I have a very easy question but I feel like some information is missing:
The point estimate of a coefficient $\beta$ (in linear regression) is $-1$ and he corresponding estimated asymptotic standard error is $\frac{3}{7}$. The level of confidence is 0.99. Then what to do with the following: $$ H_0: \beta = 0,\quad H_1:\beta < 0\quad $$ The solution is to reject $H_0$, but why? I have no number of observations... . The $F$ statistic is $$ \frac{1}{\frac{3}{7}} = \frac{7}{3} $$ if I am not mistaken.
But since I have no number of obs. (or do I) how do I judge this?
And does the solution change if $H_1: \beta \neq 0$? I guess so - in a two sided test $H_0$ could at least be kept...
Or should I look up the values in a $t$-table?
According "the corresponding estimated asymptotic standard error is..." I believe you can assume that $n \ge 6$, then you can use the $t$ table in order to verify the answer. Your t statistics is $t_{stat}= \frac{-1-0}{3/7}=-7/3$ (where $F$ is its square, which doesn't really matter here)