I took an intro stats course in college, I vaguely remember my TA explained why null hypothesis should always be equality, something like the following:
by default we can only assume there’s no change, if we already assume treatment has certain effect on the sample, then we are having a biased assumption for null hypothesis, thus, defeating the purpose of having a null hypothesis. After all, it’s called null hypothesis.
Is this a valid argument why null hypothesis should always be equality?
I was taught in college null hypothesis should always be equality, now I found out it's not true, null hypothesis can be inequality. How come textbooks/instructors still hold on to teaching null hypothesis as equality (especially for one-sided test)? Does null hypothesis stated as inequality has any effect on increasing Type I error?