Statistical Hypothesis Testing — A-Level Mathematics Revision
Revise Statistical Hypothesis Testing for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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Go to Regression & CorrelationWhat is Statistical Hypothesis Testing?
Statistical hypothesis testing at A-Level involves using a sample of data to make an inference about a population parameter. You will learn to set up a null hypothesis and an alternative hypothesis, and use a test statistic to decide whether to reject the null hypothesis.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover statistical hypothesis testing for the binomial and normal distributions. The specific contexts of the problems can vary.
Step-by-step explanationWorked example
A coin is tossed 10 times and lands on heads 8 times. Test, at the 5% significance level, whether the coin is biased towards heads. The null hypothesis is H0: p=0.5, and the alternative hypothesis is H1: p>0.5. Let X be the number of heads. We are testing P(X>=8) with X~B(10, 0.5). P(X>=8) = P(X=8) + P(X=9) + P(X=10) = 10C8(0.5)^10 + 10C9(0.5)^10 + 10C10(0.5)^10 = (45+10+1)/1024 = 56/1024 = 0.0547. Since 0.0547 > 0.05, we do not reject the null hypothesis. There is not enough evidence to suggest the coin is biased towards heads.
Mini lesson for Statistical Hypothesis Testing
1. Understand the core idea
Statistical hypothesis testing at A-Level involves using a sample of data to make an inference about a population parameter. You will learn to set up a null hypothesis and an alternative hypothesis, and use a test statistic to decide whether to reject the null hypothesis.
Can you explain Statistical Hypothesis Testing without copying the notes?
2. Turn it into marks
A coin is tossed 10 times and lands on heads 8 times. Test, at the 5% significance level, whether the coin is biased towards heads.
Underline the method, evidence, or command-word move that would earn credit in A-Level Statistics.
3. Fix the likely mark leak
Watch for this mistake: Confusing the null hypothesis and the alternative hypothesis. The null hypothesis is a statement of no effect or no difference, while the alternative hypothesis is the statement you are trying to find evidence for.
Write one correction rule before doing another practice question.
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Jump into adaptive, exam-style questions for Statistical Hypothesis Testing. Free to start; sign in to save progress.
Statistical Hypothesis Testing practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one A-Level sentence, explain what Statistical Hypothesis Testing is testing.
Answer: Statistical hypothesis testing at A-Level involves using a sample of data to make an inference about a population parameter. You will learn to set up a null hypothesis and an alternative hypothesis, and use a test statistic to decide whether to reject the null hypothesis.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Statistical Hypothesis Testing question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Confusing the null hypothesis and the alternative hypothesis. The null hypothesis is a statement of no effect or no difference, while the alternative hypothesis is the statement you are trying to find evidence for." What should their next repair task be?
Answer: Do one Statistical Hypothesis Testing question and review the mistake type.
Mark focus: Error correction and next-step practice.
Statistical Hypothesis Testing flashcards
Core idea
What is the main idea in Statistical Hypothesis Testing?
Statistical hypothesis testing at A-Level involves using a sample of data to make an inference about a population parameter. You will learn to set up a null hypothesis and an alternative hypothesis, and use a test sta...
Common mistake
What mistake should you avoid in Statistical Hypothesis Testing?
Confusing the null hypothesis and the alternative hypothesis. The null hypothesis is a statement of no effect or no difference, while the alternative hypothesis is the statement you are trying to find evidence for.
Practice
What is one useful practice task for Statistical Hypothesis Testing?
Answer one Statistical Hypothesis Testing question and review the mistake type.
Exam board
How should you use board notes for Statistical Hypothesis Testing?
All A-Level Maths boards (AQA, Edexcel, OCR) cover statistical hypothesis testing for the binomial and normal distributions. The specific contexts of the problems can vary.
Common mistakes
- 1Confusing the null hypothesis and the alternative hypothesis. The null hypothesis is a statement of no effect or no difference, while the alternative hypothesis is the statement you are trying to find evidence for.
- 2Making errors in determining the critical region for a hypothesis test. This depends on the significance level of the test and whether it is a one-tailed or two-tailed test.
- 3Incorrectly interpreting the result of a hypothesis test. A non-significant result does not prove that the null hypothesis is true; it simply means that there is not enough evidence to reject it.
Statistical Hypothesis Testing exam questions
Exam-style questions for Statistical Hypothesis Testing with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Statistical Hypothesis Testing
Core concept
Statistical hypothesis testing at A-Level involves using a sample of data to make an inference about a population parameter. You will learn to set up a null hypothesis and an alternative hypothesis, a…
Frequently asked questions
What is a p-value?
The p-value is the probability of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is true. If the p-value is less than the significance level, you reject the null hypothesis.
What is the difference between a one-tailed and a two-tailed test?
A one-tailed test is used when the alternative hypothesis is directional (e.g., p > 0.5 or p < 0.5). A two-tailed test is used when the alternative hypothesis is non-directional (e.g., p ≠ 0.5).