Pearson Edexcel · A-Level · Mathematics
Course version: 9MA0 · Version from Mar 2026
Understand and apply the language of statistical hypothesis testing,…
Full specification wording
Statistical hypothesis testing: 5.1 Understand and apply the language of statistical hypothesis testing, developed through a binomial model: null hypothesis, alternative hypothesis, significance level, test statistic, 1-tail test, 2-tail test, critical value, critical region, acceptance region, p-value; extend to correlation coefficients as measures of how close data points lie to a straight line, and be able to interpret a given correlation coefficient using a given p-value or critical value (calculation of correlation coefficients is excluded).
A hypothesis test starts with a null hypothesis H₀, usually a claim about a population parameter, and an alternative hypothesis H₁ stating the direction or difference being tested.
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Study notes
From the checked teaching notes for this specification point.
The idea
A hypothesis test starts with a null hypothesis H₀, usually a claim about a population parameter, and an alternative hypothesis H₁ stating the direction or difference being tested. The significance level α is the probability of rejecting H₀ when it is true. The test statistic is calculated from the sample; for a binomial model it is the number of successes X ~ B(n, p). A 1-tail test uses one extreme region, a 2-tail test splits α between both tails. The critical region is the set of test statistic values leading to rejection of H₀; its boundary is the critical value, and the acceptance region is the complement. The p-value is the probability, assuming H₀, of a result at least as extreme as observed. Correlation coefficients measure how closely data lie to a straight line; interpret a given coefficient against a given p-value or critical value, without calculating it.
What earns the marks
- Defines H₀ and H₁ in context, choosing a 1-tail or 2-tail alternative to match the wording of the claim.
- States the significance level and explains it as the probability of incorrectly rejecting a true H₀.
- Identifies the test statistic and its distribution, for example X ~ B(n, p) under H₀.
- Distinguishes the critical value, critical region and acceptance region, and uses them to reach a reject or do-not-reject decision.
- Interprets a p-value by comparing it with the significance level, and interprets a given correlation coefficient using a given p-value or critical value.
Common mistakes and how to put them right
Writing H₁ as an equality.
Put it right by using an inequality such as p > 0.5 or p ≠ 0.5.
Comparing the test statistic directly with the significance level.
Put it right by comparing the p-value with α, or the statistic with the critical value.
Treating a large correlation coefficient as proof of causation.
Put it right by interpreting it only as a measure of linear closeness, subject to the given p-value or critical value.
Exam tips
- Define H₀ and H₁ in words and symbols before calculating anything.
- State whether the test is 1-tail or 2-tail and show how the critical region follows from α.
- Finish with a conclusion in context that refers back to the original claim, not just to H₀.
Try the lesson
The start of the Statistical hypothesis testing: 5.1 Understand and apply the language of statistical hypothesis testing, developed through a binomial model: null hypothesis, alternative hypothesis, significance level, test statistic, 1-tail test, 2-tail test, critical value, critical region, acceptance region, p-value; extend to correlation coefficients as measures of how close data points lie to a straight line, and be able to interpret a given correlation coefficient using a given p-value or critical value (calculation of correlation coefficients is excluded). lesson, made from checked teaching notes for this specification point.
Have a go first
A test is carried out at the 5% significance level. The null hypothesis is rejected when the p-value is less than or equal to 0.05. A researcher obtains a p-value of 0.03. What is the correct conclusion?
Listen
A hypothesis test starts with a null hypothesis H₀, usually a claim about a population parameter, and an alternative hypothesis H₁ stating the direction or difference being tested. The significance level α is the probability of rejecting H₀ when it is true. The test statistic is calculated from the sample; for a binomial model it is the number of successes X ~ B(n, p). A 1-tail test uses one extreme region, a 2-tail test splits α between both tails. The critical region is the set of test statistic values leading to rejection of H₀; its boundary is the critical value, and the acceptance region is the complement. The p-value is the probability, assuming H₀, of a result at least as extreme as observed. Correlation coefficients measure how closely data lie to a straight line; interpret a given coefficient against a given p-value or critical value, without calculating it. A strong answer earns marks for these points. Defines H₀ and H₁ in context, choosing a 1-tail or 2-tail alternative to match the wording of the claim. States the significance level and explains it as the probability of incorrectly rejecting a true H₀. Identifies the test statistic and its distribution, for example X ~ B(n, p) under H₀. Distinguishes the critical value, critical region and acceptance region, and uses them to reach a reject or do-not-reject decision. A common slip: Writing H₁ as an equality. Instead, using an inequality such as p > 0.5 or p ≠ 0.5. Exam tip: Define H₀ and H₁ in words and symbols before calculating anything.
See it
Key words
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Null hypothesis
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Alternative hypothesis
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Significance level
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Test statistic
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See every definition
- Null hypothesis
- A claim about a population parameter, usually written H₀, with which a hypothesis test starts.
- Alternative hypothesis
- Written H₁, it states the direction or difference being tested against the null hypothesis.
- Significance level
- The probability α of rejecting the null hypothesis when it is true.
- Test statistic
- A value calculated from the sample; for a binomial model it is the number of successes X ~ B(n, p).
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Test your understanding of Statistical hypothesis testing: 5.1 Understand and apply the language of statistical hypothesis testing, developed through a binomial model: null hypothesis, alternative hypothesis, significance level, test statistic, 1-tail test, 2-tail test, critical value, critical region, acceptance region, p-value; extend to correlation coefficients as measures of how close data points lie to a straight line, and be able to interpret a given correlation coefficient using a given p-value or critical value (calculation of correlation coefficients is excluded).
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