Using Lists & Spreadsheet 235
2-SampÛTest
2-SampÜTest (two-sample Ü-test) computes an Ü-test to compare two
normal population standard deviations (s
1
and s
2
). The population
means and standard deviations are all unknown.
2-SampÜTest, which
uses the ratio of sample variances Sx1
2
/Sx2
2
, tests the null hypothesis
H
0
: s
1
=s
2
against one of the alternatives below.
•H
a
: s
1
ƒ
s
2
(s1:ƒs2)
•H
a
: s
1
<s
2
(s1:<s2)
•H
a
: s
1
>s
2
(s1:>s2)
Below is the definition for the
2-SampÜTest.
2-SampÜTest for the alternative hypothesis .
2-SampÜTest for the alternative hypothesis .
2-SampÜTest for the alternative hypothesis s
1
ƒ s
2
. Limits must satisfy
the following:
Sx1, Sx2 =
Sample standard deviations having
and degrees of freedom df,
respectively.
F =
F-statistic =
df(x, , )
=
Fpdf( ) with degrees of freedom df, ,
and
p =reported p value
n
1
1–
n
2
1–
Sx1
Sx2
---------
⎝⎠
⎛⎞
2
n
1
1– n
2
1– n
1
1–
n
2
1–
σ
1
σ
2
>
pf
F
α
∫
xn
1
1 n
2
1–,–,()dx=
σ
1
σ
2
<
pf
0
∫
xn
1
1 n
2
1–,–,()dx=
p
2
--- fxn
1
1 n
2
1–,–,()xd
0
L
bnd
∫
fxn
1
1 n
2
1–,–,()xd
U
bnd
∞
∫
==
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