Hypothesis testing

Is it possible to have the "=" in the alternative hypothesis? In anassignment I am asked to try to falsify a hypothesis (and surely it is not possible to falsify an alternative hyp?!?!?).
But his hypothesis is: β 3 > 0 (H1: β 3 ≤ 0)
Where β 3 is the coefficient of the interaction effect in a multipple regression.
(y = β0 + β1x1+ β2x2+ β3x1x2).

If the "=" was in the null hyp, t= (estimated β 3-0)/SE(estimated β3)
But when not, can I just say that (as i have a contiunous probability distribution) the number I should put in for zero is so extremely close to zero that i round it off to zero for practical reasons??
Is this possible to do??



TS Contributor
This doesn't appear to be a huge issue to me - just a small change is required (usually the Ho includes an = or <= or >= sign in it, and Ha is either <> or < or >)

Ho: B3 >=0
Ha: B3 < 0