A-level · Hypothesis testing

Setting up a hypothesis testExam-style questions

The language and structure of a binomial hypothesis test: the population proportion p, the null hypothesis H0 : p = p0 and the alternative hypothesis H1, deciding between a one-tailed (p < p0 or p > p0) and a two-tailed (p ≠ p0) test from the wording, the test statistic X ~ B(n, p0) under H0, and what the significance level means.

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9 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
A manufacturer claims that $30\%$ of its chocolates are dark. A sample of $20$ is taken to test whether the proportion of dark chocolates is greater than claimed. Let $X$ be the number of dark chocolates and $p$ the population proportion.
(a) State the null and alternative hypotheses.
(b) State the distribution of $X$ under the null hypothesis.
Level 2 · 3 marksTry it
2
In a binomial hypothesis test, explain what is meant by
(a) the test statistic, and (b) the significance level.
Level 2 · 2 marksTry it
3
A coin is suspected of being biased (in either direction). It is tossed $30$ times to test this. Write down suitable hypotheses for a test of the probability $p$ of heads.
Level 3 · 2 marksTry it
4
A treatment normally succeeds for $40\%$ of patients. A trial on $25$ patients is run to test whether a new version has a lower success rate. State the hypotheses and the distribution of the test statistic under $H_0$ .
Level 3 · 2 marksTry it
5
Explain why the alternative hypothesis $H_1: p > 0.2$ leads to a one-tailed test, whereas $H_1: p \ne 0.2$ leads to a two-tailed test.
Level 3 · 2 marksTry it

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