• Testing of Hypotheses concerning the Population Mean (Z-Test)
1. Null & Alternative Hypotheses
Null
0H ;
0
0
0
µ µ
µ µ
µ µ
=
≤
≥
Alternative
1H ;
0
0
0
µ µ
µ µ
µ µ
≠
>
<
2. Significance Level
α = 5 % / 1 % or 0.05 / 0.01
If significance level is not given then we take 5% by default.
3. Critical Region(C.R)
For Two Tail Test (
/ 2
1
2
Zα
α
− =
)
If Alternative
1H ;
0
µ µ
≠
C.R =
/ 2
Z Zα
≥
or
/ 2
/ 2
Z
Z Z
α
α
−
< <
For One Tail Test (0.5
Zα
α
− =
)
If Alternative
1H ;
0
µ µ
>
C.R=Z Zα
≥
For One Tail Test (0.5
Zα
α
− =
)
If Alternative
1H ;
0
µ µ
<
C.R=Z
Zα
≤ −
4. Test Statistics
When population S.D (σ ) is known
Z=
0
X
n
µ
σ
−
When population S.D (σ ) is unknown & n>30
Z=
0
X
S
n
µ
−
5. Conclusion
If z-cal is greater than or equal to z-tab so rejected
0H
If z-cal is less than z-tab so accepted
0H
________________________________________________________________________________________________
Hashim (0345-4755472) E-mail: hashim_farooqi@hotmail.com Url: http://www.pakchoicez.com Page 1 of 10
• Testing of Hypotheses concerning the difference between two Population
Mean (
1
2
X X
−
) (Z-Test)
1. Null & Alternative Hypotheses
Null
0H ;
1
0
1
0
1
0
2
2
2
µ µ
µ µ
µ µ
−
=
−
−
≤
≥
#
#
#
Alternative
1H ;
1
0
1
0
1
0
2
2
2
µ µ
µ µ
µ µ
−
−
−
≠
>
<
#
#
#
2. Significance Level
α = 5 % / 1 % or 0.05 / 0.01
If significance level is not given then we take 5% by default.
3. Critical Region(C.R)
For Two Tail Test (
/ 2
1
2
Zα
α
− =
)
If Alternative
1H ;
1
0
2
µ µ
−
≠#
C.R =
/ 2
Z Zα
≥
or
/ 2
/ 2
Z
Z Z
α
α
−
< <
For One Tail Test (0.5
Zα
α
− =
)
If Alternative
1H ;
1
0
2
µ µ
−
>#
C.R=Z Zα
≥
For One Tail Test (0.5
Zα
α
− =
)
If Alternative
1H ;
1
0
2
µ µ
−
<#
C.R=Z
Zα
≤ −
4. Test Statistics
0
1
2
µ µ
∴ = −
#
When population S.D (σ ) is known
Z=
1
2
0
2
2
1
2
1
2
(
)
X X
n
n
σ
σ
−
−
+
#
When population S.D (σ ) is un