Confidence Interval Formulae
Parameter Confidence Interval Usage Sample
X z 2 Normal Known
n
1
s
X z 2 Large Unknown
n
s
2 X t n 1, 2 Normal Small Unknown
n
ˆ 1 ˆ
p p
3 p ˆ z 2
p Binomial Large
n
sD
4 X Y D z 2 Normal Matched pairs
n
X
2
Y
2
Known ,
X Y X Y z / 2 Normal
nX nY Independent Samples
5
2 2
s X sY
X Y X Y z / 2 Large
n X nY
p X 1 p X pY 1 pY
ˆ ˆ ˆ ˆ
6 p X pY p X pY z / 2
ˆ ˆ Binomial Large
nX nY
1
Single Mean
or
Large/Normal Difference?
4
or
Small? Matched
or
2 Independent?
5
Mean
or
Proportion?
3
Single p
or
Difference?
6