7-10-7

Confidence Intervals

2-Sample t Interval

Command: TwoSampleTInt ￿

Description: This command obtains the confidence interval for the difference between two population means when the population standard deviations are unknown.

The confidence interval is obtained using the following expressions.

The confidence level is 100 (1 – α)%.

When the two population standard deviations are equal (pooled)

Left = (o1 – o2)– tn1+n2 –2

α

xp σn–12

 

1

 

1

 

 

 

 

 

 

+

 

 

 

2

 

n1

n2

Right = (o1 – o2)+ tn1+n2 –2

 

α

xp σn–12

1

1

 

 

 

 

+

 

 

2

 

n1

n2

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

Left = (o1 – o2)– tdf

α x1σn–12

x2 σn–12

 

 

 

 

 

 

 

 

 

+

 

 

 

2

 

 

 

 

n1

 

n2

Right = (o1 – o2)+ tdf

 

α x1σn–12

+

x2 σn–12

 

2

 

 

n1

 

 

n2

df =

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C2

(1–C)2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+

 

 

 

 

 

 

 

 

 

 

 

 

 

 

n1–1

n2–1

 

 

 

 

 

 

 

 

 

 

x1σn–12

C = x1σn–12n1x2 σn–12

n1 + n2

Command Syntax

Syntax 1 (list format)

C-Level value, List(1), List(2), Freq(1) (or 1), Freq(2) (or 1), Pooled condition (On or Off)

*“Freq” can be omitted. Doing so sets “1” for “Freq”.

*“Pooled” can be omitted. Doing so sets “Off” for “Pooled”.

Syntax 2 (parameter format)

C-Level value, o1 value, x1σn-1value, n1 value, o2 value, x2σn-1value, n2 value, Pooled condition (On or Off)

* “Pooled” can be omitted. Doing so sets “Off” for “Pooled”.

20050501