#stats 

variance:
$\frac{\sigma_m^2}{n_m} + \frac{\sigma_w^2}{n_w}$

hypothesis test:
$H_0: (\mu_m-\mu_w)=0$
$H_a: (\mu_m-\mu_w) < 0$
$\alpha = 0.05$

$\frac{(\bar X_m-\bar X_w)-(\mu_m-\mu_w)}{\sqrt{\frac{\sigma_m^2}{n_m} + \frac{\sigma_w^2}{n_w}}}$

If you need to estimate it
$\frac{(\bar x_m-\bar x_w)-(\mu_m-\mu_w)}{\sqrt{\frac{s_m^2}{n_m} + \frac{s_w^2}{n_w}}}$