LAB SESSION 11
ANALYZING THE
POPULATION PROPORTION
INTRODUCTION: In this lab we will investigate the inferences that can be made about the binomial parameter p. Inferences concerning the population binomial parameter p are made using procedures that closely parallel the inference procedures for the population mean m (see lab 10).
CONFIDENCE INTERVALS
Consider the following sample problem.
A telephone survey was conducted to estimate the proportion of households with a personal computer. Of the 350 households surveyed, 75 had a personal computer. Give a point estimate for the portion of the population that had a personal computer. Give the 95% confidence interval.
The data to be entered will be a series of 0's and 1's, each number designating one of two categories. Since the parameter of concern is the proportion of households with a personal computer, we use 1 to represent 'has a personal computer' and use 0 to represent 'does not have a personal computer'.
To enter the data:
Enter: 1 in Cell A1
Drag: Lower right corner down to Cell A75
Enter 0 in Cell A76
Drag: Lower right corner down to Cell A350
Finally, determine a 95% confidence interval for p:
Choose: Tools
> Data Analysis Plus> ZEstimate: Proportion
Enter: Input Range: A1:A350 > OK
Code for Success: 1
Alpha: .05 > OK
The output looks
like this:
zEstimate:
Proportion 


Column 1 
Sample
Proportion 
0.2143 
Observations 
350 
LCL 
0.1713 
UCL 
0.2573 
HYPOTHESIS TESTING
This sample problem will take you through the steps of entering the data and performing a hypothesis test for exercise 9.87 in your textbook.
Since the parameter of concern is the proportion of claims settled within 30 days, we'll let 1 represent 'claim settled within 30 days' and 0 represent 'claim not settled within 30 days'.
Enter the data as before:
Enter: 1 in Cell A1
Drag: Lower right corner down to Cell A55
Enter 0 in Cell A56
Drag: Lower right corner down to Cell A75
The hypotheses for this test are H_{0}: p = .9 vs H_{a}: p < .9
To test the hypothesis :
Choose: Tools
> Data Analysis Plus> ZTest: Proportion >
OK
Enter: Input Range: A1:A75 >
OK
Code for Success: 1
Hypothesized Proportion: p
Alpha: .05 > OK
This creates the
following output on a new sheet.
zTest:
Proportion 










Column 1 
Sample
Proportion 

0.7333 

Observations


75 

Hypothesized
Proportion 
0.9 

z Stat 


4.8113 
P(Z<=z)
onetail 

0 

z Critical
onetail 

1.6449 

P(Z<=z)
twotail 

0 

z Critical
twotail 

1.96 





1. What decision should be made based on these results?
2. What does p value = 0.0 tell us?
ASSIGNMENT: Do Exercises 9.68, 9.90, and 9.92 in your
text.