Two-sample tests for means Problem set B Answers

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

1. (a) p = 0.0842
2. (b) p = 0.0240

p = 0.00424

1. (a) p = 0.102
2. (b) p = 0.0952

p = 0.00223

1. (a) H0: μ1 = μ2, H1: μ1 ≠ μ2
2. (b) p = 0.0133
3. (c) 0.0133 > 0.01, so do not reject H0. There is insufficient evidence, at the 1% significance level, that the nurseries grow sunflowers of different mean heights.

1. (a) H0: μ1 = μ2, H1: μ1 > μ2
2. (b) p = 0.00841
3. (c) 0.00841 < 0.05, so reject H0. There is sufficient evidence, at the 5% significance level, that the app increases the mean number of daily steps.

1. (a) Two-sample z-test. H0: μ1 = μ2, H1: μ1 ≠ μ2
2. (b) p = 0.0373
3. (c) 0.0373 < 0.1, so reject H0. There is sufficient evidence, at the 10% significance level, that the mean masses of apples from the two orchards differ.

1. (a) p = 0.0123
2. (b) 0.0123 < 0.05, so reject H0. There is sufficient evidence, at the 5% significance level, that the mean masses of bags from the two suppliers differ.
3. (c) 0.0123 > 0.01, so do not reject H0. There is insufficient evidence, at the 1% significance level, that the mean masses of bags from the two suppliers differ.