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Logﬁﬂ acceﬁql/ 0L $04 (Mllcair: . _ .otliesis is an assertion about the dis?
tribution of one or more random variables. If the statistical hypothesis completely speciﬁes the distribution, it is called a gamble statistical
hypothesis; if it does not, it is called a wposite statistical hypothesis. Deﬁnition 2. A Lest of a statistical hypothesis is a rule which, when
the experimental sample values have been obtained, leads to a decision
to accept or to reject the hypothesis under consideration. Deﬁnition 3. Let C be that subset of the sample space which, in
accordance with a prescribed test, leads to the rejection of the hypoth—
esis under consideration. Then C is called the critical regigjg of the test. Deﬁnition 4. The powerfmiction of a test of a statistical hypothesis
H 0 against an alternatﬁiypothesis H 1' is that function, deﬁned for
all distributions under consideration, which yields the probability that
the sample point falls in the critical region C of the test, that is, a
function that yields the probability of rejecting the hypothesis under
consideration. The value of the power function at a parameter pOint is
called the pm of the test at that point. Deﬁnition 5. Let H0 denote a hypothesis that is to be tested
against an alternative hypothesis H1 in accordance with a prescribed
test. The sjgﬁiﬁcaiice level of the test (or the w of the critical region C)
is the maximum value (actually supremum) of the power function of
the test when H 0 is true. ...
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 Spring '08
 AlexeiStepanov
 Statistics, Probability

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