Lesson O3

O3 Hypothesis test for the mean of a Normal distribution Quiz: AQA Maths, Unit 11

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson O3, Hypothesis test for the mean of a Normal distribution: 20 multiple choice questions for the AQA Maths (7357), Unit 11: Statistics, written with Revision Ninja.

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The 20 questions

  1. For sample mean x-bar from N(mu, sigma^2), what is the correct test statistic Z?

    • (mu - x-bar) / (sigma / n)
    • (x-bar - mu) / (sigma * sqrt(n))
    • (x-bar - mu) / sigma
    • (x-bar - mu) / (sigma / sqrt(n))

  2. What are the critical values for a 2-tail test of a mean at the 5% level with known variance?

    • 1.96 only
    • -1.645 and 1.645
    • -1.96 and 1.96
    • 0 and 1.96

  3. For an upper 1-tail test at the 5% level, the critical value of Z is approximately:

    • 2.326
    • 1.282
    • 1.645
    • 1.96

  4. When the population variance is known, which distribution is used for the sample mean in a test?

    • The Normal distribution
    • The uniform distribution
    • The exponential distribution
    • The binomial distribution

  5. What is the variance of the sample mean x-bar for sample size n?

    • sigma^2 / n
    • sigma^2 / sqrt(n)
    • sigma / sqrt(n)
    • sigma / n

  6. A two-tailed Normal test at 5% gives test statistic Z = 1.6. What is the conclusion?

    • Reject H1
    • Do not reject H0
    • Reject H0
    • Accept H1

  7. A one-tailed upper Normal test at 5% gives Z = 1.6. What is the conclusion?

    • Accept H1
    • Reject H1
    • Do not reject H0
    • Reject H0

  8. A sample of 25 from N(mu, 9) gives x-bar = 21.5. What is Z for H0: mu = 20?

    • Z = 1.5
    • Z = 0.5
    • Z = 2.5
    • Z = 1.25

  9. For the test in which Z = 2.5 as a 2-tail test, what is the approximate p-value?

    • 0.012
    • 0.006
    • 0.994
    • 0.025

  10. Testing H0: mu = 50 against H1: mu > 50 at 1% gives Z = 2. What is the conclusion?

    • Do not reject H0
    • Accept H1
    • Reject H0
    • Reject H1

  11. A test rejects H0: mu = 500 in favour of H1: mu > 500 at 5%. What is the conclusion?

    • Evidence supports H0
    • Evidence supports H1
    • Insufficient evidence for H1
    • Proves H1 is true

  12. What is the significance level of a hypothesis test equal to?

    • P(Type I error)
    • P(Type II error)
    • P(H0 is true)
    • P(H1 is true)

  13. A sample gives Z = 1.6 in a 2-tail test. Approximately what is the p-value?

    • 0.05
    • 0.95
    • 0.89
    • 0.11

  14. A sample of 9 from N(mu, 4) has mean 12. What is the calculated Z-statistic for H0: mu = 10?

    • 1.5
    • 4.5
    • 2
    • 3

  15. If the sample size is quadrupled while keeping the sample mean constant, how does Z change?

    • It doubles
    • It quadruples
    • It stays equal
    • It halves

  16. What is the critical value for a 2-tail test at the 1% level with known variance?

    • 2.576
    • 1.645
    • 1.96
    • 2.326

  17. In a standard Z-test for a Normal mean, how is the population variance treated?

    • Calculated from data
    • Assumed known
    • Estimated from sample
    • Variable

  18. A hypothesis test gives a p-value of 0.03. What is the conclusion at the 5% significance level?

    • Inconclusive
    • Accept H0
    • Do not reject H0
    • Reject H0

  19. Testing H0: mu = 30 with known sigma = 0.5 and n = 4 gives x-bar = 30.4. What is Z?

    • 0.8
    • 1.6
    • 3.2
    • 1.96

  20. When should the significance level and hypotheses be set in a hypothesis test?

    • After calculating p-value
    • After collecting data
    • During data collection
    • Before collecting data

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