12.1 Sampling Techniques and Misuses of Statistics 761 According to the American Pet Products Association, 70% of U.S. households own a pet. How did this organization determine this percentage? It would have been very expensive for the American Pet Products Association to ask people in every U.S. household if they owned a pet. Instead, to collect this information, the polling company asked a subset of households, called a sample. If the American Pet Products Association did not ask people in every household if they owned a pet, how do we know that the American Pet Products Association’s results are accurate? In this section, we will discuss different techniques statisticians use to collect numerical information, called data, and how they make accurate conclusions about an entire set of data from the sample collected. We will also discuss how to examine statistical statements before accepting them as fact. Sampling Techniques and Misuses of Statistics SECTION 12.1 LEARNING GOALS Upon completion of this section, you will be able to: 7 Understand sampling techniques, including: random, systematic, cluster, stratified, and convenience sampling. 7 Understand the misuses of statistics. Why This Is Important Samples are used to determine a variety of information, such as the percentage of college graduates in a city and the age of viewers of a particular television program. If advertisers know the ages of viewers of a particular television program, they can design their advertisements to appeal to a particular age group. Sampling Techniques In Chapter 2 we used sets to help us organize data. Recall that data refers to information that is collected and analyzed to help with decision making. The study of statistics was originally used by governments to manage large amounts of numerical data. The use of statistics has grown significantly and today is applied in all walks of life, including estimating the unemployment rate and the cost of living, comparing achievements of individuals, and providing the results of different polls. Statistics is used in scores of other professions; in fact, it is difficult to find any profession that does not depend on some aspect of statistics. Before we discuss different techniques used to collect numerical information, we will first introduce a few important definitions. Statistics is the art and science of gathering, analyzing, and making inferences (predictions) from numerical data obtained in an experiment. Statistics is divided into two main branches: descriptive and inferential. Descriptive statistics is concerned with the collection, organization, and analysis of data. Inferential statistics is concerned with making generalizations or predictions from the data collected. Probability and statistics are closely related. Someone in the field of probability is interested in computing the chance of occurrence of a particular event when all the possible outcomes are known. A statistician’s interest lies in drawing conclusions about possible outcomes through observations of only a few particular events. If a probability expert and a statistician find identical boxes, the probability expert might open the box, observe the contents, replace the cover, and proceed to compute the probability of randomly selecting a specific object from the box. The statistician might select a few items from the box without looking at the contents and make a prediction as to the total contents of the box. The entire contents of the box constitute the population. A population consists of all items or people of interest. The statistician often uses a subset of the population, Soloviova Liudmyla/Shutterstock
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