need help: setting alternative hypothesis

[confusedme]

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}?

 

[marcmtlca]

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

 

[tkhunny]

"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