Sample Tests for a Population Mean

1. a. \(Z=2.277\)
    b. \(Z=2.277\)
   c. \(Z=-1.435\)

3. a. \(Z \geq 1.645\); reject \(H_{0}\).
    b. \(Z \leq-1.96\) or \(Z \geq 1.96\); reject \(H_{0}\).
    c. \(Z \leq-1.645 ;\) do not reject \(H_{0}\).

5. a. \(p\)-value \(=0.0116, \alpha=0.05\); reject \(H_{0}\).
    b. \(p\)-value \(=0.0232, \alpha=0.05 ;\) reject \(H_{0}\).
    c. \(p\)-value \(=0.0749, \alpha=0.05\); do not reject \(H_{0}\).

7. a. \(Z=1.74, z_{0.05}=1.645\), reject \(H_{0}\).
    b. \(Z=-1.98,-z_{0.005}=-2.576\), do not reject \(H_{0}\)

9. a. \(Z=2.24, p\)-value \(=0.025, \alpha=0.005\), do not reject \(H_{0}\).
    b. \(Z=2.92, p\)-value \(=0.0018, \alpha=0.05\), reject \(H_{0}\).

11. \(z=1.11, z_{0.025}=1.96\), do not reject \(H_{0}\).

13. \(Z=1.93, z_{0.10}=1.28\), reject \(H_{0}\).

15. \(Z=-0.523, \pm z_{0.05}=\pm 1.645\), do not reject \(H_{0}\).

17. a. \(Z=-1.798,-z_{0.05}=-1.645\), reject \(H_{0}\);
    b. \(p-\)-value \(=0.0359\).

19. a. \(Z=-8.92,-z_{0.01}=-2.33\), reject \(H_{0}\);
    b. \(p\)-value \(\approx 0\).

21. \(Z=3.04, z_{0.01}=2.33\), reject \(H_{0}\).

23. \(H_{0}: p=1 / 6\) vs. \(H_{a}: p \neq 1 / 6\). Test Statistic: \(Z=-0.76\). Rejection Region: \((-\infty,-1.28] \cup[1.28, \infty)\). Decision: Fail to reject \(H_{0}\).

25. \(H_{0}: p=0.25\) vs. \(H_{a}: p < 0.25\). Test Statistic: \(Z=-1.17\). Rejection Region: \((-\infty,-1.28].\) Decision: Fail to reject \(H_{0}\).