What a hypothesis test is Problem set B Answers

\(H_0: \mu = 40\), \(H_1: \mu < 40\); one-tailed (lower)

\(H_0: \mu = 3.5\), \(H_1: \mu > 3.5\); one-tailed (upper)

\(H_0: \mu = 72\), \(H_1: \mu \neq 72\); 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) 9
2. (b) 0.0225
3. (c) Yes: the proportion is less than 0.05

1. (a) \(H_0: \mu = 8\), \(H_1: \mu > 8\); one-tailed (upper)
2. (b) Reject \(H_0\): sufficient evidence that the adverts run longer than 8 minutes

Yes: every count is within 3 of 40

No: 14 and 66 are far from 40