Casio SERIES FX-9860G - Manual (Page 326)

20070201
u 2-Sample t Test
2-Sample t Test compares the population means when the population standard deviations
are unknown. The 2-Sample t Test is applied to t -distribution.
The following applies when pooling is in effect.
df
=
n
1
+
n
2
– 2
t =
o
1
– o
2
n
1
1 +
n
2
1
x
p n –1
2
σ
t =
o
1
– o
2
n
1
1 +
n
2
1
x
p n –1
2
σ
x
p n –1
=
σ
n
1
+ n
2
– 2
(n
1
–1)x
1 n–1
2 +(n
2
–1)x
2 n–1
2
σ σ
x
p n –1
=
σ
n
1
+ n
2
– 2
(n
1
–1)x
1 n–1
2 +(n
2
–1)x
2 n–1
2
σ σ
¯x
1
: mean of sample 1
¯x
2
: mean of sample 2
x
1
σ
n -1
: standard deviation of
sample 1
x
2
σ
n -1
: standard deviation of
sample 2
n
1
: size of sample 1
n
2
: size of sample 2
x
p
σ
n -1
: pooled sample standard
deviation
df : degrees of freedom
The following applies when pooling is not in effect.
t =
o
1
– o
2
x
1 n –1
2
σ
n
1
+
x
2 n –1
2
σ
n
2
t =
o
1
– o
2
x
1 n –1
2
σ
n
1
+
x
2 n –1
2
σ
n
2
df =
1
C 2
n
1
–1
+
(1–C ) 2
n
2
–1
df =
1
C 2
n
1
–1
+
(1–C ) 2
n
2
–1
C =
x
1 n–1
2
σ
n
1
+
x
2 n–1
2
σ
n
2
x
1 n–1
2
σ
n
1 C =
x
1 n–1
2
σ
n
1
+
x
2 n–1
2
σ
n
2
x
1 n–1
2
σ
n
1
6-5-13
Tests
¯x
1
: mean of sample 1
¯x
2
: mean of sample 2
x
1
σ
n -1
: standard deviation of
sample 1
x
2
σ
n -1
: standard deviation of
sample 2
n
1
: size of sample 1
n
2
: size of sample 2
df : degrees of freedom
Perform the following key operations from the statistical data list.
3(TEST)
2(t)
2(2-S)