Sample Tests for a Population Mean

1. a. \(Z \leq-1.645\)
    b. \(T \leq-2.571\) or \(T \geq 2.571\)
    c. \(T \geq 1.319\)
    d. \(Z \leq-1645\) or \(Z \geq 1.645\)

3. a. \(T \leq-0.855\)
    b. \(Z \leq-1.645\)
    c. \(T \leq-2.201\) or \(T \geq 2.201\)
    d. \(T \geq 3.435\)

5. a. \(T=-2.690, d f=19,-t_{0.005}=-2.861\), do not reject \(H_{0}\).
    b. \(0.01 < p\)-value \( < 0.02, \alpha=0.01\), do not reject \(H_{0}\).

7. a. \(T=2.398, d f=7, t_{0.05}=1.895\), reject \(H_{0}\).
    b. \(0.01 < p\)-value \( < 0.025, \alpha=0.05\), reject \(H_{0}\)

9. \(T=-7.560, d f=12,-t_{0.10}=-1.356\), reject \(H_{0}\).

11. \(T=-7.076, d f=5,-t_{0.0005}=-6.869\), reject \(H_{0}\)

13. a. \(T=-1.483, d f=14,-t_{0.05}=-1.761\), do not reject \(H_{0}\);
      b. \(T=-1.483, d f=14,-t_{0.10}=-1.345\), reject \(H_{0}\);

15. a. \(T=2.069, d f=6, t_{0.10}=1.44\), reject \(H_{0}\);
      b. \(T=2.069, d f=6, t_{0.05}=1.943\), reject \(H_{0}\).

17. \(T=4.472, d f=4, t_{0.10}=1.533\), reject \(H_{0}\).

19. \(T=0.798, d f=24, t_{0.10}=1.318\), do not reject \(H_{0}\)

21. a. \(T=-1.773, d f=4,-t_{0.05}=-2.132\), do not reject \(H_{0}\).
      b. \(0.05 < p\)-value \( < 0.10\)
      c. \(\alpha=0.05\), do not reject \(\mathrm{H}_{0}\)