Lesson 3B.4.1

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

20 questions

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Lesson 3B.4.1, Hypothesis tests for the Poisson distribution: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 13: Hypothesis testing, written with Revision Ninja.

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The 20 questions

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

    • The number of trials n
    • The sample mean x-bar
    • The sample variance only
    • The parameter lambda

  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 a critical region in a hypothesis test?

    • The mean of the test statistic under the alternative hypothesis, calculated first
    • The set of values where H0 is accepted, with the probability of a Type I error
    • The p-value of the sample, which is always the largest tail probability observed
    • The set of values of the test statistic that lead to rejection of 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. H0: lambda = 3 and H1: lambda > 3. An observation X = 7 is made. What is the p-value and the decision at the 5% level?

    • About 0.966, do not reject H0
    • About 0.034, reject H0
    • About 0.093, do not reject H0
    • About 0.017, 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 describes a two-tailed test for a Poisson mean?

    • H1: lambda is greater than zero
    • H1: lambda is not equal to lambda0
    • H1: lambda > lambda0 only
    • H1: lambda = lambda0 + 1

  9. A count of 4 calls is observed in 10 minutes. H0: rate 1 per 5 minutes, H1: rate greater than 1 per 5 minutes, at the 5% level. What is the conclusion?

    • p is about 0.052, so reject H0
    • p is about 0.857, so reject H0
    • p is about 0.143, so do not reject H0
    • p is about 0.143, so reject H0

  10. Why is a Poisson distribution used to find the p-value of a test about a Poisson mean?

    • The distribution under H0 is unknown
    • The test statistic follows the normal distribution always
    • The test statistic follows Po(lambda0) if H0 is true
    • The test is based on the sample mean only

  11. H0: lambda = 2 and H1: lambda < 2 at the 5% level. X = 0 is observed. What is the conclusion?

    • P(X <= 0) is about 0.1353, so do not reject H0
    • P(X <= 0) is about 0.1353, so reject H0
    • P(X <= 0) is about 0.0498, so reject H0
    • P(X <= 0) is about 0.6767, so do not reject H0

  12. What is the effect of raising the significance level from 5% to 10%?

    • Rejection of H0 becomes less likely
    • Rejection of H0 becomes equally likely
    • Rejection of H0 becomes more likely
    • Rejection of H0 becomes impossible

  13. H0: lambda = 0.5 per unit and H1: lambda > 0.5. X = 3 is observed in one unit. What is the decision at the 5% level?

    • p is about 0.076, so do not reject H0
    • p is about 0.025, so reject H0
    • p is about 0.986, so do not reject H0
    • p is about 0.014, so reject H0

  14. H0: lambda = 6 and H1: lambda < 6. X = 2 is observed. What is the conclusion at the 5% level?

    • p is about 0.062, so do not reject H0
    • p is about 0.062, so reject H0
    • p is about 0.446, so do not reject H0
    • p is about 0.017, so reject H0

  15. Which statement about hypotheses in a Poisson test is correct?

    • H1 specifies one value of the sample mean
    • H0 specifies one value of lambda
    • H1 always contains the same value of lambda as H0
    • H0 must always be one-tailed

  16. A test at the 5% level gives a p-value of 0.03. What is the correct conclusion?

    • Do not reject H0 at the 5% level
    • Reject H0 at the 5% level
    • Accept H1 as proven true
    • Accept H0 as proven true

  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. In a Poisson hypothesis test, what is the distribution of X under H0?

    • Poisson with parameter lambda0
    • Binomial with parameter p0
    • Geometric with parameter p0
    • Normal with mean lambda0

  20. At a 5% significance level, when is H0 rejected in terms of the p-value?

    • When the p-value is less than 0.05
    • When the p-value is less than 0.5
    • When the p-value is greater than 0.95
    • When the p-value is less than 0.005

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