A-level · Hypothesis testing

Hypothesis testing for a normal meanExam-style questions

Testing a claim about the mean μ of a normal population from a sample, using that the sample mean is N(μ, σ²/n) — forming the test statistic z = (x̄ − μ₀)/(σ/√n) and comparing it to the critical z-value.

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

DifficultyAll Level 3 Level 4 Level 5

1
A population is $N(\mu, 25)$ . A sample of $25$ has mean $\bar{x} = 48$ . Test at the $5\%$ level whether $\mu = 50$ (two-tailed).
Level 4 · 5 marksTry it
2
A population has $\sigma = 8$ . A sample of $16$ has mean $\bar{x} = 104$ . Test at the $1\%$ level $H_0: \mu = 100$ against $H_1: \mu > 100$ .
Level 4 · 4 marksTry it
3
A population has $\sigma = 6$ . A sample of $36$ has mean $\bar{x} = 18$ . Test at the $5\%$ level $H_0: \mu = 20$ against $H_1: \mu < 20$ .
Level 4 · 4 marksTry it
4
A population is $N(\mu, 144)$ . A sample of $9$ has mean $\bar{x} = 44$ . Test at the $5\%$ level whether $\mu = 50$ (two-tailed).
Level 4 · 5 marksTry it
5
A population has standard deviation $\sigma = 8$ . A random sample of $64$ observations has mean $\bar{x} = 73.5$ .

Test, at the $5\%$ significance level, $H_{0}: \mu = 75$ against $H_{1}: \mu \neq 75$ . (5 marks)
Level 4 · 5 marksTry it

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