What is the significance of the measures of variation in hypothesis testing?

Question

As my question title implies, I'd like a brief explanation of the significance of measures of variation in hypothesis testing.

Answer 1

I shall assume you intended no pun and I won't even mention it.

If the observed mean is far from the hypothetical mean by comparison to what you would expect given its normal range of variation, then one rejects the hypothesis. But you can't know how far is far by comparison unless you know what you're comparing it with. The latter is the measure of variation.