Two-sample t-tests Problem set B Answers

1. (a) Two-sample pooled t-test. Both populations normal; equal variance.
2. (b) One-sample t-test
3. (c) Two-sample pooled t-test. Both populations normal; equal variance.

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

t = −2.59, p = 0.00790; reject H0

t = −0.680, p = 0.500; do not reject H0

t = 2.28, p = 0.0219; reject H0

1. (a) Both populations are normally distributed. The two populations have equal variance.
2. (b) H0: μ1 = μ2, H1: μ1 > μ2
3. (c) t = 2.43, p = 0.0103
4. (d) There is sufficient evidence, at the 10% significance level, that the mean number of press-ups is greater after plan A than after plan B.

1. (a) H0: μ1 = μ2, H1: μ1 ≠ μ2
2. (b) t = 2.96, p = 0.00481
3. (c) There is sufficient evidence, at the 1% significance level, that the mean daily screen time differs between Year 10 and Year 12.

1. (a) There is sufficient evidence, at the 5% significance level, that the mean battery life differs between the two models.
2. (b) There is insufficient evidence, at the 1% significance level, that the mean battery life differs between the two models.

1. (a) Both populations are normally distributed. The two populations have equal variance.
2. (b) H0: μ1 = μ2, H1: μ1 > μ2
3. (c) t = 3.02, p = 0.00490. There is sufficient evidence, at the 5% significance level, that the mean mass of fish is greater with bait A.

1. (a) H0: μ1 = μ2, H1: μ1 > μ2
2. (b) t = 1.04, p = 0.154
3. (c) There is insufficient evidence, at the 10% significance level, that the mean distance before a puncture is greater with the new tyre.