Page 74 - Basic Statistics

69

Spool = The pooled variance of the samples.

2
S1 = The variance the first sample
S2 = The variance of second sample
2
n1 = Number of observations in the first sample

n2 = Number of observations in the second sample

The degrees of freedom for the t statistic in this special are simply given by

Df = n1 + n2 - 2

b. If both the variance of the population are not equal ( 1  2 ), then
2
2

X X −
t = 1 2 ( T6 )
S
X 1 − X 2
where

S 2 S 2
S = 1 + 2 ( T7 )
X 1 − X 2 n n
1 2

Where :

S = The standard deviation of difference between two sample means.
X 1 − X 2
S1 = The variance the first sample
2
S2 = The variance of second sample
2
n1 = Number of observations in the first sample
n2 = Number of observations in the second sample

The effective degrees of freedom for the t statistic given by expression

2
2
[ (S / n ) + (S / n )] 2
Dbef = 1 1 2 2 ( T8 )
2
2
(S / n 1 ) 2 + (S / n 2 ) 2
2
1
n 1 − 1 n 1 − 1

~~* CHAPTER 4 TESTING HYPOTHESIS *~~