Lesson O1-O2

O1-O2 Hypothesis testing for a binomial proportion Quiz: AQA Maths, Unit 11

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson O1-O2, Hypothesis testing for a binomial proportion: 20 multiple choice questions for the AQA Maths (7357), Unit 11: Statistics, written with Revision Ninja.

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The 20 questions

  1. In hypothesis testing, what does the null hypothesis represent?

    • Sample statistic
    • Critical region
    • Default parameter value
    • Alternative outcome

  2. The significance level of a test equals the probability of which event?

    • Rejecting true $\text{H}_0$
    • Rejecting false $\text{H}_0$
    • Accepting false $\text{H}_0$
    • Accepting true $\text{H}_0$

  3. What condition must the alternative hypothesis specify to use a one-tailed test?

    • Non-directional change
    • No change
    • Exact equality
    • Directional change

  4. For a population proportion $p$, which alternative hypothesis requires a two-tailed test?

    • $p < p_0$
    • $p = p_0$
    • $p > p_0$
    • $p \neq p_0$

  5. What is the critical region of a hypothesis test?

    • Sample mean range
    • Range where $p > 0.05$
    • Range accepting $\text{H}_0$
    • Range rejecting $\text{H}_0$

  6. What does the p-value measure in a hypothesis test?

    • Significance level
    • Critical value
    • Test statistic
    • Probability

  7. If the $p$-value is less than the significance level, what decision is made?

    • Accept $\text{H}_0$
    • Reject $\text{H}_1$
    • Change significance level
    • Reject $\text{H}_0$

  8. What is the main goal of taking a sample from a population in statistics?

    • Calculate exact parameters
    • Infer population parameters
    • Change population size
    • Eliminate sample bias

  9. The significance level of a hypothesis test is equal to the probability of what?

    • Accepting $\text{H}_0$
    • Type I error
    • Type II error
    • Correct rejection

  10. Under H0: B(10, 0.3), H1: p < 0.3, what is the conclusion for x = 0 at 5% significance?

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

  11. Under H0: B(10, 0.3), H1: p < 0.3, what is the conclusion for x = 1 at 5% significance?

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

  12. For X ~ B(20, 0.5), a two-tailed test at 5% gives observed X = 15. What is the conclusion?

    • Accept H0
    • Reject H0
    • Test is inconclusive
    • Do not reject H0

  13. What does rejecting H0 at the 5% level indicate about the alternative hypothesis?

    • H0 is proven true
    • Sufficient evidence exists
    • No evidence exists
    • H1 is proven true

  14. What does a p-value of 0.03 indicate about the probability that H0 is true?

    • Nothing about P(H0)
    • It equals 0.05
    • It equals 0.97
    • It equals 0.03

  15. For X ~ B(10, 0.3) with H1: p < 0.3 at the 5% level, what is the critical region?

    • Empty set
    • {0}
    • {0, 1, 2}
    • {0, 1}

  16. For X ~ B(20, 0.5), a two-tailed test at 5% gives observed X = 6. What is the conclusion?

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

  17. What is a Type I error in hypothesis testing?

    • Accepting false H0
    • Accepting true H0
    • Rejecting true H0
    • Rejecting false H0

  18. What is the test statistic when testing a binomial proportion?

    • Sample mean
    • Standard deviation
    • Sample variance
    • Number of successes

  19. A test yields a p-value of 0.04. What is the conclusion at the 1% level?

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

  20. A test for positive correlation yields p-value = 0.02 at the 5% level. What is concluded?

    • Proof of causation
    • No correlation exists
    • H0 is true
    • Evidence of correlation

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