Philip J. McCarthy

ESTIMATING POPULATION PROPORTIONS

A FREQUENT problem in polling public opinion is to try to find from a sample the number or percentage of people in the country who hold differing attitudes on a particular issue. A common method is to use the answers to a single question on a poll to estimate the percentages of people in the nation who, for example, favor or oppose the given issue. The complexity of most social issues, however, makes this procedure of very limited value. One method of taking into account this complexity is to construct a battery of questions each closely related to the general issue we are trying to categorize. In the method here proposed we decide in advance the number of categories into which we are trying to divide the population. Each question is constructed in such a manner that there are the same number of possible responses as there are categories, indeed each of the possible responses to a given question is assumed to be characteristic of an individual who actually belongs to one of the categories. The purpose of this paper is to supply a method of estimating from the responses (in the sample) to several questions, the proportions of people in the country who belong to these categories.

Introduction to Statistical Reasoning.

University and Departmental Mission: Seattle Pacific University seeks to be a premier Christian university fully committed to engaging the culture and changing the world by graduating people of competence and character, becoming people of wisdom, and modeling grace-filled community. The mathematics department at Seattle Pacific University seeks to provide excellent instruction to enable our students to be competent in the mathematics required for their chosen fields, and to share our expertise with the community through service and leadership. Hence, common goals for students in mathematics courses include 1) becoming competent in the topics covered in the course, 2) demonstrating skills and attitudes which contribute to professional, ethical behavior, 3) the ability to communicate mathematically, in both written and verbal form, and 4) learning to appreciate the beauty and utility of mathematics.