A-Level Mathematics Revision — Statistical Hypothesis Testing
Revise Statistical Hypothesis Testing for A-Level Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
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What 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 examples
Worked 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.
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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
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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).