3B.4.1 Hypothesis tests for the Poisson distribution Quiz: Pearson Edexcel Further Maths, Unit 13

The 20 questions

1. In a hypothesis test for a Poisson distribution, which parameter is used in the hypotheses?

   • p
   • x
   • n
   • λ

2. What does the significance level alpha of a test represent?

   • P(reject H0 | H0 is true)
   • P(H0 is true)
   • P(reject H0 | H1 is true)
   • P(accept H0 | H1 is true)

3. What is the critical region in a statistical hypothesis test?

   • Values under H1
   • Values accepting H0
   • Sample mean values
   • Values rejecting H0

4. H0: lambda = 4 and H1: lambda < 4. An observation X = 1 is made. What is the p-value and the decision at the 5% level?

   • 0.0916, reject H0
   • 0.0916, do not reject H0
   • 0.0183, reject H0
   • 0.4335, do not reject H0

5. If X ~ Po(3), H1: λ > 3 and x = 7, what is the decision at 5% significance?

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

6. H0: lambda = 5 and H1: lambda < 5. What is the 5% critical region?

   • X >= 10
   • X <= 2
   • X <= 1
   • X >= 9

7. H0: lambda = 4 and H1: lambda > 4. What is the 5% critical region?

   • X >= 10
   • X <= 1
   • X >= 8
   • X >= 9

8. Which alternative hypothesis represents a two-tailed test for a Poisson parameter λ?

   • λ < λ₀
   • λ ≠ λ₀
   • λ > λ₀
   • λ = λ₀

9. Testing H₀: λ = 2 against H₁: λ > 2 for Po(2) with observed X = 4, what is the decision?

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

10. In a hypothesis test for a Poisson mean, what distribution does the test statistic follow under H₀?

    • N(0, 1)
    • Po(λ)
    • Po(λ₀)
    • B(n, p)

11. Testing H₁: λ < 2 for Po(2) at the 5% significance level with X = 0 observed, what is the decision?

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

12. What happens to the probability of rejecting H₀ when increasing the significance level from 5% to 10%?

    • It decreases
    • It stays constant
    • It increases
    • It becomes zero

13. Testing H₁: λ > 0.5 for Po(0.5) at 5% significance with X = 3 observed, what is the decision?

    • Accept H₀
    • Inconclusive
    • Do not reject H₀
    • Reject H₀

14. Testing H₁: λ < 6 for Po(6) at the 5% significance level with observed X = 2, what is the decision?

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

15. What parameter value must the null hypothesis H₀ specify in a Poisson hypothesis test?

    • A range of values
    • A single value
    • Two separate values
    • An inequality

16. A hypothesis test conducted at the 5% level yields a p-value of 0.03. What is the decision?

    • Accept H₀
    • Reject H₀
    • Increase sample size
    • Do not reject H₀

17. H0: lambda = 1 and H1: lambda < 1. One unit of time gives X = 0. What is the p-value?

    • About 0.050
    • About 0.632
    • About 0.368
    • About 0.184

18. Which hypotheses test whether the rate has increased from 2 per hour?

    • H0: lambda = 2 and H1: lambda > 2
    • H0: lambda > 2 and H1: lambda = 2
    • H0: x-bar = 2 and H1: x-bar > 2
    • H0: lambda < 2 and H1: lambda > 2

19. Under H₀: λ = λ₀, what is the sampling distribution of the test statistic X?

    • Po(λ₀)
    • Po(λ)
    • N(λ₀, λ₀)
    • B(n, p)

20. At the 5% significance level, under what condition is H₀ rejected in a hypothesis test?

    • p-value < 0.05
    • p-value > 0.05
    • p-value > 0.10
    • p-value = 0.05

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