Stat 312: Lecture 10
Hypothesis testing
Moo K. Chung
[email protected]
Feb 20, 2003
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 sam
ple 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 resulting
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).
Inclass problem
I believe that dogs are as smart as people. Assume
IQ of a dog follows
X
i
∼
N
(
μ,
10
2
). IQ of 10 dogs
are measured: 30, 25, 70, 110, 40, 80, 50, 60, 100,
60. We want to test if dogs are as smart as people
by testing
H
0
:
μ
= 100 vs.
H
1
:
μ <
100
.
One reasonable thing one may try is to see how high