1.6 Types of Hypotheses

The choice of \(H_1\) is determined by the logic of the problem, not by the data.

(i).

Two-tailed: \(H_0 : \mu = \mu _0\) against \(H_1 : \mu \neq \mu _0\), when a departure in either direction matters.

(ii).

One-tailed: \(H_0 : \mu = \mu _0\) against \(H_1 : \mu > \mu _0\) (or \(<\)), when only one direction is of interest and the other would be treated as no effect.

Choosing one tail after seeing which way the data fell doubles the true error rate and is not legitimate.

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