One-sample t-tests Problem set A Answers

1. (a) H0: μ = 1200, H1: μ < 1200
2. (b) H0: μ = 62, H1: μ > 62
3. (c) H0: μ = 24.0, H1: μ ≠ 24.0

t = 2.22, p = 0.0340; reject H0

t = −2.71, p = 0.0211; reject H0

t = 2.17, p = 0.0661; do not reject H0

t = −2.39, p = 0.0276; reject H0

1. (a) H0: μ = 200, H1: μ > 200
2. (b) t = 3.89, p = 0.00299
3. (c) There is sufficient evidence, at the 10% significance level, that the mean weekly water use has increased.
4. (d) The weekly water use is normally distributed.

1. (a) t = −3.35, p = 0.00114
2. (b) There is sufficient evidence, at the 1% significance level, that the mean battery life of the new version is lower than 50 hours.

1. (a) There is sufficient evidence, at the 5% significance level, that the mean height of the plants has increased.
2. (b) There is insufficient evidence, at the 1% significance level, that the mean height of the plants has increased.

1. (a) t = −1.19, p = 0.264. There is insufficient evidence, at the 5% significance level, that the mean volume is not 500 mL.
2. (b) The volumes of bottles are normally distributed.

1. (a) H0: μ = 100, H1: μ > 100
2. (b) t = 2.71, p = 0.00844
3. (c) There is sufficient evidence, at the 5% significance level, that the mean mark has increased.