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 --

2 thoughts on “Unexpectedly, the theoretically best reject-region of T-test is bounded.”

  1. The complication dwells in that the alternative hypothesis is single. If the alternative are multiple, that is, [tex] \mu>0[/tex], the theoretically best reject-region is still [tex] T > criterion[/tex].

    Multiple alternatives usually involve the bias problem. The best reject-region for one single alternative may be inappropriate (biased) for the other single alternative. The appropriate RD set for multiple alternatives is a strict subset of the appropriate RD set for a single alternative.

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