# Is this a valid argument why null hypothesis should always be equality?

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?

• Null hypothesis can be inequality. But it must be either $\leq$ or $\geq.$ This is because of calculation pf $p$-value. When do we calculation, if null hypothesis has no equality, I think calculation cannot be made and thus $p$-value cannot be calculated? – Idonknow Dec 24 '19 at 12:33
• In addition to the other answers: The null hypothesis doesn't have to state that there is "no effect" or "no difference". The null hypothesis $\mu_{A}-\mu_{B} = 5$, for example, is perfectly valid. – COOLSerdash Dec 24 '19 at 12:57

• Although correct and revealing, this answer doesn't address the question because its null still concerns an equality (formally, $H_0:\mu_1 - \mu_2 = 9$). The question asks about inequalities. This (strongly) suggests a good answer ought to invoke the distinction between simple and composite hypotheses. – whuber Dec 24 '19 at 16:09