2. Let X and Y denote the tarsus lengths of male and female grackles, respectively. Assume that X is $N(\mu_x, \sigma_x^2)$ and Y is $N(\mu_Y, \sigma_Y^2)$. A sample of size n=25 yielded $\overline{x}=33.80$, $s_x^2=4.88$, and a sample of size $m=30$ yielded $\overline{y}=31.66$, $s_Y^2=5.81$. Test
(Some critical values $F_\alpha(df_1, df_2)$ and $t_\alpha(df)$, where $\Pr(F > F_\alpha(df_1, df_2)) = \alpha$ and $\Pr(t > t_\alpha(df)) = \alpha$, are given as follows: $$ \begin{array}{l} F_{0.02}(24, 29) = 2.236, F_{0.01}(24, 29) = 2.495, F_{0.02}(29, 24) = 2.306, \\ F_{0.01}(29, 24) = 2.589, F_{0.02}(30, 25) = 2.267, F_{0.01}(30, 25) = 2.538, \\ t_{0.01}(53) = 2.398, t_{0.01}(54) = 2.397, t_{0.01}(55) = 2.396, \\ t_{0.005}(53) = 2.672, t_{0.005}(54) = 2.670, t_{0.005}(55) = 2.668 \end{array} $$