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284
uu
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u2-Sample t Test
2-Sample t Test uses the sample means, variance, and sample sizes when the
sample standard deviations for two populations are unknown to test the hypoth-
esis that the two samples were taken from the same population. The 2-Sample t
Test is applied to standard normal distribution.
t =
o
1
– o
2
x
1 n–1
2
σ
n
1
+
x
2 n–1
2
σ
n
2
o1 : sample 1 mean
o2 : sample 2 mean
x1
σ
n-1 : sample 1 standard deviation
x2
σ
n-1 : sample 2 standard deviation
n1 : sample 1 size
n2 : sample 2 size
This formula is applicable when the sample is not pooled, and the denominator is
different when the sample is pooled.
Degrees of freedom df and xp
σ
n-1 differs according to whether or not pooling is in
effect.
The following applies when pooling is in effect.
df
= n1 + n2 – 2
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
The following applies when pooling is not in effect.
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
Perform the following key operation from the statistical data list.
3(TEST)
2(t)
2(2-S)
18 - 6 Tests
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