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a-priori Hypotheses

It is important to state the hypotheses of an experiment when the experiment is being designed, and not after the experiment has been conducted, the data gathered, and the analysis started (or finished).
When an experiment is meant to support verification or validation of a product or process, this includes a statement of the action standard against which the success of the experimental outcome will be judged.  It is important to state and agree to the action standard prior to conducting this type of experiment.
Hypotheses that are stated after the experiment has been run, and that are tested using the data from that experiment, need to be verified with another experiment.

Hypotheses that are not formed and stated "a-priori" are generally considered to be "post-hoc" hypotheses.  Post-hoc hypotheses formed after a study and its data analysis require an additional study (or studies) to verify the hypotheses.

Common Errors in Hypothesis Testing

See also Wikipedia entries for "data dredging" (aka "data snooping", "data fishing"), the Texas sharpshooter fallacy, and similar concepts related to the misuse of statistics.
A useful article "Why We Don’t “Accept” the Null Hypothesis" is offered here.