Lesson 2.05b

2.05b Hypothesis tests Quiz: OCR Maths, Unit 15

20 questions

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Lesson 2.05b, Hypothesis tests: 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. When carrying out a hypothesis test for proportion p, which value of p is assumed true?

    • Critical value
    • Alternative value
    • Hypothesised value
    • Sample proportion

  2. What is the maximum probability of incorrectly rejecting H0 when H0 is true called?

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

  3. Why is the actual significance level in a binomial test often less than the nominal level?

    • Discrete distribution
    • Two-tailed test
    • Continuous distribution
    • Biased sample

  4. In a binomial hypothesis test with alternative hypothesis H1: p > p0, where is the critical region?

    • Lower tail
    • Upper tail
    • Distribution centre
    • Both tails

  5. A test of H0: p = 0.5 against H1: p < 0.5 uses n = 10. If X = 1 is observed, what is the p-value?

    • 0.0107
    • 0.0547
    • 0.0010
    • 0.9893

  6. A test of H0: p = 0.5 against H1: p < 0.5 uses n = 10 at the 5% level. Which set of values for X forms the critical region?

    • X <= 2
    • X >= 8
    • X <= 1
    • X = 0 only

  7. X ~ B(12, 0.3) under H0. For H1: p > 0.3 and an observed value X = 6, what is the p-value to 4 decimal places?

    • 0.1179
    • 0.1178
    • 0.0547
    • 0.8821

  8. X ~ B(12, 0.3). What is P(X = 0) to 4 decimal places?

    • 0.0085
    • 0.0138
    • 0.0712
    • 0.2397

  9. A factory claims 5% of items are defective. A sample of 10 items contains 1 defective item. H1 is p > 0.05. Which is the p-value to 4 decimal places?

    • 0.0500
    • 0.3151
    • 0.4013
    • 0.5987

  10. For a hypothesis test at the 5% significance level with a p-value of 0.0207, what is the outcome?

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

  11. A coin is tossed 10 times and 9 heads are observed. A test of H0: p = 0.5 against H1: p > 0.5 is carried out. What is the p-value to 4 decimal places?

    • 0.0098
    • 0.0010
    • 0.0547
    • 0.0107

  12. If a hypothesis test at the 5% significance level yields a p-value of 0.12, what is the conclusion?

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

  13. What does rejecting H0 at the 5% significance level indicate about a hypothesis test result?

    • Significant evidence
    • Invalid test
    • Absolute certainty
    • Zero uncertainty

  14. For X ~ B(8, 0.5), P(X <= 1) = 0.0352 and P(X = 0) = 0.0039. A two-tailed test at the 5% level is carried out. Which critical region is used?

    • X <= 2 or X >= 6, giving 0.1445
    • X <= 1 or X >= 7, giving 0.0703
    • X = 8 only, giving 0.0039
    • X = 0 or X = 8, giving 0.0078

  15. For X ~ B(5, 0.5), what is the actual significance level if the critical region is X = 5?

    • 0.15625
    • 0.015625
    • 0.03125
    • 0.05000

  16. What is the maximum probability of incorrectly rejecting H0 when H0 is true for a 5% test?

    • At most 0.05
    • Exactly 0.00
    • Exactly 0.50
    • At least 0.05

  17. In a hypothesis test, what is a sample used to make a statistical inference about?

    • The test statistic
    • The sample mean
    • The population
    • The critical region

  18. For X ~ B(15, 0.2) and H1: p < 0.2, what is the p-value for an observed value X = 0?

    • 0.2000
    • 0.0500
    • 0.9648
    • 0.0352

  19. A two-tailed binomial test has H0: p = 0.5 with n = 20 and the observed count is 15, so P(X >= 15) = 0.0207 under H0. What is the two-tailed p-value?

    • 0.9793
    • 0.5
    • 0.0207
    • 0.0414

  20. For X ~ B(12, 0.3) and H1: p < 0.3 at the 5% level, what is the critical region?

    • X <= 3
    • X <= 4
    • X = 0
    • X <= 1

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