Answer
Read problem 17.
Left-tailed test: in this case the alternative hypothesis is $M_X\lt M_Y$. If it is true, we will find a small test statistic $T$ (or a negative $z_0$). Then, we find the critical value, $w_α$ (or $-z_α$) in an appropriated Table. If $T\lt w_α$ (or $z_0\lt-z_α$), we reject the null hypothesis. If $T\gt w_α$ (or $z_0\gt-z_α$), we do not reject the null hypothesis.
Right-tailed test: in this case the alternative hypothesis is $M_X\gt M_Y$. If it is true, we will find a large test statistic $T$ (or a positive $z_0$). Then, we find the critical value, $w_{1-α}$ (or $z_α$) in an appropriated Table. If $T\gt w_{1-α}$ (or $z_0\gt z_α$), we reject the null hypothesis. If $T\lt w_{1-α}$ (or $z_0\lt z_α$), we do not reject the null hypothesis.
Two-tailed test: in this case the alternative hypothesis is $M_X\ne M_Y$, that is, $M_X\lt M_Y$ or $M_X\gt M_Y$. If the first case is true, we will find a small test statistic $T$ (or a negative $z_0$). Then, we find the critical value, $w_{\frac{α}{2}}$ (or $-z_{\frac{α}{2}}$) in an appropriated Table. If $T\lt w_{\frac{α}{2}}$ (or $z_0\lt-z_{\frac{α}{2}}$), we reject the null hypothesis. If the second case is true, we will find a large test statistic $T$ (or a positive $z_0$). Then, we find the critical value, $w_{1-\frac{α}{2}}$ (or $z_{\frac{α}{2}}$) in an appropriated Table. If $T\gt w_{1-\frac{α}{2}}$ (or $z_0\gt z_{\frac{α}{2}}$), we reject the null hypothesis. If $w_{\frac{α}{2}}\lt T\lt w_{1-\frac{α}{2}}$ (or $-z_{\frac{α}{2}}\lt z_0\lt z_{\frac{α}{2}}$), we do not reject the null hypothesis.
Work Step by Step
Given above.
