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> Z-Estimate: Proportion

                        Enter:     Input Range: A1:A350  >  OK

                                      Code for Success:  1

                                      Alpha: .05 > OK

 

 

           

 

 

The output looks like this:

           

z-Estimate: 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  H0: p = .9 vs Ha: p < .9

            To test the hypothesis :

 

Choose: Tools > Data Analysis Plus> Z-Test: 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.

 

z-Test: Proportion

 

 

 

 

 

 

 

 

 

Column 1

Sample Proportion

 

0.7333

Observations

 

75

Hypothesized Proportion

0.9

z Stat

 

 

-4.8113

P(Z<=z) one-tail

 

0

z Critical one-tail

 

1.6449

P(Z<=z) two-tail

 

0

z Critical two-tail

 

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.