Texas Instruments TI-82 STATS

A–52 Tables and Reference Information
826DEC~1.DOC TI-83 international English Bob Fedorisko Revised: 10/26/05 2:20 PM Printed: 10/27/05 3:09
PM Page 52 of 58
Below is the definition for the 2.SampÜ
ÜÜ
ÜTest.
Sx1, Sx2 = Sample standard deviations having n
1
-1
and n
2
-1 degrees of freedom df,
respectively.
Û = Û-statistic =
Sx
Sx
1
2
2






df(x, n
1
-1, n
2
-1) = Ûpdf( ) with degrees of freedom
df, n
1
-1, and n
2
-1
p = reported p value
2.SampÜ
ÜÜ
ÜTest for the alternative hypothesis s
1
> s
2
.
pfxnn dx
F
=−−
∞
∫
(),,
12
11
2.SampÜ
ÜÜ
ÜTest for the alternative hypothesis s
1
< s
2
.
pfxnn dx
F
=−−
∫
(),,
12
0
11
2.SampÜ
ÜÜ
ÜTest for the alternative hypothesis s
1
ƒ s
2
. Limits
must satisfy the following:
p
f x n n dx f x n n dx
L
U
bnd
bnd
2
11 11
12
0
12
=−−=−−
∫∫
∞
()(),, ,,
where: [Lbnd,Ubnd] = lower and upper limits
The
Û-statistic is used as the bound producing the smallest
integral. The remaining bound is selected to achieve the
preceding integral’s equality relationship.
Statistics Formulas (continued)
2.SampÜ
ÜÜ
ÜTest