Two-sample t-tests Problem set A 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 = 2.15, p = 0.0201; reject H0

t = 0.908, p = 0.370; do not reject H0

t = −2.57, p = 0.0131; 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 = 2.20, p = 0.0165
4. (d) There is sufficient evidence, at the 10% significance level, that the mean mark is higher with the new method than with the standard method.

1. (a) H0: μ1 = μ2, H1: μ1 ≠ μ2
2. (b) t = 3.42, p = 0.00176
3. (c) There is sufficient evidence, at the 1% significance level, that the mean weekly grocery spend differs between the two towns.

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

1. (a) Both populations are normally distributed. The two populations have equal variance.
2. (b) H0: μ1 = μ2, H1: μ1 > μ2
3. (c) t = 3.10, p = 0.00422. There is sufficient evidence, at the 5% significance level, that the mean typing speed is higher after the course.

1. (a) H0: μ1 = μ2, H1: μ1 > μ2
2. (b) t = 0.935, p = 0.179
3. (c) There is insufficient evidence, at the 10% significance level, that the mean memory score is higher with music than in silence.