Binomial and Poisson tests: mixed practice Problem set B Answers

1. (a) H0: λ = 8.5, H1: λ < 8.5, where λ is the mean number of calls per hour.
2. (b) H0: λ = 1.3, H1: λ > 1.3, where λ is the mean number of accidents per week.

1. (a) X ~ Po(6.75)
2. (b) p = 0.0817; do not reject H0

p = 0.0312; reject H0

1. (a) X ≥ 26
2. (b) do not reject H0: 25 is not in the critical region

28.3% (17 out of 60)

1. (a) P(X ≤ 0) = 0.122 > 0.05, so there is no critical region
2. (b) 13%
3. (c) X ≤ 4

1. (a) H0: λ = 2.4, H1: λ < 2.4, where λ is the mean number of complaints per week.
2. (b) p = 0.0165; reject H0

1. (a) p = 0.0641; do not reject H0
2. (b) p = 0.0670; do not reject H0
3. (c) Any level between 6.41% and 6.70%

1. (a) 22.0%
2. (b) 29.0%
3. (c) The larger sample gives a higher percentage (29.0% against 22.0%), closer to 35%.

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