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.
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.