6.5.3—Hypothesis tests

Under H₀, the statistic has a known or approximated distribution. Critical values or p-values are calculated from that distribution and the direction of H₁.

Use the stated variance or standard error, preserve tails and degrees of freedom, and conclude in the original units.

A one-sided upper test uses P(T≥t_obs), whereas a two-sided test counts both tails of comparable extremity.

The same statistic value can lead to different decisions at different α or under different alternative hypotheses.