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 a sample mean from a Normal population with known sigma, which expression is the test statistic?

    • (xbar - mu0) / (sigma / sqrt(n))
    • sigma / (xbar - mu0)
    • (xbar - mu0) x sqrt(n) / sigma^2
    • (xbar - mu0) / sigma

  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. Why is sigma/sqrt(n) used as the standard error of the sample mean?

    • Because the population mean changes with n
    • Because the variance of the sample mean is sigma^2/n
    • Because the sample size equals the standard deviation
    • Because n is always divided by sigma

  6. A 2-tail test at 5% gives Z = 1.6. What is the conclusion?

    • Accept H1, since 1.6 is positive
    • Reject H0, since 1.6 is less than 1.645
    • Do not reject H0, since |1.6| is less than 1.96
    • Reject H0, since 1.6 is greater than 1.282

  7. A 1-tail upper test at 5% gives Z = 1.6. What is the conclusion?

    • Do not reject H0, since 1.6 is less than 1.645
    • Accept H1, since the test is one-sided
    • Reject H0, since 1.6 is greater than 1.96
    • Reject H0, since 1.6 is greater than 1.282

  8. A sample of 25 from a Normal population with sigma = 3 has mean 21.5. H0: mu = 20 is tested against H1: mu not equal to 20 at 5%. Which is correct?

    • Z = 0.5, so do not reject H0
    • Z = 1.25, so do not reject H0
    • Z = 2.5, so do not reject H0 at the 5% level
    • Z = 2.5, so reject H0 at the 5% two-tail level

  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. A sample of 36 has mean 52 and sigma = 6. H0: mu = 50 against H1: mu > 50 at the 1% level. What is the conclusion?

    • Reject H0 at 1%, since 2 exceeds 1.645
    • Reject H1 at 1%, since the statistic is positive
    • Do not reject H0 at 1%, since Z = 2 is less than 2.326
    • Reject H0 at 1%, since the sample mean exceeds 50 by 2

  11. A test concludes at the 5% level that the mean fill weight exceeds 500 g. Which statement is the correct interpretation?

    • The mean fill weight is definitely greater than 500 g
    • The mean fill weight is at most 500 g
    • Every bottle weighs more than 500 g
    • There is sufficient evidence at the 5% level that the mean fill weight is greater than 500 g

  12. In a test of a mean at the 5% level, what does the significance level mean?

    • The mean is 5% above the hypothesised value
    • There is a 95% chance that H0 is true
    • There is a 5% chance that H1 is true
    • There is a 5% chance of rejecting H0 when H0 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. Test H0: mu = 10 against H1: mu not equal to 10 at 5%. What is the conclusion?

    • Z = 3, so reject H0
    • Z = 3, so do not reject H0
    • Z = 6, so reject H0
    • Z = 1, so do not reject H0

  15. If the sample size is quadrupled while the observed difference xbar - mu0 stays the same, how does Z change?

    • It stays the same
    • It halves
    • It quadruples
    • It doubles

  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 test with variance assumed known, what does this assumption mean?

    • The variance is assumed to equal the mean
    • The variance is estimated from the sample and is always larger than sigma
    • The mean is assumed to be zero
    • The variance is taken as given and not estimated from the sample in the test

  18. A 2-tail test on a Normal mean gives a p-value of 0.03. What is the conclusion at the 5% level?

    • Do not reject H0 at 5%
    • Accept H1 with certainty
    • Reject H0
    • Accept H0

  19. A manufacturer tests whether mean length is 30 cm with known sigma 0.5. A sample of 4 has mean 30.4. What is the conclusion at the 5% two-tail level?

    • Reject H0, since Z = 1.6 exceeds 1.282
    • Reject H0, since the mean is above 30
    • Do not reject H0, since Z = 0.4
    • Do not reject H0, since Z = 1.6 lies between -1.96 and 1.96

  20. Why must the significance level and hypotheses be chosen before collecting data?

    • To avoid choosing hypotheses that fit the observed data
    • Because the significance level changes with the data
    • Because H1 must be proved by the test
    • Because the null hypothesis can only be tested once the sample is large

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