Two-sample tests for means Problem set A Answers

1. (a) H0: μ1 = μ2, H1: μ1 ≠ μ2
2. (b) H0: μ1 = μ2, H1: μ1 > μ2

1. (a) p = 0.0399
2. (b) p = 0.0453

p = 0.0567

1. (a) p = 0.109
2. (b) p = 0.0497

p = 0.000570

1. (a) H0: μ1 = μ2, H1: μ1 ≠ μ2
2. (b) p = 0.0122
3. (c) 0.0122 < 0.05, so reject H0. There is sufficient evidence, at the 5% significance level, that the machines fill bags to different mean masses.

1. (a) H0: μ1 = μ2, H1: μ1 > μ2
2. (b) p = 0.0164
3. (c) 0.0164 < 0.05, so reject H0. There is sufficient evidence, at the 5% significance level, that the technique increases the mean number of words recalled.

1. (a) Two-sample z-test. H0: μ1 = μ2, H1: μ1 ≠ μ2
2. (b) p = 0.128
3. (c) 0.128 > 0.1, so do not reject H0. There is insufficient evidence, at the 10% significance level, that the mean marks of the two classes differ.

1. (a) p = 0.0179
2. (b) 0.0179 < 0.05, so reject H0. There is sufficient evidence, at the 5% significance level, that the mean breaking loads of the two suppliers differ.
3. (c) 0.0179 > 0.01, so do not reject H0. There is insufficient evidence, at the 1% significance level, that the mean breaking loads of the two suppliers differ.