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One-sided Lower Bound
One-sided Upper Bound
π
≥
p
−
z
α
p
(1
−
p
)
n
π
≤
p
+
z
α
p
(1
−
p
)
n
π
1
−
π
2
≥
(
p
1
−
p
2
)
−
z
α
p
1
(1
−
p
1
)
n
1
+
p
2
(1
−
p
2
)
n
2
π
1
−
π
2
≤
(
p
1
−
p
2
) +
z
α
p
1
(1
−
p
1
)
n
1
+
p
2
(1
−
p
2
)
n
2
σ
2
>
(
n
−
1)
s
2
χ
2
α
σ
2
<
(
n
−
1)
s
2
χ
2
1
−
α
σ
2
1
σ
2
2
>
s
2
1
s
2
2
f
1
−
α,ν
2
,ν
1
σ
2
1
σ
2
2
<
s
2
1
s
2
2
f
α,ν
2
,ν
1
Sample sizes
n
=
z
α/
2
σ
E
2
n
=
p
(1
−
p
)
z
α/
2
E
2
One-way ANOVA
Two-way ANOVA
SST =
k
i
=1
n
j
=1
x
2
ij
−
1
N
x
2
..
SST =
a
i
=1
b
j
=1
r
k
=1
x
2
ijk
−
1
abr
x
2
...
SSTr =
k
i
=1
x
2
i.
n
i
−
1
N
x
2
..
SSA =
1
br
a
i
=1
x
2
i..
−
1
abr
x
2
...
SSB =
1
ar
b
j
=1
x
2
.j.
−
1
abr
x
2
...
SSAB =
1
r
a
i
=1
b
j
=1
x
2
ij.
−
1
abr
x
2
...
−
SSA
−
SSB
SSE = SST - SSTr
SSE = SST - SSA - SSB - SSAB
Simple Linear Regression and Correlation
r
=
S
xy
S
xx
S
yy
8
Statistical Tables and Formulae 2.0