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IB Mathematics: Applications and Interpretation HL · 13.4: Hypothesis Testing · 13.4.20

Type II errors Problem set A Answers

Skills

    1. (a) 0.0228
    2. (b) 0.841
    1. (a) 0.268
    2. (b) 0.679
    1. (a) 0.0497
    2. (b) 0.0783
    3. (c) 0.0426
    1. (a) H0: p = 0.4, H1: p > 0.4, where p is the proportion of customers who order a flat white.
    2. (b) H0: λ = 7.2, H1: λ > 7.2, where λ is the mean number of sales a day.
    3. (c) Type I: concluding that the proportion ordering a flat white has risen when it is still 40%. Type II: concluding there is no evidence of a rise when the proportion has risen.

In context

    1. (a) \(\bar X > 14.3\)
    2. (b) 0.400
    1. (a) 0.850
    2. (b) P(Type I) stays the same; P(Type II) decreases.
    1. (a) Type I: telling a healthy patient they have the condition. Type II: telling a patient with the condition that they are healthy.
    2. (b) A Type II error: a patient who needs treatment goes untreated. A false alarm can be corrected by a second test.
    1. (a) 0.0207
    2. (b) 0.584

Stretch

    1. (a) H0: p = 0.3, H1: p > 0.3; critical region X ≥ 12
    2. (b) 0.345
    1. (a) H0: λ = 9, H1: λ < 9; critical region X ≤ 5
    2. (b) 0.116
    1. (a) 0.154
    2. (b) 0.242

jmaths.xyz · AI HL · 13.4.20 Type II errors and how they link to Type I