What a hypothesis test is Problem set A Answers

\(H_0: \mu = 500\), \(H_1: \mu < 500\); one-tailed (lower)

\(H_0: \mu = 32\), \(H_1: \mu > 32\); one-tailed (upper)

\(H_0: \mu = 6.0\), \(H_1: \mu \neq 6.0\); two-tailed

1. (a) One-tailed (upper)
2. (b) Two-tailed
3. (c) One-tailed (lower)

1. (a) Reject \(H_0\): sufficient evidence for \(H_1\)
2. (b) Do not reject \(H_0\): insufficient evidence for \(H_1\)
3. (c) Do not reject \(H_0\): insufficient evidence for \(H_1\)

1. (a) 11
2. (b) 0.022
3. (c) Yes: the proportion is less than 0.05

1. (a) \(H_0: \mu = 65\), \(H_1: \mu > 65\); one-tailed (upper)
2. (b) Reject \(H_0\): sufficient evidence that the mean mark is higher than 65

Yes: every count is within 4 of 50

No: 19 and 83 are far from 50