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IB Mathematics: Applications and Interpretation HL · 13.4: Hypothesis Testing · 13.4.13

Paired-sample t-test Problem set A Answers

Skills

    1. (a) −0.5, −0.9, −0.1, −0.3, −0.9, −0.1
    2. (b) p = 0.0132
    3. (c) Reject H0 (0.0132 < 0.1)
    1. (a) 3, −2, 1, −1, 3, 2, −2, 1
    2. (b) p = 0.210
    3. (c) Do not reject H0 (0.210 > 0.05)
    1. (a) H0: μ_d = 0, H1: μ_d < 0
    2. (b) The population of differences is normally distributed.

In context

    1. (a) A paired test removes the differences between patients, so it detects only the change caused by the medicine.
    2. (b) H0: μ_d = 0, H1: μ_d < 0
    3. (c) p = 0.000515. 0.000515 < 0.05, so reject H0. There is sufficient evidence, at the 5% significance level, that the medicine reduces mean blood pressure.
    1. (a) 1, 0, −2, 1, 2, 0, 2
    2. (b) H0: μ_d = 0, H1: μ_d > 0; p = 0.160. 0.160 > 0.05, so do not reject H0. There is insufficient evidence, at the 5% significance level, that the scheme increases the mean mark.
    3. (c) The population of differences is normally distributed.

Stretch

    1. (a) p = 0.254
    2. (b) p = 0.0000365
    3. (c) The paired test is correct. The p-values differ because pairing removes the variation between individuals. 0.0000365 < 0.05, so reject H0: there is sufficient evidence that the revision course increases the mean mark.
    1. (a) Paired: the same 10 people are measured twice.
    2. (b) Two-sample: two separate groups.
    3. (c) Paired: both hands come from the same person.

jmaths.xyz · AI HL · 13.4.13 The paired-sample t-test