Answers to Selected Exercises

2.43.

Test statistic 3.33, critical values $1.645$ . Reject
$P 0.0010$
The power of the test at 10.05 is approximately 0.0509.
Sample size 223

2.44.

Test statistic $3.464$ , critical value $1.665$ . Reject
$P 0.0001$ so reject

2.45.

Test statistic 2.828, critical value 1.2988. Reject
$P 0.0071$ so reject

2.46.

Test statistic 2.0, critical value 2.363. Fail to reject
$P 0.0001$ so reject

2.47. Test statistic $1$ , critical value $2.328$ . Fail to reject

2.48. Test statistic 15.49, critical value 2.6270. Reject

2.49. Test statistic $1.269$ , critical value $1.7017$ . Fail to reject

2.50. Test statistic $3.730$ , critical value $1.6748$ . Reject

2.51.

Test statistic $1.563$ , critical values $1.672$ . Fail to reject
Test statistic 4.556, critical value 1.2988. Reject
Test statistic $1.028$ , critical value $1.2988$ Fail to Reject

3.9. Test statistic 1.743, critical value 1.282. Reject

3.10. Test statistic 1.743, critical values $1.961$ . Reject ; The coin is almost certainly unfair.

3.11. Test statistic $1.333$ , critical value $1.645$ . Fail to reject .

3.12. Test statistic 0.707, critical value 1.282. Fail to reject .

3.13.

Test statistic 0.162, critical values $1.645$ Fail to reject .
Test statistic $4.117$ , critical value $1.282$ Reject .
Test statistic 8.266, critical value 1.282. Reject .

3.19. Test statistic 3.286, critical value 1.282. Reject .

3.20.

Test statistic 3.394, critical values $1.645$ Reject .
Test statistic $1.980$ , critical value $1.282$ Reject .
Test statistic $0.566$ , critical value $1.282$ . Fail to reject .

4.15.

Test statistic 0.4, critical values 0.585, 1.667. Reject .
Test statistic 1.0, critical values $1.6625$ . Fail to reject .
Probably not

4.16. Test statistic 2.8, critical value 1.3184. Reject .

4.17.

Test statistic 1.1, critical values 0.6227, 1.6072. Fail to reject .
Test statistic $11.4$ , critical value $1.6602$ . Reject .

4.18.

Test statistic 0.56, critical values 0.7175, 1.3942. Reject .
Test statistic $4.97$ , critical values $1.645$ . Reject .

6.15. 1 degree of freedom, $V 1$ , $P 0.3173$ .

6.16.

3 degree of freedom, $V 11.78$ , $P 0.008$ .
2 degree of freedom, $V 2.301$ , $P 0.316$ .

6.17.

5 degree of freedom, $V 5.383$ , $P 0.371$ .
5 degree of freedom, $V 18.45$ , $P 0.002$ .

6.18.

10 degree of freedom, $V 6.2$ , $P 0.798$ .
5 degree of freedom, $V 7.103$ , $P 0.213$ .

6.19. 1 degree of freedom, $V 4.332$ , $P 0.037$ .

6.20. We use the following partition of : $01234 8910$ .

7 degrees of freedom, $V 11.321$ , $P 0.125$ .
6 degrees of freedom, $V 8.141$ , $P 0.228$ .

6.21. 3 degrees of freedom, $V 70.111$ , $P 0$ .

6.22. Using the following partition of : $750750775775800800825825850850875875900900925925950950975975$ . we have 8 degrees of freedom, $V 11.443$ , $P 0.178$ .

Answers to Selected Exercises

8. Hypothesis Testing

2. Tests in the Normal Model

3. Tests in the Bernoulli Model

4. Tests in the Two-Sample Normal Model

6. Chi-Square Tests