16 / 68
For
σ
2
1
=
σ
2
2
,
For
σ
2
1
=
σ
2
2
,
(¯
x
1
−
¯
x
2
)
±
t
α/
2
,ν
s
p
1
n
1
+
1
n
2
t
test
=
(¯
x
1
−
¯
x
2
)
−
µ
0
s
p
1
n
1
+
1
n
2
∼
t
α,ν
where
ν
=
n
1
+
n
2
−
2
and
s
p
=
(
n
1
−
1)
s
2
1
+ (
n
2
−
1)
s
2
2
n
1
+
n
2
−
2
Confidence Interval for
µ
D
Hypothesis testing for
µ
D
¯
x
D
−
z
α/
2
σ
D
√
n
,
¯
x
D
+
z
α/
2
σ
D
√
n
z
test
=
¯
x
D
−
µ
D
σ
D
/
√
n
∼
z
α
¯
x
D
−
z
α/
2
s
D
√
n
,
¯
x
D
+
z
α/
2
s
D
√
n
z
test
=
¯
x
D
−
µ
D
s
D
/
√
n
∼
z
α
¯
x
D
−
t
α/
2
,ν
s
D
√
n
,
¯
x
D
+
t
α/
2
,ν
s
D
√
n
t
test
=
¯
x
D
−
µ
D
s
D
/
√
n
∼
t
α,ν
where
ν
=
n
−
1
Confidence intervals for
π
Hypothesis testing for
π
p
−
z
α/
2
p
(1
−
p
)
n
, p
+
z
α/
2
p
(1
−
p
)
n
z
test
=
p
−
π
0
π
0
(1
−
π
0
)
n
∼
z
α
Confidence intervals for
π
1
−
π
2
Hypothesis testing for
π
1
−
π
2
(
p
1
−
p
2
)
±
z
α/
2
p
1
(1
−
p
1
)
n
1
+
p
2
(1
−
p
2
)
n
2
For
π
0
= 0
,
z
test
=
(
p
1
−
p
2
)
−
π
0
π
1
(1
−
π
1
)
n
1
+
π
2
(1
−
π
2
)
n
2
∼
z
α
For
π
0
= 0
,
z
test
=
(
p
1
−
p
2
)
−
π
0
p
p
(1
−
p
p
)
1
n
1
+
1
n
2
∼
z
α
where
p
p
=
x
1
+
x
2
n
1
+
n
2
6
Statistical Tables and Formulae 2.0