User Manual

6-56
k Confidence Interval
Confidence Interval
Left: confidence interval lower limit (left edge)
Right: confidence interval upper limit (right edge)
1-Sample
Z Interval
Left, Right = o + Z( /2) · σ/
'
n
α
2-Sample Z Interval
Left, Right = (o
1
– o
2
) + Z( /2) σ /n
1
+ σ /n
2
2
1
2
2
α
1-Prop
Z Interval
Left, Right = x/n + Z( /2) 1/n · (x/n · (1 – x/n))
α
2-Prop
Z Interval
Left, Right = (x
1
/n
1
– x
2
/n
2
)
+ Z( /2) (x
1
/n
1
· (1 – x
1
/n
1
))/n
1
+ (x
2
/n
2
· (1 – x
2
/n
2
))/n
2
α
1-Sample
t Interval
Left, Right = o + t
n−1
( /2) · s
x
/'n
α
2-Sample
t Interval
(pooled)
Left, Right = (o
1
– o
2
) + t
n
1
+n
2
−2
( /2) s
p
2
(1/n
1
+ 1/n
2
)
s
p
= ((n
1
– 1)s
x
1
2
+ (n
2
– 1)s
x
2
2
)/(n
1
+ n
2
– 2)
α
2-Sample
t Interval
(not pooled)
Left, Right = (o
1
– o
2
) + t
df
( /2) s
x
1
2
/n
1
+ s
x
2
2
/n
2
df = 1/(C
2
/(n
1
– 1) + (1 – C)
2
/(n
2
– 1))
α
C = (s
x
1
2
/n
1
)/(s
x
1
2
/n
1
+ s
x
2
2
/n
2
)
α : level of significance α = 1 − [C-Level ] C-Level : confidence level (0  C-Level < 1)
Z ( α /2): upper α /2 point of standard normal distribution
t
df
( α /2): upper α /2 point of t distribution with df degrees of freedom
k Distribution (Continuous)
Distribution Probability Density Cumulative Distribution
Normal
Distribution
πσ
2
p(x) =
1
e
–
2
2
σ
(x – μ)
2
μ
( > 0)
σ
p = p(x)dx
Upper
Lower
∫
Student- t
Distribution
p(x) =
×
Γ
Γ
× df
π
–
df+1
2
2
df
2
df + 1
df
x
2
1 +
χ
2
Distribution
p(x) =
×
(x  0)
Γ
1
2
df
df
2
× x
2
1
df
2
–1
x
2
–
× e
F Distribution
ndf
2
x
ddf
ndf
ndf
2
–1
ddf
ndf × x
1 +
ndf + ddf
2
p(x) =
–
Γ
2
ndf + ddf
Γ
2
ndf
× Γ
2
ddf
(x  0)