need help: setting alternative hypothesis

I'm really confused. So for null hypothesis, what I think I need to have is usually a statement of quality that I'm testing. What about the alternative hypothesis, how do I decide whether it is left/right tailed or two tailed?

Here's some of the problems and answers that confuse me:

Test the manufacturer's claim that A exceeds B by at least 12.
H0: ua-ub=12
H1: ua-ub<12

Test the hypothesis that the mean salary for associate professors in research institutions is $2000 higher than for those in other institutions.
H0: u1-u2=2000
H1: u1-u2>2000

so in the first case, I understand that the null hypothesis is a statement of what I want to test, i.e. the manufacturer's claim of A exceeding B by at least 12, while the alternative hypothesis is the opposite of the null hypothesis.

but in the second case, why is it thay the alternative hypothesis is not the opposite of {u1-u2>=2000}?

You set the alternative based on what you suspect is going to happen.

"the opposite of" is not well defined. You would do well to stop using that phrase. Since when is "<" the opposite of "="? It makes no sense.

Here's one way to think about it:

\(\displaystyle H_{0}\): Some sort of Status Quo
\(\displaystyle H_{a}\): Should we change our thinking.

"At Least 12" is Greater Than or Equal to, not just Greater Than