quartz/content/Obsidian Vault/joint distribution.md
2022-06-07 14:39:39 -06:00

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#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
$\frac{(\bar x_m-\bar x_w)-(\mu_m-\mu_w)}{\sqrt{\frac{s_m^2}{n_m} + \frac{s_w^2}{n_w}}}$