3B.8.1 Type I and Type II errors Quiz: Pearson Edexcel Further Maths, Unit 17

The 20 questions

1. What is the definition of a Type I error in a hypothesis test?

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

2. What is the definition of a Type II error in a hypothesis test?

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

3. How is the power of a statistical test defined in terms of Type II error probability, beta?

   • 1 minus beta
   • Beta
   • 1 minus alpha
   • 1 plus beta

4. What probability is equal to the significance level alpha of a hypothesis test?

   • 1 minus P(Type I)
   • 1 minus P(Type II)
   • P(Type II error)
   • P(Type I error)

5. What does the power function of a hypothesis test evaluate?

   • P(accept H0)
   • P(Type I error)
   • P(reject H0)
   • P(H0 is true)

6. X ~ Po(lambda). H0: lambda = 2, reject H0 if X >= 5. What is P(Type I error)?

   • About 0.947
   • About 0.017
   • About 0.135
   • About 0.053

7. X ~ B(10, 0.5). H0: p = 0.5, H1: p > 0.5, reject if X >= 9. What is P(Type I error)?

   • About 0.011
   • About 0.5
   • About 0.001
   • About 0.055

8. For the test in which X ~ B(10, 0.5) and H0 is rejected if X >= 9, what is the power when p = 0.7?

   • About 0.5
   • About 0.851
   • About 0.011
   • About 0.149

9. For the same test with p = 0.7 as the true value, what is the probability of a Type II error?

   • About 0.5
   • About 0.989
   • About 0.851
   • About 0.149

10. X ~ Po(lambda). H0: lambda = 1, reject H0 if X >= 3. What is P(Type I error)?

    • About 0.080
    • About 0.027
    • About 0.920
    • About 0.184

11. For the test in which H0 is lambda = 1 and H0 is rejected if X >= 3, what is the power when lambda = 3?

    • About 0.080
    • About 0.250
    • About 0.423
    • About 0.577

12. The probability of a Type I error is calculated assuming which hypothesis is true?

    • Null hypothesis H0
    • Alternative hypothesis H1
    • Neither H0 nor H1
    • Both H0 and H1

13. How does increasing the sample size affect the power of a hypothesis test at a fixed significance level?

    • Power becomes zero
    • Power stays constant
    • Power increases
    • Power decreases

14. In a court trial, convicting an innocent defendant corresponds to which error?

    • A Type II error
    • A power error
    • A Type I error
    • No error

15. X ~ B(8, 0.5). H0: p = 0.5, H1: p < 0.5, reject if X <= 1. What is P(Type I error)?

    • About 0.965
    • About 0.004
    • About 0.035
    • About 0.145

16. For the test in which X ~ B(8, 0.5) and H0 is rejected if X <= 1, what is the probability of a Type II error when p = 0.3?

    • About 0.745
    • About 0.965
    • About 0.255
    • About 0.035

17. A test has P(Type I error) = 0.05 and P(Type II error) = 0.2 for a given alternative. What is the power against that alternative?

    • 0.05
    • 0.2
    • 0.8
    • 0.95

18. Which error is controlled directly by the significance level?

    • Both errors equally
    • Neither error
    • Type II error
    • Type I error

19. If the critical region is moved outward to reduce the Type I error, what happens to the Type II error?

    • It is unchanged
    • It decreases
    • It becomes zero
    • It increases

20. How does power change as the true parameter value moves further from the value specified under H0?

    • Power decreases
    • Power remains constant
    • Power approaches zero
    • Power increases

Related quizzes

• Proof by mathematical induction Quiz · 1.1 · 20 questions
• Quadratic equations and complex arithmetic Quiz · 2.1-2.2 · 20 questions
• Matrix arithmetic and inverses Quiz · 3.1-3.2 · 20 questions
• Expectation of discrete random variables Quiz · 3B.1.1 · 20 questions
• The Poisson distribution Quiz · 3B.2.1 · 20 questions
• Geometric and negative binomial models Quiz · 3B.3.1 · 20 questions
• Hypothesis tests for the Poisson distribution Quiz · 3B.4.1 · 20 questions
• Applying the Central Limit Theorem Quiz · 3B.5.1 · 20 questions
• Goodness of fit tests for discrete distributions Quiz · 3B.6.1 · 20 questions
• Definition and derivation of probability generating functions Quiz · 3B.7.1 · 20 questions