I noticed that in problems about hypothesis-testing there are sometimes problmes like this: A researcher wonders if level of unemployment in city A decreased compared to previous year. S/he takes "level of unemployment is the same" as the null hypothesis and "level of unemployment decreased" as the alternative hypothesis.
What puzzles me here is that such research ignores the third possibility: in this case that level of unemployment increased. If unemployment really increased we will have to reject the null hypothesis, yet logically speaking the data would NOT support (if not undermine) our alternative hypothesis. Is it just incorrect research design (like maybe the researcher should use "level of unemployment is the same OR larger" as the null hypothesis) or it's acceptable result when both null hypothesis is rejected AND the alternative hypothesis is NOT supported?
With all the usual caveats that null hypothesis significance testing is the devil, the situation you describe is what would be called a one-tailed test, where being “more extreme” means the level of unemployment decreases more, not that it changes in either direction by a greater magnitude.
If you like, you can think of the null hypothesis as being that the unemployment does not decrease. The problem with this is that you can only compute the p value for a simple hypothesis (a single value of the parameter). So you are really just choosing the most conservative simple hypothesis within the range of the null hypothesis: that there is no impact on employment.