2 Chapter 1 Basic Ideas SECTION 1.1 Sampling Objectives 1. Construct a simple random sample 2. Determine when samples of convenience are acceptable 3. Describe stratified sampling, cluster sampling, systematic sampling, and voluntary response sampling 4. Distinguish between statistics and parameters In the months leading up to an election, polls often tell us the percentages of voters that prefer each of the candidates. How do pollsters obtain this information? The ideal poll would be one in which every registered voter were asked his or her opinion. Of course, it is impossible to conduct such an ideal poll, because it is impossible to contact every voter. Instead, pollsters contact a relatively small number of voters, usually no more than a couple of thousand, and use the information from these voters to predict the preferences of the entire group of voters. The process of polling requires two major steps. First, the voters to be polled must be selected and interviewed. In this way the pollsters collect information. In the second step, the pollsters analyze the information to make predictions about the upcoming election. Both the collection and the analysis of the information must be done properly for the results to be reliable. The field of statistics provides appropriate methods for the collection, description, and analysis of information. DEFINITION Statistics is the study of procedures for collecting, describing, and drawing conclusions from information. The polling problem is typical of a problem in statistics. We want some information about a large group of individuals, but we are able to collect information on only a small part of that group. In statistical terminology, the large group is called a population, and the part of the group on which we collect information is called a sample. Explain It Again Why do we draw samples? It’s usually impossible to examine every member of a large population. So we select a group of a manageable size to examine. This group is called a sample. DEFINITION • A population is the entire collection of individuals about which information is sought. • A sample is a subset of a population, containing the individuals that are actually observed. Ideally, we would like our sample to represent the population as closely as possible. For example, in a political poll, we would like the proportions of voters preferring each of the candidates to be the same in the sample as in the population. Unfortunately, there are no methods that can guarantee that a sample will represent the population well. The best we can do is to use a method that makes it very likely that the sample will be similar to the population. The best sampling methods all involve some kind of random selection. The most basic, and in many cases the best, sampling method is the method of simple random sampling. Objective 1 Construct a simple random sample Simple Random Sampling To understand the nature of a simple random sample, think of a lottery. Imagine that 10,000 lottery tickets have been sold, and that 5 winners are to be chosen. What is the fairest way to choose the winners? The fairest way is to put the 10,000 tickets in a drum, mix them thoroughly, then reach in and draw 5 tickets out one by one. These 5 winning tickets are a simple random sample from the population of 10,000 lottery tickets. Each ticket is equally likely to be one of the 5 tickets drawn. More importantly, each collection of 5 tickets that can be formed from the 10,000 is equally likely to comprise the group of 5 that is drawn.
navidi_monk_essential_statistics_1e_ch1_3
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