The Observed Significance of a Test

1. a. $p$-value $=0.0427$
    b. $p$-value $=0.0384$
    c. $p$-value $=0.0055$

3. a. $p$-value $=0.0009$
    b. $p$-value $=0.0064$
    c. $p$-value $=0.0146$

5. a. reject $H_{0}$
    b. do not reject $\mathrm{H}_{0}$

7. a. $Z=3.23, z_{0.01}=2.33$, reject $H_{0}$
    b. $p$-value $=0.0006$
    c. reject $\mathrm{H}_{0}$

9. a. $Z=0.68, z_{0.05}=1.645$, do not reject $H_{0}$
    b. $p$-value $=0.4966$
    c. do not reject $H_{0}$

11. a. $Z=2.22, z_{0.05}=1.645$, reject $H_{0}$
      b. $p$-value $=0.0132$
      c. reject $\mathrm{H}_{0}$