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

Paired-sample t-test Problem set B Answers

Skills

    1. (a) −0.2, 0.2, −0.4, 0.1, −0.4, −0.1
    2. (b) p = 0.124
    3. (c) Do not reject H0 (0.124 > 0.05)
    1. (a) 3, 5, 1, 5, 0, 8, 2, 4
    2. (b) p = 0.00310
    3. (c) Reject H0 (0.00310 < 0.1)
    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 services, so it detects only the change caused by the new system.
    2. (b) H0: μ_d = 0, H1: μ_d < 0
    3. (c) p = 0.00183. 0.00183 < 0.05, so reject H0. There is sufficient evidence, at the 5% significance level, that the system reduces the mean delay.
    1. (a) 5, 0, 5, 3, 4, 5, 1, 6
    2. (b) H0: μ_d = 0, H1: μ_d > 0; p = 0.000978. 0.000978 < 0.05, so reject H0. There is sufficient evidence, at the 5% significance level, that the course increases the mean number of press-ups.
    3. (c) The population of differences is normally distributed.

Stretch

    1. (a) p = 0.182
    2. (b) p = 0.0000248
    3. (c) The paired test is correct. The p-values differ because pairing removes the variation between individuals. 0.0000248 < 0.05, so reject H0: there is sufficient evidence that the interval training increases the mean score.
    1. (a) Paired: the same 8 drivers are measured twice.
    2. (b) Two-sample: two separate groups.
    3. (c) Paired: both marks come from the same student.

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