Lesson 3B.4.2

3B.4.2 Hypothesis tests for the binomial distribution Quiz: Pearson Edexcel Further Maths, Unit 13

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson 3B.4.2, Hypothesis tests for the binomial distribution: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 13: Hypothesis testing, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. In a hypothesis test for a binomial distribution, in terms of what are the hypotheses stated?

    • The sample size n only
    • The probability p
    • The mean of a normal approximation
    • The sample proportion x/n only

  2. Under H0 with success probability p0, what is the distribution of X in a binomial test with n trials?

    • Po(n p0)
    • B(n, p0)
    • N(n p0, 1)
    • Geo(p0)

  3. X ~ B(10, 0.5). H0: p = 0.5, H1: p > 0.5. X = 8 is observed. What is P(X >= 8) and the decision at the 5% level?

    • 0.0107, reject H0
    • 0.1094, do not reject H0
    • 0.0547, do not reject H0
    • 0.0547, reject H0

  4. X ~ B(10, 0.5). H0: p = 0.5, H1: p > 0.5. X = 9 is observed. What is P(X >= 9) and the decision at the 5% level?

    • 0.0547, reject H0
    • 0.0107, do not reject H0
    • 0.0107, reject H0
    • 0.0010, reject H0

  5. X ~ B(20, 0.3). H0: p = 0.3, H1: p < 0.3. X = 2 is observed. What is the p-value to 3 decimal places and the decision at the 5% level?

    • About 0.278, do not reject H0
    • About 0.035, reject H0
    • About 0.107, reject H0
    • About 0.035, do not reject H0

  6. For H1: p < p0 in a binomial test, which values of X form the critical region?

    • Values near n/2 only
    • Small values of X
    • All values of X
    • Large values of X

  7. A fair die is rolled 10 times and no sixes appear. H0: p = 1/6, H1: p < 1/6. What is the decision at the 5% level?

    • P(X = 0) is about 0.8385, so do not reject H0
    • P(X = 0) is about 0.0323, so reject H0
    • P(X = 0) is about 0.1615, so reject H0
    • P(X = 0) is about 0.1615, so do not reject H0

  8. X ~ B(8, 0.25). H0: p = 0.25, H1: p > 0.25. X = 4 is observed. What is the decision at the 5% level?

    • P(X >= 4) is about 0.114, so reject H0
    • P(X >= 4) is about 0.021, so reject H0
    • P(X >= 4) is about 0.886, so do not reject H0
    • P(X >= 4) is about 0.114, so do not reject H0

  9. X ~ B(12, 0.5). H0: p = 0.5, H1: p > 0.5. X = 10 is observed. What is the decision at the 5% level?

    • P(X >= 10) is about 0.0193, so reject H0
    • P(X >= 10) is about 0.0461, so reject H0
    • P(X >= 10) is about 0.0384, so reject H0
    • P(X >= 10) is about 0.0193, so do not reject H0

  10. X ~ B(20, 0.5). H0: p = 0.5, H1: p > 0.5, at the 5% level. What is the smallest value of X in the critical region?

    • 18
    • 15
    • 14
    • 16

  11. X ~ B(10, 0.1). H0: p = 0.1, H1: p > 0.1. X = 3 is observed. What is the decision at the 5% level?

    • P(X >= 3) is about 0.070, so reject H0
    • P(X >= 3) is about 0.070, so do not reject H0
    • P(X >= 3) is about 0.930, so reject H0
    • P(X >= 3) is about 0.013, so reject H0

  12. What does a significance level of 5% guarantee in a binomial test?

    • A Type I error probability of at most 0.05
    • A power of exactly 0.95
    • A Type II error probability of exactly 0.05
    • Exactly 5% of samples will be rejected

  13. X ~ B(15, 0.2). H0: p = 0.2, H1: p > 0.2. X = 6 is observed. What is the decision at the 5% level?

    • P(X >= 6) is about 0.939, so do not reject H0
    • P(X >= 6) is about 0.061, so reject H0
    • P(X >= 6) is about 0.103, so reject H0
    • P(X >= 6) is about 0.061, so do not reject H0

  14. A machine is set to a 10% defect rate. In 20 items there are no defects. H0: p = 0.1, H1: p < 0.1. What is the decision at the 5% level?

    • P(X = 0) is about 0.1216, so do not reject H0
    • P(X = 0) is about 0.1216, so reject H0
    • P(X = 0) is about 0.0180, so reject H0
    • P(X = 0) is about 0.8784, so do not reject H0

  15. X ~ B(40, 0.25) under H0. What is the expected count E(X)?

    • 15
    • 10
    • 40
    • 0.25

  16. Two-tailed test with H1: p is not equal to 0.5 and n = 10 at the 5% level. Which critical region is appropriate?

    • X = 5 only
    • X <= 1 or X >= 9
    • X <= 3 or X >= 7
    • X <= 2 or X >= 8

  17. In a hypothesis test, what does it mean when the observed value lies in the critical region?

    • H1 is proven false, which means the null hypothesis has been accepted as correct
    • H0 is rejected at the chosen significance level
    • The sample size was too small to give a reliable answer to the question asked
    • H0 is proven true, so the alternative hypothesis must be false in every case

  18. X ~ B(15, 0.5). H0: p = 0.5, H1: p > 0.5. X = 12 is observed. What is the decision at the 5% level?

    • P(X >= 12) is about 0.018, so do not reject H0
    • P(X >= 12) is about 0.018, so reject H0
    • P(X >= 12) is about 0.302, so do not reject H0
    • P(X >= 12) is about 0.059, so reject H0

  19. X ~ B(20, 0.5). H0: p = 0.5, H1: p < 0.5. X = 5 is observed. What is the decision at the 5% level?

    • P(X <= 5) is about 0.021, so do not reject H0
    • P(X <= 5) is about 0.021, so reject H0
    • P(X <= 5) is about 0.058, so reject H0
    • P(X <= 5) is about 0.979, so do not reject H0

  20. When H0 is true, what is the largest probability with which a discrete binomial test can wrongly reject H0 at the 5% level?

    • At least 0.5
    • Exactly 0.95
    • Exactly 0.5
    • At most 0.05

All Pearson Edexcel Further Maths quizzes