7-10-9

Confidence Intervals

When the two population standard deviations are equal (pooled)

 

 

α

2

 

1

 

1

Left = (o1 – o2)– tn1+n2 –2

 

xp σn–1

n1 + n2

 

 

 

 

 

2

 

Right = (o1 – o2)+ tn1+n2

 

 

α

xp σn–12

 

1 + 1

–2

 

 

 

 

2

 

 

 

 

 

n1

n2

When the two population standard deviations are not equal (not pooled)

Left = (o1 – o2)– tdf

 

α

x1σn–12

+

x2 σn–12

 

 

 

 

n1

 

n2

 

2

 

 

Right = (o1 – o2)+ tdf

 

α

x1σn–12

+

x2 σn–12

 

 

n1

 

n2

2

 

df =

 

 

1

 

 

 

C2

(1–C)2

 

 

 

 

+ n2–1

 

 

n1–1

 

 

x1σn–12

C =

 

n1

x1σn–12x2 σn–12

 

 

n1

+

n2

 

Definition of Terms

C-Level :

confidence level (0 <C-Level < 1)

List(1) :

list where sample 1 data is located

List(2) :

list where sample 2 data is located

Freq(1) :

frequency of sample 1 (1 or list name)

Freq(2) :

frequency of sample 2 (1 or list name)

Pooled :

On or Off

o1 :

sample mean of sample 1 data

x1σn−1 :

sample standard deviation of sample 1 (x1σn−1 >0)

n1 :

size of sample 1 (positive integer)

o2 :

sample mean of sample 2 data

x2σn−1 :

sample standard deviation of sample 2 (x2σn−1 >0)

n2 :

size of sample 2 (positive integer)

Calculation Result Output

Left : interval lower limit (left edge)

Right : interval upper limit (right edge)

df : degrees of freedom

o1 : sample mean of sample 1 data

o2 : sample mean of sample 2 data

x1σn–1 : sample standard deviation of sample 1

x2σn–1 : sample standard deviation of sample 2

xpσn–1 : pooled sample standard deviation (Displayed only when pooling is turned on.)

n1 : size of sample 1

n2 : size of sample 2

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