7-10-5

Confidence Intervals

2-Prop Z Interval

Command: TwoPropZInt￿

Description: This command obtains the confidence interval of the difference between the proportions of successes of two populations.

The confidence interval is obtained using the following expressions. The confidence level is 100 (1 – α)%.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x1

x1

 

 

 

x2

 

x2

 

x1

 

x2

 

 

α

n1 1– n1

+

 

n2

1– n2

Left =

 

 

–

 

 

– Z

 

 

 

 

 

 

 

 

 

 

 

 

n1

n2

 

2

 

 

 

n1

 

 

 

n2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x1

x1

 

 

x2

x2

Right =

x1

–

x2

+ Z

 

α

 

n1

1– n1

+

n2

1– n2

n1

n2

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

n1

 

 

 

 

n2

Command Syntax

C-Level value, x1 value, n1 value, x2 value, n2 value

Definition of Terms

C-Level: confidence level (0 <C-Level < 1)

x1 : data value (integer, x1 >0) of sample 1

n1 : size of sample 1 (positive integer)

x2 : data value (integer, x2 >0) of sample 2

n2 : size of sample 2 (positive integer)

Input Example:

TwoPropZInt 0.95,132,200,90,150

Calculation Result Output

Left : interval lower limit (left edge)

Right : interval upper limit (right edge)

pˆ1 : estimated proportion of sample 1

pˆ2 : estimated proportion of sample 2

n1 : size of sample 1

n2 : size of sample 2

n1, n2 : sample size

x1, x2 : data

20050501