Section 1.1 Getting Started

Objectives Learn the basic vocabulary of statistics. Distinguish between population and sample; parameters and statistics.

Getting Started The goal of the branch of mathematics called statistics is to provide information so that informed decisions can be made. The goal of this text is to enable you to filter through the statistics you encounter so that you can be better prepared for the decisions you make in your daily life.

Getting Started Statistics Statistics is the science of gathering, describing, and analyzing data. OR Statistics are the actual numerical descriptions of sample data.

Getting Started A population is a particular group of interest. A variable is a value or characteristic that changes among members of the population. Data are the counts, measurements, or observations gathered about a specific variable in a population in order to study it. A census is a study in which data are obtained from every member of the population.

Getting Started A parameter is a numerical description of a population characteristic. A sample is a subset of the population from which data are collected. Sample statistics are numerical descriptions of sample characteristics.

Getting Started It is essential that you are mindful of the relationship between a population and a sample. Figure 1.1 is a picture to help you visualize this relationship. The large oval represents the entire population, and the smaller oval represents the sample chosen from the population.

Table 1.1: Population vs. Sample Getting Started Table 1.1: Population vs. Sample Population Sample Whole group Group we want to know about Characteristics are called parameters Parameters are generally unknown Parameters are fixed Part of the group Group we do know about Characteristics are called statistics Statistics are always known Statistics change with the sample

Example 1.1: Identifying Population and Sample Identify the population and the sample. a. In a survey, 359 college students at the University of Jackson were asked if they had tried the October flavor of the month at the campus coffee shop. Eighty‑three of the students surveyed said yes. b. A survey of 1125 households in the United States found that 24% subscribe to satellite radio.

Example 1.1: Identifying Population and Sample (cont.) Solution a. Population: All college students at the University of Jackson Sample: The 359 college students who were surveyed b. Population: All households in the United States Sample: The 1125 households in the United States that were surveyed

Example 1.2: Identifying Population, Sample, Parameters, and Statistics Read each of the shortened survey reports below. For each report: a. Identify the population. b. Identify the sample. c. Determine whether the highlighted value is a parameter or statistic.

Example 1.2: Identifying Population, Sample, Parameters, and Statistics (cont.) I. After an airplane security scare on Christmas day, 2009, the Gallup organization interviewed 542 American air travelers about increased security measures at airports. The report stated that 78% of American air travelers are in favor of United States airports using full-body‑scan imaging on airline passengers. Source: Jones, Jeffrey M. “In U.S., Air Travelers Take Body Scans in Stride.” 11 Jan. 2010. http://www.gallup.com/poll/125018/Air-Travelers-Body-Scans-Stride.aspx (12 Dec. 2011).

Example 1.2: Identifying Population, Sample, Parameters, and Statistics (cont.) II. Rasmussen Reports also conducted a survey in response to the airport security scare on Christmas day, 2009. The national telephone survey of 1000 adult Americans found that 59% of Americans surveyed favor racial profiling as a means of determining which passengers to search at airport security checkpoints. Source: Rasmussen Reports. “59% Favor Racial, Ethnic Profiling For Airline Security.” 7 Jan. 2010. http://www.rasmussenreports.com/public_content/lifestyle/general_lifestyle/january_2010/59_favor_racial_ethnic_profiling_for_airline_security (12 Dec. 2011).

Example 1.2: Identifying Population, Sample, Parameters, and Statistics (cont.) Solution I. a. Population: All American air travelers b. Sample: The 542 American air travelers who were surveyed c. The value 78% refers to all American air travelers; thus this is a population parameter.

Example 1.2: Identifying Population, Sample, Parameters, and Statistics (cont.) II. a. Population: All adult Americans b. Sample: The 1000 adult Americans who were surveyed c. The value 59% refers to only those adult Americans who were surveyed, thus this is a sample statistic.

Two Branches of Statistics The branch of descriptive statistics, as a science, gathers, sorts, summarizes, and displays the data. The branch of inferential statistics, as a science, involves using descriptive statistics to estimate population parameters.

Two Types an Analysis Exploratory analysis uses data to estimate parameters. Confirmatory analysis uses statistics to test claims about reality (hypotheses).

Example 1.3: Identifying Descriptive and Inferential Statistics In a news report on the state of the media by Tom Rosenstiel and Amy Mitchell, they write the following: “AOL had 900 journalists, 500 of them at its local Patch news operation.... By the end of 2011, Bloomberg expects to have 150 journalists and analysts for its new Washington operation, Bloomberg Government.” Source: Rosenstiel, Tom and Amy Mitchell. “Overview.” The State of the News Media: An Annual Report on American Journalism. Pew Research Center’s Project for Excellence in Journalism. 2011. http://stateofthemedia.org/2011/overview-2/ (12 Dec. 2011). Identify the descriptive and inferential statistics used in this excerpt from their article.

Example 1. 3: Identifying Descriptive and Inferential Statistics (cont Solution When the authors identify AOL as having “had 900 journalists, 500 of them at its local Patch news operation,” they are describing the actual counts, not estimates; thus these numbers of journalists are descriptive statistics. On the other hand, when the authors state “By the end of 2011, Bloomberg expects to have 150 journalists and analysts for its new Washington operation,” they are referring to an estimate based on past descriptive statistics. Therefore the estimate, 150 journalists and analysts, is an inferential statistic.