Stat 312: Lecture 13
Twosample tests
Moo K. Chung
[email protected]
March 6, 2003
Concepts
1. The
P
value is the smallest level of signiFcance
at which
H
0
would be rejected.
P
value
≤
α
→
reject
H
0
at level
α
.
P
value
> α
→
do not reject
H
0
at level
α
.
The smaller the
P
value, the easier to reject
H
0
.
2. Let
X
1
,
···
, X
n
and
Y
1
,
···
, Y
m
be two indepen
dent samples with mean
μ
X
,
μ
Y
and variance
σ
2
X
,
σ
2
Y
respectively.
Assume
n
and
m
to be
large
. The test statistic for testing
H
0
:
μ
X
=
μ
Y
vs.
H
1
:
μ
X
6
=
μ
Y
Z
=
¯
Y

¯
X
q
σ
2
X
/n
+
σ
2
Y
/m
∼
N
(0
,
1)
.
3. Let
X
1
,
···
, X
n
and
Y
1
,
···
, Y
m
be two inde
pendent samples with
X
i
∼
N
(
μ
X
, σ
2
X
) and
Y
j
∼
N
(
μ
Y
, σ
2
Y
). Then we can show that
Z
=
¯
Y

¯
X
q
σ
2
X
/n
+
σ
2
Y
/m
∼
N
(0
,
1)
.
Inclass problems
Example 8.11. 47 out of 102 doctors did not know
the generic name for the drug methadone.
Let
p
be the proportion of doctors who knew the generic
name. Determine the
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This note was uploaded on 01/31/2008 for the course STAT 312 taught by Professor Chung during the Spring '04 term at University of Wisconsin.
 Spring '04
 Chung
 Statistics

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