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.