Casio FX-CG20 AU - Page 272

6-70
k Confidence Interval
Confidence Interval
Lower: confidence interval lower limit
Upper: confidence interval upper limit
1-Sample
Z Interval
Lower, Upper = o + Z( /2) · σ/
'
n
α
2-Sample Z Interval
Lower, Upper = (o
1
– o
2
) + Z( /2) σ /n
1
+ σ /n
2
2
1
2
2
α
1-Prop
Z Interval
Lower, Upper = x/n + Z( /2) 1/n · (x/n · (1 – x/n))
α
2-Prop
Z Interval
Lower, Upper = (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
Lower, Upper = o + t
n−1
( /2) · s
x
/'n
α
2-Sample
t Interval
(pooled)
Lower, Upper = (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)
Lower, Upper = (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