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

1. (a) \(H_0: \mu = 180\), \(H_1: \mu < 180\); z-test
2. (b) \(H_0: \mu = 250\), \(H_1: \mu \neq 250\); t-test
3. (c) \(H_0: \mu = 42\), \(H_1: \mu > 42\); z-test

p = 0.0549: do not reject H0

p = 0.0231: reject H0

p = 0.0213: reject H0

p = 0.115: do not reject H0

p = 0.0276: reject H0

p = 0.0105: reject H0

1. (a) \(H_0: \mu = 240\), \(H_1: \mu \neq 240\); z-test
2. (b) p = 0.0263
3. (c) At 5%: reject H0. At 1%: do not reject H0.

1. (a) \(\bar{x} = 19.1\), \(s = 0.857\)
2. (b) p = 0.0212: reject H0
3. (c) The population standard deviation is not known, so it is estimated by s.