How to formulate these hypotheses?

Ulf Hamster 2 min.
statistics hypothesis

$H_0$ — Null Hypothesis

$H_a$ — Alternative Hypothesis

Is it better?

Super cool new treatment will shorten the recovery time $\mu$ from the current standard of 12.3 hours. That’s the alternative hypothesis $H_a$. The null hypothesis $H_0$ is the opposite, or resp. that the treatment is even worse.

$$ H_a : \mu < 12.3 , \text{hours} $$

$$ H_0 : \mu \geq 12.3 , \text{hours} $$

Does it have any effect at all?

There are some actions or measures or treatment imposed that are beneficial for something else (e.g. cost reductions). Does this action has any effect on a variable we care about? For example does the new treatment change the recovery time $\mu$ compared to the current standard of 12.3 hours? The null hypothesis $H_0$ states that nothing will change.

$$ H_0 : \mu = 12.3 , \text{hours} $$

$$ H_a : \mu \neq 12.3 , \text{hours} $$