• Confidence Interval for Population Mean With Replacement (Z-Test)
When Population Standard Deviation (σ ) is known
/ 2
/ 2
1
P X Z
X Z
n
n
α
α
σ
σ
µ
α
−
≤ ≤
+
= −
Or
/ 2
/ 2
X Z
X Z
n
n
α
α
σ
σ
µ
−
≤ ≤
+
When Population Standard Deviation (σ ) is unknown & n>30
/ 2
/ 2
1
S
S
P X Z
X Z
n
n
α
α
µ
α
−
≤ ≤
+
= −
Or
/ 2
/ 2
S
S
X Z
X Z
n
n
α
α
µ
−
≤ ≤
+
• Confidence Interval for Population Mean With Out Replacement (Z-Test)
When Population Standard Deviation (σ ) is known
/ 2
/ 2
1
1
1
N n
N n
P X Z
X Z
N
N
n
n
α
α
σ
σ
µ
α
−
−
−
≤ ≤
+
= −
−
−
Or
/ 2
/ 2
1
1
N n
N n
X Z
X Z
N
N
n
n
α
α
σ
σ
µ
−
−
−
≤ ≤
+
−
−
When Population Standard Deviation (σ ) is unknown
/ 2
/ 2
1
1
1
S
N n
S
N n
P X Z
X Z
N
N
n
n
α
α
µ
α
−
−
−
≤ ≤
+
= −
−
−
Or
/ 2
/ 2
1
1
S
N n
S
N n
X Z
X Z
N
N
n
n
α
α
µ
−
−
−
≤ ≤
+
−
−
• Confidence Interval for Difference Between Population Mean (
1
2
µ µ
− ) With
Replacement (Z-Test)
When population S.D (σ ) is known
(
)
(
)
2
2
2
2
1
2
1
2
1
2
/ 2
1
2
1
2
/ 2
1
2
1
2
1
P X X
Z
X X
Z
n
n
n
n
α
α
σ
σ
σ
σ
µ µ
α
−
−
+
≤
−
≤
−
+
+
= −
Or
________________________________________________________________________________________________
Hashim (0345-4755472) E-mail: hashim_farooqi@hotmail.com Url: http://www.pakchoicez.com Page 1 of 4-
(
)
(
)
2
2
2
2
1
1
1
2
2
2
1
1
1
2
2
2
1
2
/ 2
1
2
1
2
/ 2
1
1
2
2
1
1
2
2
1
1
1
1
1
N n
N
n
N
n
N
n
P X
X
Z
X
X
Z
n
N
n
N
n
N
n
N
α
α
σ
σ
σ
σ
µ
µ
α
−
−
−
−
−
−
+
≤
−
≤
−
+
+
= −
−
−
−
−
(
)
(
)
2
2
2
2
1
1
1
2
2
2
1
1
1
2
2
2
1
2
/ 2
1
2
1
2
/ 2
1
1
2
2
1
1
2
2
1
1
1
1
N n
N
n
N
n
N
n
X
X
Z
X
X
Z
n
N
n
N
n
N
n
N
α
α
σ
σ
σ
σ
µ
µ
−
−
−
−
−
−
+
≤
−
≤
−
+
+
−
−
−
−
(
)
(
)
2
2
2
2
1
2
1
2
1
2
/ 2
1
2
1
2
/ 2
1
2
1
2
X X
Z
X X
Z
n
n
n
n
α
α
σ
σ
σ
σ
µ µ
−
−
+
≤
−
≤
−
+
+
When population S.D (σ ) is unknown & 1
2
,
n n >30
(
)
(
)
2
2
2
2
1
2
1
2
1
2
/ 2
1
2
1
2
/ 2
1
2
1
2
1
S
S
S
S
P X X
Z
X X