Casio FX-9750GII - Manual (Page 194)

6-54
I Confidence Interval
Confidence Interval
Left: confidence interval lower limit (left edge)
Right: confidence interval upper limit (right edge)
1-Sample Z Interval =
o
+ ( /2) · /
' α
2-Sample Z Interval = (
o
1
–
o
2
) + ( /2) /
1
+ /
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
)
A: level of significance A = 1 − [C-Level ] C-Level : confidence level (0
Z ( A/2): upper A/2 point of standard normal distribution
t
df
( A/2): upper A/2 point of t distribution with df degrees of freedom
I Distribution (Continuous)
Distribution Probability Density Cumulative Distribution
Normal
Distribution
2
p (x) =
1
e
–
2
2
(x – ) 2
( > 0)
p = p ( x ) dx
Upper
Lower
Student- t
Distribution
p (x) =
df
–
df + 1
2
2
df
2
df + 1
df
x 2
1 +
C 2 Distribution
p (x) =
(x 0)
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) =
–
2
ndf + ddf
2
ndf
2
ddf
(x 0)