SBE12ch12 - IS 310 Business Statistics CSU LONG BEACH Business Statistics IS 310 Slide 1 Chapter 12 Comparing Multiple Proportions Test of Independence

1 1 Slide Slide IS 310 – Business Statistics Business Statistics IS 310 . . . . . . . . . . . CSU LONG BEACH

2 2 Slide Slide IS 310 – Business Statistics Chapter 12 Comparing Multiple Proportions, Test of Independence and Goodness of Fit  Testing the Equality of Population Proportions for Three or More Populations  Goodness of Fit Test  Test of Independence

3 3 Slide Slide IS 310 – Business Statistics Comparing Multiple Proportions, Test of Independence and Goodness of Fit  In this chapter we introduce three additional hypothesis-testing procedures.  The test statistic and the distribution used are based on the chi-square (  2 ) distribution.  In all cases, the data are categorical.

4 4 Slide Slide IS 310 – Business Statistics Using the notation p 1 = population proportion for population 1 p 2 = population proportion for population 2 and p k = population proportion for population k H 0 : p 1 = p 2 = . . . = p k H a : Not all population proportions are equal Testing the Equality of Population Proportions for Three or More Populations The hypotheses for the equality of population proportions for k > 3 populations are as follows:

5 5 Slide Slide IS 310 – Business Statistics  If H 0 cannot be rejected, we cannot detect a difference among the k population proportions.  If H 0 can be rejected, we can conclude that not all k population proportions are equal.  Further analyses can be done to conclude which population proportions are significantly different from others. Testing the Equality of Population Proportions for Three or More Populations

6 6 Slide Slide IS 310 – Business Statistics  Example: Finger Lakes Homes Finger Lakes Homes manufactures three models of prefabricated homes, a two-story colonial, a log cabin, and an A-frame. To help in product-line planning, management would like to compare the customer satisfaction with the three home styles. Testing the Equality of Population Proportions for Three or More Populations p 1 = proportion likely to repurchase a Colonial for the population of Colonial owners p 2 = proportion likely to repurchase a Log Cabin for the population of Log Cabin owners p 3 = proportion likely to repurchase an A-

7 7 Slide Slide IS 310 – Business Statistics We begin by taking a sample of owners from each of the three populations. Each sample contains categorical data indicating whether the respondents are likely or not likely to repurchase the home. Testing the Equality of Population Proportions for Three or More Populations

8 8 Slide Slide IS 310 – Business Statistics Home Owner Colonial Log A-Frame Total Likely to Yes 100 81 83 264 Repurchase No 35 20 41 96 Total 135 101 124 360  Observed Frequencies (sample results) Testing the Equality of Population Proportions for Three or More Populations