Testing a mean: z-test or t-test Problem set B Answers

1. (a) \(H_0: \mu = 8.0\), \(H_1: \mu < 8.0\); z-test
2. (b) \(H_0: \mu = 6\), \(H_1: \mu \neq 6\); t-test
3. (c) \(H_0: \mu = 35\), \(H_1: \mu > 35\); z-test

p = 0.0124: reject H0

p = 0.0382: reject H0

p = 0.209: do not reject H0

p = 0.0142: reject H0

p = 0.0115: reject H0

p = 0.0200: reject H0

1. (a) \(H_0: \mu = 1500\), \(H_1: \mu \neq 1500\); z-test
2. (b) p = 0.0455
3. (c) At 5%: reject H0. At 1%: do not reject H0.

1. (a) \(\bar{x} = 7.20\), \(s = 0.477\)
2. (b) p = 0.0479: reject H0
3. (c) The population standard deviation is not known, so it is estimated by s.