Unexpectedly, the theoretically best reject-region of T-test is bounded.

For NHST vs , theoretically, is s.t. , rather than zero. Nevertheless, pratically a large t, rejecting both and , should not be counted as any evidence to retain or reject .

To verify the shape of --

Confidence Region and Not-reject Region

Either Confidence Interval (CI) or Null Hypothesis Significance Test (NHST) has the same business, to advise whether some sample is or is not disliked by some hypothesized parameter .

NHST.com manages a database. For each Miss , NHST spies out all she dislikes. Mr X logs in NHST.com and inputs a girl name and his credit card number, to bet his luck whispering-- Does she dislike me?

CI.com manages a database too. For each Mr X, CI only needs his credit card with his name X on it, then serves him a full list of available girls.

NHST.com has been historically monopolizing the market. Nevertheless, somebody prefer visiting CI.com and find that the two may share database in most cases.

Not-reject Region of is defined as .

Confidence Region of x is defined as .