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Inferential Statistics
Confidence intervals for
µ
Hypothesis testing for
µ
¯
x
−
z
α/
2
σ
√
n
,
¯
x
+
z
α/
2
σ
√
n
z
test
=
¯
x
−
µ
0
σ/
√
n
∼
z
α
¯
x
−
z
α/
2
s
√
n
,
¯
x
+
z
α/
2
s
√
n
z
test
=
¯
x
−
µ
0
s/
√
n
∼
z
α
¯
x
−
t
α/
2
,ν
s
√
n
,
¯
x
+
t
α/
2
,ν
s
√
n
t
test
=
¯
x
−
µ
0
s/
√
n
∼
t
α,ν
where
ν
=
n
−
1
Confidence intervals for
µ
1
−
µ
2
Hypothesis testing for
µ
1
−
µ
2
(¯
x
1
−
¯
x
2
)
±
z
α/
2
σ
2
1
n
1
+
σ
2
2
n
2
z
test
=
(¯
x
1
−
¯
x
2
)
−
µ
0
σ
2
1
n
1
+
σ
2
2
n
2
∼
z
α
For
σ
2
1
=
σ
2
2
,
For
σ
2
1
=
σ
2
2
,
(¯
x
1
−
¯
x
2
)
±
z
α/
2
s
2
1
n
1
+
s
2
2
n
2
z
test
=
(¯
x
1
−
¯
x
2
)
−
µ
0
s
2
1
n
1
+
s
2
2
n
2
∼
z
α
For
σ
2
1
=
σ
2
2
,
For
σ
2
1
=
σ
2
2
,
(¯
x
1
−
¯
x
2
)
±
t
α/
2
,ν
s
2
1
n
1
+
s
2
2
n
2
t
test
=
(¯
x
1
−
¯
x
2
)
−
µ
0
s
2
1
n
1
+
s
2
2
n
2
∼
t
α,ν
where
ν
=
s
2
1
n
1
+
s
2
2
n
2
2
s
2
1
n
1
2
n
1
−
1
+
s
2
2
n
2
2
n
2
−
1
For
σ
2
1
=
σ
2
2
,
For
σ
2
1
=
σ
2
2
,
(¯
x
1
−
¯
x
2
)
±
z
α/
2
s
p
1
n
1
+
1
n
2
z
test
=
(¯
x
1
−
¯
x
2
)
−
µ
0
s
p
1
n
1
+
1
n
2
∼
z
α
5
Statistical Tables and Formulae 2.0