Lesson 2.05b

2.05b Hypothesis test for a binomial proportion Quiz: OCR Maths, Unit 15

20 questions

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Lesson 2.05b, Hypothesis test for a binomial proportion: 20 multiple choice questions for the OCR Maths (H240), Unit 15: Statistical Hypothesis Testing, written with Revision Ninja.

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The 20 questions

  1. In a statistical hypothesis test for a binomial distribution, what population parameter is being tested?

    • Sample mean
    • Population variance
    • Sample size
    • Population proportion

  2. What does the significance level represent in a hypothesis test?

    • Critical region size
    • Sample proportion variance
    • Type I error probability
    • Type II error probability

  3. For a discrete binomial test, how does actual significance compare to specified?

    • Less than or equal
    • Always exactly equal
    • Greater than or equal
    • Unrelated to specified

  4. What is the correct null hypothesis for testing whether a coin is biased towards heads?

    • H0: p > 0.5
    • H0: p < 0.5
    • H0: p = 0.5
    • H0: p != 0.5

  5. Which alternative hypothesis corresponds to a two-tailed test for a binomial proportion p0?

    • H1: p < p0
    • H1: p != p0
    • H1: p > p0
    • H1: p = p0

  6. What term describes the set of all outcome values that lead to rejecting H0?

    • Critical region
    • Acceptance region
    • Confidence interval
    • Sample space

  7. If a test p-value is 0.03, what is the decision at 5% significance level?

    • Reject H0
    • Reject H1
    • Inconclusive result
    • Accept H0

  8. If a test p-value is 0.08, what is the decision at 5% significance level?

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

  9. For a two-tailed test at 10% significance, what is the target probability per tail?

    • 2.5%
    • 10%
    • 20%
    • 5%

  10. Why is a sample collected when carrying out a hypothesis test on a population?

    • To guarantee certainty
    • To make inferences
    • To replace census
    • To prove hypotheses

  11. For X ~ B(20, p) under H0: p = 0.5, what is expected number of successes?

    • 10
    • 20
    • 5
    • 15

  12. For X ~ B(10, 0.5), what is the exact probability of obtaining 10 successes?

    • 1/10
    • 1/100
    • 1/1024
    • 1/512

  13. Which tail forms the critical region for a test with alternative hypothesis H1: p < 0.2?

    • Lower tail
    • Both tails
    • Upper tail
    • Central region

  14. What test statistic is directly observed when testing a single binomial proportion?

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

  15. For X ~ B(8, 0.5) and H1: p > 0.5 at 5% significance, find critical region.

    • X = 6, 7, 8
    • X >= 5
    • X = 8
    • X = 7, 8

  16. Why can actual significance level in binomial tests differ from nominal specified level?

    • Variable is continuous
    • Sample is biased
    • Variable is discrete
    • Distribution is normal

  17. If X ~ B(5, 0.5) and observed X = 5, what is one-tailed p-value for H1: p > 0.5?

    • 0.03125
    • 0.0625
    • 0.15625
    • 0.3125

  18. Which condition regarding trials is required for a valid binomial probability model?

    • Unknown trial count
    • Changing probability
    • Dependent trials
    • Independent trials

  19. What boundary value separates the acceptance region from the rejection region in a test?

    • Test statistic
    • p-value
    • Critical value
    • Significance level

  20. When an observed test statistic lies inside the critical region, how is result described?

    • Statistically significant
    • Inconclusive data
    • Not significant
    • Proves H0 true

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