]> Answers to Selected Exercises

Answers to Selected Exercises

8. Set Estimation

  1. Estimation in the Normal Model
  2. Estimation in the Bernoulli Model
  3. Estimation in the Two-Sample Normal Model
  4. Bayesian Set Estimation

2. Estimation in the Normal Model

2.35.

  1. 10.14 10.26
  2. 10.25
  3. 10.15

2.36.

  1. 248.1 251.9
  2. 8.8 11.6
  3. 247.70 252.30 8.62 11.92

2.37.

  1. 314.3.
  2. 51.6.

2.38. 25

2.39. 68

2.40.

  1. 836.8 868.0 . No, the true value is not in the interval.
  2. 69.4 91.8

2.41.

  1. 5.364 5.532 . Yes, the true value is in the interval.
  2. 0.1725 0.3074

2.42.

  1. 8.410 8.822 . Yes, the true value is in the interval.
  2. 0.629 0.927

2.43.

  1. 14.21 15.03
  2. 54.21 56.83
  3. 41.95 44.49

3. Estimation in the Bernoulli Model

3.13. 0.396 0.458

3.14. 0.579. No, the coin is almost certainly not fair.

3.15. 0.034 0.116

3.16. 1068

3.17. 3382

3.18. 0.443 0.634 . The theoretical value is approximately 0.637, which is not in the confidence interval.

4. Estimation in the Two-Sample Normal Model

4.15.

  1. The two methods are equivalent.
  2. The bivariate normal model works better.

4.16.

  1. 1.149 1.936
  2. 24.834 23.166
  3. Perhaps not.
  4. Yes

4.17. A 90% confidence lower bound for the difference in IQ is 2.675. There may be a vary small increase.

4.18.

  1. 0.8 1.3
  2. 10.5 14.1
  3. Yes

4.19.

  1. 1.127 1.578
  2. 0.832 0.168
  3. Perhaps not.

5. Bayesian Set Estimation

5.2. 0.436 0.865

5.4. 0.783 2.406