Hypothesis Testing: Distinguishing Zero vs Practical Equivalence

[engineer23]

What is the difference between NOT being able to reject the hypothesis that a particular parameter is zero and being able to conclude that it is within some acceptable distance from zero ("practical equivalence")?

I guess this is more of a logic question, but I'm still having trouble understanding this distinction.

 

[Focus]

One of them says that the value is not zero, the other says it is. In hypothesis testing you never accept the null hypothesis, you only fail to reject it.

Is this what you were after?