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

Type II errors Problem set B Answers

Skills

    1. (a) 0.0416
    2. (b) 0.183
    1. (a) 0.270
    2. (b) 0.733
    1. (a) 0.00345
    2. (b) 0.0294
    3. (c) 0.111
    1. (a) H0: p = 0.65, H1: p < 0.65, where p is the proportion of students who walk to school.
    2. (b) H0: λ = 14, H1: λ < 14, where λ is the mean number of emails an hour.
    3. (c) Type I: concluding that the proportion who walk has fallen when it is still 65%. Type II: concluding there is no evidence of a fall when the proportion has fallen.

In context

    1. (a) \(\bar X < 242\)
    2. (b) 0.211
    1. (a) 0.382
    2. (b) P(Type I) stays the same; P(Type II) decreases.
    1. (a) Type I: blocking a genuine payment as fraud. Type II: letting a fraudulent payment go through.
    2. (b) It depends on the cost. Letting fraud through (Type II) loses the customer's money. Blocking genuine payments (Type I) annoys customers, but a call can fix it, so a bank may accept more Type I errors to keep Type II small.
    1. (a) 0.0191
    2. (b) 0.510

Stretch

    1. (a) H0: p = 0.2, H1: p > 0.2; critical region X ≥ 11
    2. (b) 0.291
    1. (a) H0: λ = 11, H1: λ < 11; critical region X ≤ 6
    2. (b) 0.0786
    1. (a) 0.0333
    2. (b) 0.333

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