Testing the fit of a model Problem set B Answers

16.7, 108, 85.3, 39.7

1. (a) \(X \sim B(3, 0.7)\)
2. (b) 5.4, 37.8, 88.2, 68.6

45, 60, 75, 90

1. (a) \(H_0\): masses follow \(N(150, 12^2)\); \(H_1\): they do not
2. (b) \(H_0\): the number defective follows \(B(6, 0.2)\); \(H_1\): it does not
3. (c) df = 6

1. (a) 4
2. (b) χ² = 3.75, p = 0.441

1. (a) \(H_0\): the number of penalties scored follows \(B(3, 0.7)\); E = 5.4, 37.8, 88.2, 68.6
2. (b) χ² = 3.10
3. (c) 3.10 < 7.815: do not reject \(H_0\). Insufficient evidence that the number of penalties scored does not follow \(B(3, 0.7)\)

1. (a) 28.8, 57.4, 77.7, 57.4, 28.8
2. (b) \(H_0\): the reaction times follow \(N(120, 15^2)\); \(H_1\): they do not; df = 4
3. (c) χ² = 7.54, p = 0.11
4. (d) 0.11 > 0.05, so do not reject \(H_0\). Insufficient evidence, at the 5% level, that the reaction times do not follow \(N(120, 15^2)\).

1. (a) \(H_0\): the wheel is fair; \(H_1\): it is not
2. (b) E = 35; df = 5
3. (c) χ² = 4.17, p = 0.525
4. (d) 0.525 > 0.02, so do not reject \(H_0\). Insufficient evidence, at the 2% level, that the wheel is not fair.

1. (a) \(H_0\): the number germinating follows \(B(4, 0.5)\); \(H_1\): it does not
2. (b) 20, 80, 120, 80, 20
3. (c) df = 4; χ² = 19.5, p = 6.17 × 10⁻⁴
4. (d) 6.17 × 10⁻⁴ < 0.05, so reject \(H_0\). Sufficient evidence, at the 5% level, that the number germinating does not follow \(B(4, 0.5)\).

1. (a) 24, 36, 48, 60, 72
2. (b) \(H_0\): the number of hot drinks follows the model; \(H_1\): it does not; df = 4
3. (c) χ² = 2.88, p = 0.578; 0.578 > 0.05, so do not reject \(H_0\). Insufficient evidence, at the 5% level, that the model does not fit.