I need to find an appropriate statistical test (likelihood ratio test, t-test, etc.) on the following: Let $\{X_i;Y_i\}^n_{i=1}$ be an i.i.d. sample of a random vector $(X;Y)$ and assume that $\bigl( \begin{smallmatrix} Y\\ X \end{smallmatrix} \bigr)$~$N$ $\left[\bigl( \begin{smallmatrix} \mu_1\\ \mu_2 \end{smallmatrix} \bigr), \bigl( \begin{smallmatrix} 1 & .5\\ .5 & 1 \end{smallmatrix} \bigr) \right]$. The hypotheses are: $H_0=\mu_1+\mu_2\le 1$; $H_1=\mu_1+\mu_2\gt 1$
By looking at this information, how do I know which test is the most appropriate? Is it because the data is i.i.d. I can simply take a likelihood ratio test? A good explanation on what test is more appropriate than another one would be greatly appreciated. This would definitely clear my mind.