Page 73 - Basic Statistics

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H0 : μ = μ
1
2
( T1)
H1 : μ  μ
2
1

Where,
μ = Mean of the first population
1
μ = Mean of the second population
2

2. To test whether the means of the first population is smaller than the mean of

second population, one-tailed test was used, with the following formulation
of the test hypothesis:

H0 : μ = μ
1
2
( T2 )
H1 : μ < μ
2
1

To test the both hypotheses above, using approach the t-student
distribution, the test statistical t-value is calculated as:

a. Special case, there are indications that both populations variances are equal.
( 1 = 2 ),
2
2

X X −
t = 1 2 ( T3 )
S
X 1 − X 2
where

1 1
S = Sp + ( T4 )
X 1 − X 2 n 1 n 2

2
(n - 1)S + (n - 1)S 2
Sp = 1 1 2 2 ( T5 )
n 1 n + 2 2 -

Where:

S = The standard deviation of difference between two sample means.
X 1 − X 2

~~* CHAPTER 4 TESTING HYPOTHESIS *~~