This is a bit of a noob question so bear with me. Is it not true that the null hypothesis test determines the type of test (one tailed or two tailed) you would use.
For example null hypothesis could be $\mu = x$. And the alternative hypothesis would be that $\mu \ne x$. You would have to use a two-tailed test here because the null hypothesis is a certain value, and the alternative says that it could either be greater than or less than that value.
Another example is that null hypothesis could be $\mu \ge x$. The alternative hypothesis would be that $\mu < x$. You would use a one tailed test here because you are only looking at the side that is less than.
Does my train of thought make sense? I ask because I was posed this question on a quiz, as a true and false:
The null hypothesis determines the type of test (one tailed or two tailed) to be used to verify it.
And I put true, because of my explanation above - I was marked wrong. My instructor has not clarified so I would like to know. Thank you.