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IB Mathematics: Applications and Interpretation HL · 13.4: Hypothesis Testing · 13.4.15

Testing a proportion Problem set A Answers

Skills

    1. (a) H0: p = 0.25, H1: p > 0.25
    2. (b) H0: p = 0.04, H1: p < 0.04
    3. (c) H0: p = 1/5, H1: p > 1/5
    1. (a) p-value = 0.0294; reject H0
    2. (b) p-value = 0.0628; reject H0
    1. (a) X ≤ 8
    2. (b) X ≤ 20
    1. (a) X ≥ 37
    2. (b) X ≥ 22

In context

    1. (a) H0: p = 0.2, H1: p > 0.2
    2. (b) p = 0.0772
    3. (c) There is insufficient evidence, at the 5% significance level, that the proportion of customers who pay by card has increased.
    1. (a) H0: p = 0.45, H1: p < 0.45
    2. (b) X ≤ 16
    3. (c) There is insufficient evidence, at the 5% significance level, that the proportion of plants with a flower is less than 0.45.
    1. (a) X ≥ 15
    2. (b) 0.0344
    3. (c) X is discrete. Adding the next value to the critical region would take the probability over 5%, and there is nothing in between.

Stretch

    1. (a) X ≥ 9; actual significance level 0.0107
    2. (b) X ≥ 15; actual significance level 0.0207
    3. (c) X ≥ 20; actual significance level 0.0494

jmaths.xyz · AI HL · 13.4.15 Testing a proportion: the binomial test