Binomial and Poisson tests: mixed practice Problem set A Answers

1. (a) H0: λ = 3.2, H1: λ < 3.2, where λ is the mean number of admissions per night.
2. (b) H0: λ = 7.4, H1: λ > 7.4, where λ is the mean number of wasps per hive per day.

1. (a) X ~ Po(7)
2. (b) p = 0.0533; do not reject H0

p = 0.0467; reject H0

1. (a) X ≥ 33
2. (b) reject H0: 34 is in the critical region

16.3% (13 out of 80)

1. (a) P(X ≤ 0) = 0.223 > 0.05, so there is no critical region
2. (b) 23%
3. (c) X ≤ 3

1. (a) H0: λ = 0.8, H1: λ < 0.8, where λ is the mean number of jams per day.
2. (b) p = 0.00423; reject H0

1. (a) p = 0.0253; reject H0
2. (b) p = 0.0266; reject H0
3. (c) Any level between 2.53% and 2.66%

1. (a) 7.50%
2. (b) 14.4%
3. (c) The larger sample gives a higher percentage (14.4% against 7.50%), closer to 20%.

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