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

Testing a Poisson mean Problem set A Answers

Skills

    1. (a) p-value = 0.155; do not reject H0
    2. (b) p-value = 0.0591; do not reject H0
    1. (a) p-value = 0.0214; reject H0
    2. (b) p-value = 0.0835; reject H0
    1. (a) X ≤ 6
    2. (b) X ≤ 4
    1. (a) X ≥ 13
    2. (b) X ≥ 6

In context

    1. (a) H0: λ = 21, H1: λ < 21
    2. (b) p = 0.0716
    3. (c) There is insufficient evidence, at the 5% significance level, that the mean rate of complaints has decreased.
    1. (a) H0: λ = 6.4, H1: λ > 6.4
    2. (b) p = 0.0614
    3. (c) There is insufficient evidence, at the 5% significance level, that the mean rate of arrivals has increased.
    1. (a) H0: λ = 11, H1: λ < 11
    2. (b) X ≤ 5
    3. (c) There is sufficient evidence, at the 5% significance level, that the mean number of meteors per night has decreased.
    1. (a) X ≥ 15
    2. (b) X ≥ 12

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 = 12, H1: λ > 12; X ≥ 19
    3. (c) There is sufficient evidence, at the 5% significance level, that the mean rate of calls has increased.

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