# In hypothesis testing why do we need to use the reject null hypothesis approach but not the other way round?

In hypothesis testing, the common approach is to first set a null hypothesis and a hypothesis we want to test. Then apply some statistical techniques and see whether the observation is likely to happen under the assumption If null hypothesis is true. If the likelihood is low we will then reject the null hypothesis and claim our assumption is true.

But why we are not doing this the other way round? That is setting only the assumption we want to test and look at the observation. By applying some statistical technique I believe we can get how likely the observation happens under the assumption/hypothesis. We can then just use this probability to accept/reject hypothesis.

Why we are not using the second approach? It seems indirect to me in the first approach.

The second approach is also used. For example, you want to test, if your sample is from gamma distribution family. This would be your null hypothesis $$H_0,$$ and if you don't set alternative hypothesis $$H_1$$ (such as "sample is from beta distribution family"), it would be automatically set as "sample is not from gamma distribution family". The problem is if you choose such a general alternative, the power of your test will decrease (probability of type II error will increase).