by Qiang Gao, updated at May 11, 2017
...
The
- Same as above.
- Find the critical value
$$t_\alpha$$ such that the area in the$$t$$ distribution to the right of$$t_\alpha$$ is$$\alpha$$ . Note the difference from the two-tailed test: the left tail is ignored and the area of$$\alpha$$ is assigned to the upper tail only. - Accept if
$$t_k < t_\alpha$$ ; reject otherwise.
Show that the size (significance level) of this one-tailed
The size of a test is the probability of falsely rejection. When $$\mathrm{H}0$$ is true, the test statistic $$t_k$$ has a $$ t(n-K) $$ distribution. If we reject whenever $$t_k \ge t\alpha$$, then the probability is
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