A-level · Beta
Statistical hypothesis testing
See critical regions and test binomial proportions or normal means.
Choose a model and alternative hypothesis, then set the evidence and significance level.
Reject H₀: the result is in the critical region.
- Observed successes
- 15 of 20
- p-value (approx.)
- 0.020695
- Chosen significance
- 5%
- Actual critical probability
- 2.0695%
- Critical successes
- 15, 16, 17, 18, 19, 20
Red bars are the critical region under H₀; the green line marks the observed result. Two-tailed tests use at most α/2 in each tail and p = min(1, 2 × smaller inclusive tail). Discreteness can make the actual level lower than α. A p-value is not P(H₀ is true).
Predict, test and explain
Step 1 of 3
Predict
Does not rejecting H₀ prove that H₀ is true?
Explore and compare
Choose the investigation above. Predict what will change before you move a control.
Try it in the simulation. Change one thing at a time.
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Hints, self-check and connections
Try a self-check
Fixed values, separate from the diagram controls.
Does not rejecting H₀ prove that H₀ is true?
Hint
State hypotheses about a population parameter before using the evidence.
Reveal answer
A hypothesis test assesses how unusual the evidence is under H₀; its p-value is not the probability that H₀ is true.
Build an explanation
Hint 1
State hypotheses about a population parameter before using the evidence.
Hint 2
A hypothesis test assesses how unusual the evidence is under H₀; its p-value is not the probability that H₀ is true.
Hint 3
Use the model to check a prediction, then explain the result.
Worked example
This example uses fixed values, separate from the diagram controls.
Under H₀, X ~ Bin(10, 0.5). Test H₁: p > 0.5 when X = 9 at 5%.
- Use the upper inclusive tail P(X ≥ 9).
- Add P(X = 9) and P(X = 10) = (10 + 1)/1024.
- The p-value is approximately 0.01074, below 0.05.
Answer: Reject H₀; evidence supports a greater population proportion.
Connect this idea
Watch out: A hypothesis test assesses how unusual the evidence is under H₀; its p-value is not the probability that H₀ is true.
Specification and learning route
AQA O1, O2, O3 · Edexcel Statistics 5.1, Statistics 5.2, Statistics 5.3
AS core; A-level extension. This model illustrates selected content; references are not a claim of full coverage or exam-board endorsement.
Useful starting knowledge: Probability; Binomial probabilities; Samples and population parameters; Normal distribution for normal-mean tests.