= Solution
{c}
\b[True, with the test's rejection rule fixed.] If its <rejection region> in the space of the <test statistic> is $C$, its <statistical power> against the specified <simple hypothesis> $H_1$ is
$$
\boxed{\mathbb P_{H_1}(T\in C)}.
$$
Thus the <probability distribution> of $T$ under the <alternative hypothesis> determines the <statistical power> of this test. The <null distribution> is used to choose a rule with the desired <test size>, but <statistical power> is evaluated under the <alternative hypothesis>. Different rejection rules can have different <statistical power> even for the same <probability distribution> of $T$.
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