Stat 312: Lecture 11
Hypothesis testing
Moo K. Chung
[email protected]
Oct 20, 2004
Concepts
1. The
null hypothesis
H
0
is a claim about
the value of a population parameter. The
alternate hypothesis
H
1
is a claim opposite
to
H
0
.
2. A
test of hypothesis
is a method for using
sample data to decide whether to reject
H
0
.
H
0
will be assumed to be true until
the sample evidence suggest otherwise.
3. A
test statistic
is a function of the sample
data on which the decision is to be based.
4. A
rejection region
is the set of all values
of a test statistic for which
H
0
is rejected.
5.
Type I error
:
you reject
H
0
when
H
0
is
true.
P
(Type I error)
=
P
(reject
H
0

H
0
true)
=
α.
The re
sulting
α
is called the
signiﬁcance level
of the test and the corresponding test
is called a
level
α
test
.
We will use
test procedures that give
α
less than a
speciﬁed level (0.05 or 0.01).
Class example
I believe that dogs are as smart as people. As
sume IQ of a dog follows
X
i
∼
N
(
μ,
10
2
). IQ
of 10 dogs are measured: 30, 25, 70, 110, 40,
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 Fall '04
 Chung
 Statistics, Null hypothesis, Statistical hypothesis testing, H0, rejection region, [email protected], Moo K. Chung

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