level, when 10 successes are observed.

Under H₀, P(X ≥ 10) = 0.0480 (3 s.f.)
0.0480 < 0.05, so the result is significant

Answer: Reject H₀: there is evidence at the 5% level that p > 0.3

Common mistakes

Binomial probabilities: "at least" and "more than" read wrongly
Comparing P(X = x) with the significance level instead of a tail probability such as P(X ≥ x)
A conclusion with no context, or one that says H₀ is true

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

Learn the language of hypothesis testing, including null and alternative hypotheses, the test statistic, the significance level and what it means to reject H₀.
Find critical values and critical regions for a binomial hypothesis test at a given significance level, and state the actual significance level of the test.
Carry out one-tailed and two-tailed binomial hypothesis tests, halving the significance level for each tail, and write a conclusion in the context of the problem.
Carry out hypothesis tests for zero correlation using the PMCC and critical values from the tables, writing conclusions in context.
Carry out hypothesis tests for the mean of a normal distribution using the distribution of the sample mean, and write conclusions in context.

The printable sheet

Hypothesis testing knowledge organiser for A Level Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Hypothesis testing knowledge organiser (A Level Maths), A4. Download the PDF.

Revise it next

Other A Level Maths topics: Proof · Algebra and functions · Coordinate geometry · Sequences and series · Trigonometry · Exponentials and logarithms · Differentiation · Integration · Numerical methods · Vectors · Sampling and data · Probability · Binomial and normal distributions · Kinematics · Forces and Newton's laws · Moments · All A Level Maths organisers