6-5-13 Tests

u 2-Sample t Test

2-Samplet Test compares the population means when the population standard deviations are unknown. The 2-Samplet Test is applied to t-distribution.

The following applies when pooling is in effect.

to1 – o2

=

xp σn–12n1 + n1

1 2

 

 

 

 

 

xpσn–1

=

(n1–1)x1σn–12

+(n2–1)x2σn–12

n1

+ n2 – 2

 

 

df = n1 + n2 – 2

The following applies when pooling is not in effect.

t =

 

o1 – o2

 

 

 

 

 

 

 

x1σn–12

x2σn–12

 

 

 

+

 

 

 

 

n1

n2

df =

 

 

 

 

 

1

 

 

 

 

 

C2

(1–C)2

 

 

 

 

 

 

 

 

+

 

 

 

 

 

 

 

 

n1–1

n2–1

 

 

 

 

x1σ n–12

C =

 

 

 

 

 

n1

 

 

2

2

 

 

 

 

 

x1σn–1

 

+

x2σn–1

 

 

 

 

n1

 

 

 

n2

 

o1 : mean of sample 1

o2 : mean of sample 2 x1σn-1 : standard deviation of

sample 1

x2σn-1 : standard deviation of sample 2

n1 : size of sample 1

n2 : size of sample 2

xpσn-1 : pooled sample standard deviation

df : degrees of freedom

o1 : mean of sample 1

o2 : mean of sample 2 x1σn-1 : standard deviation of

sample 1

x2σn-1 : standard deviation of sample 2

n1 : size of sample 1

n2 : 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)

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