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 normal population has $\sigma = 4$ . A sample of $25$ has mean $\bar{x} = 21$ . Test, at the $5\%$ level, $H_0: \mu = 20$ against $H_1: \mu > 20$ .
Level 3 · 4 marksTry it
2
A normal population has $\sigma = 10$ . A sample of $40$ has mean $\bar{x} = 53$ . Test at the $5\%$ level $H_0: \mu = 50$ against $H_1: \mu > 50$ .
Level 3 · 4 marksTry it
3
A normal population has standard deviation $\sigma = 5$ . A random sample of $25$ observations has mean $\bar{x} = 52.1$ .

Test, at the $5\%$ significance level, $H_{0}: \mu = 50$ against $H_{1}: \mu > 50$ . (5 marks)
Level 3 · 5 marksTry it
4
A population has standard deviation $\sigma = 12$ . A random sample of $36$ observations has mean $\bar{x} = 97$ .

Test, at the $5\%$ significance level, $H_{0}: \mu = 100$ against $H_{1}: \mu < 100$ . (5 marks)
Level 3 · 5 marksTry it
5
A population has standard deviation $\sigma = 6$ . A random sample of $9$ observations has mean $\bar{x} = 105$ .

Test, at the $5\%$ significance level, $H_{0}: \mu = 100$ against $H_{1}: \mu \neq 100$ . (5 marks)
Level 3 · 5 marksTry it

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