User Manual


k 置信区间
置信区间
󰅣󰇱󰂙
󰅣󰁘󰂙

Z 

Left, Right = o + Z( /2) · σ/
'
n
α


Z 

Left, Right = (o
1
– o
2
) + Z( /2) σ /n
1
+ σ /n
2
2
1
2
2
α


Z 

Left, Right = x/n + Z( /2) 1/n · (x/n · (1 – x/n))
α


Z 

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


t 

Left, Right = o + t
n−1
( /2) · s
x
/'n
α


t 

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


t 

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 󰆘 α 
=
󰅣< < 
Z  α 󰆺󰄿 α 
t
df
 α t  α 󰇒󰁏df 
k 分布（连续）
分布 概率密度 累积分布
󰄿

πσ
2
p(x) =
1
e
–
2
2
σ
(x – μ)
2
μ
( > 0)
σ


p = p(x)dx
Upper
Lower
∫


t 

p(x) =
×
Γ
Γ
× df
π
–
df+1
2
2
df
2
df + 1
df
x
2
1 +


χ



p(x) =
×
(x  0)
Γ
1
2
df
df
2
× x
2
1
df
2
–1
x
2
–
× e



F 

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)
