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

Testing a proportion Problem set B Answers

Skills

    1. (a) H0: p = 0.35, H1: p < 0.35
    2. (b) H0: p = 0.12, H1: p > 0.12
    3. (c) H0: p = 1/6, H1: p < 1/6
    1. (a) p-value = 0.0714; do not reject H0
    2. (b) p-value = 0.0419; reject H0
    1. (a) X ≤ 23
    2. (b) X ≤ 6
    1. (a) X ≥ 25
    2. (b) X ≥ 33

In context

    1. (a) H0: p = 0.3, H1: p < 0.3
    2. (b) p = 0.0471
    3. (c) There is sufficient evidence, at the 5% significance level, that the proportion of pupils who walk to school has decreased.
    1. (a) H0: p = 0.8, H1: p < 0.8
    2. (b) X ≤ 42
    3. (c) There is sufficient evidence, at the 5% significance level, that the proportion of buses that arrive on time is less than 0.8.
    1. (a) X ≥ 14
    2. (b) 0.0401
    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 ≥ 5; actual significance level 0.0273
    2. (b) X ≥ 7; actual significance level 0.0796
    3. (c) X ≥ 10; actual significance level 0.0547

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