Sample Tests for a Population Mean

Large Sample Tests for a Population Mean

Answers

1.

a. $Z \leq-1.645$
b. $Z \leq-1.96$ or $Z \geq 1.96$
c. $Z \geq 1.28$
d. $Z \leq-1.645$ or $Z \geq 1.645$

3.

a. $Z \leq-0.84$
b. $Z \leq-1.645$
c. $Z \leq-1.96$ or $Z \geq 1.96$
d. $Z \geq 3.1$

5.

a. $Z=2.235$
b. $Z=2.592$
c. $Z=-2.122$
d. $Z=3.002$

7.

a. $Z=-2.18,-z_{0.10}=-1.28$ , reject $H_{0}$ .
b. $Z=1.61, z_{0.05}=1.645$ , do not reject $H_{0}$ .
c. $Z=-4.47,-z_{0.01}=-2.33$ , reject $H_{0}$ .

9. $Z=-2.86,-z_{0.01}=-2.33$ , reject $H_{0}$ .

11. $Z=-1.69,-z_{0.025}=-1.96$ , do not reject $H_{0}$ .

13. $Z=8.33, z_{0.05}=1.645$ , reject $H_{0}$ .

15. $Z=.2.02, z_{0.10}=1.28$ , reject $H_{0}$ .

17. $Z=-2.08,-z_{0.01}=-2.33$ , do not reject $H_{0}$ .

19.

a. $Z=2.54, z_{0.05}=1.645$ , reject $H_{0}$ ;
b. $Z=2.54, z_{0.10}=1.28$ , reject $H_{0}$ .

21. $H_{0}: \mu=1510$ vs. $H_{a}: \mu > 1510$ . Test Statistic: $Z=2.7882$ . Rejection Region: $[2.33, \infty).$ Decision: Reject $H_{0}$

23.

a.

$\mu_{0}=1528.74$
b.

$H_{0}: \mu=1510$ vs.

$H_{a}: \mu > 1510$ . Test Statistic:

$Z=-1.41.$ Rejection Region:

$[1.28, \infty)$ . Decision: Fail to reject

$H_{0}$ .
c. No, it is a Type II error.