I'm wondering how do we decide the "shape" of region of rejection in a hypothesis testing problem. Let's take a two-tailed z-test as an example. What if we choose the weird-looking region of rejection on the left instead of the more widely-used one on the right?
While I intuitively believe choosing the classic one is a better idea, the significance level of both tests are 0.05, so what makes one superior to the other?