Sample Tests for a Population Mean

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.