I'm testing two different settings (say 'A' and 'B') for a machine. From physical arguments, I know that $\mu_B >= \mu_A$. If really $\mu_B < \mu_A$, there's something fundamentally wrong with my model. So there are three options:
- $H_0: \mu_B = \mu_A$ (setting doesn't make a difference)
- $H_1: \mu_B > \mu_A$ (setting make a difference, according to model)
- $H_2: \mu_B < \mu_A$ (model wrong)
I never see the material treated this way - am I violating some principles of experimental design this way? How do I analyze the results of the experiment?
Edit: I see this is related to the answer in Justification of one-tailed hypothesis testing , but I still would like to know how to analyze the resulting data.