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
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '04
 Chung
 Statistics, Null hypothesis, Hypothesis testing, Harshad number, Statistical hypothesis testing, Type I and type II errors, rejection region

Click to edit the document details