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IB Mathematics: Applications and Interpretation HL · 13.4: Hypothesis Testing · 13.4.16

Testing a Poisson mean Problem set B Answers

Skills

    1. (a) p-value = 0.118; do not reject H0
    2. (b) p-value = 0.0463; reject H0
    1. (a) p-value = 0.0267; reject H0
    2. (b) p-value = 0.0765; reject H0
    1. (a) X ≤ 10
    2. (b) X ≤ 2
    1. (a) X ≥ 23
    2. (b) X ≥ 4

In context

    1. (a) H0: λ = 36, H1: λ < 36
    2. (b) p = 0.0345
    3. (c) There is sufficient evidence, at the 5% significance level, that the mean rate of faults has decreased.
    1. (a) H0: λ = 10, H1: λ > 10
    2. (b) p = 0.0835
    3. (c) There is sufficient evidence, at the 10% significance level, that the mean rate of motorbikes has increased.
    1. (a) H0: λ = 16, H1: λ < 16
    2. (b) X ≤ 9
    3. (c) There is insufficient evidence, at the 5% significance level, that the mean number of loaves sold per hour has decreased.
    1. (a) X ≥ 17
    2. (b) X ≥ 20

Stretch

    1. (a) The events occur independently of each other and at a constant average rate (and singly, in a fixed period).
    2. (b) H0: λ = 9, H1: λ > 9; X ≥ 15
    3. (c) There is sufficient evidence, at the 5% significance level, that the mean rate of rockfalls has increased.

jmaths.xyz · AI HL · 13.4.16 Testing a Poisson mean