Chapter 1: The Nature of Statistics STP 226: Elements of Statistics Jenifer Boshes Arizona State University

1.1: Statistics Basics

Descriptive Statistics Descriptive statistics consists of methods for organizing and summarizing information.

Example 1: 80% of a class receives a passing grade. The Chicago Cubs had a winning record of 97-64 for the 2008 season. The U.S. won 11.92% of the Gold Medals in the 2008 Olympics.

Population & Sample A population is the collection of all individuals or items under consideration in a statistical study. A sample is the part of the population from which information is obtained.

Inferential Statistics Inferential statistics consists of methods for drawing and measuring the reliability of conclusions about a population based on information obtained from a sample of the population.

Example 2: Political polling. Archaeological digs. Average salary of a football player.

Descriptive vs. Inferential Statistics If the intent of the study is to examine and explore the information obtained for its own intrinsic interest only, the study is descriptive. If the information is obtained from a sample of a population and the intent of the study is to use that information to draw conclusions about the population, the study is inferential.

Example 3a: Classify the following studies as descriptive or inferential. (a) (Example 1.3; Page 6) The 1948 Presidential Election - Ticket Votes Percentage Truman-Barkley (Democratic) 24,179,345 49.7 Dewey-Warren (Republican) 21,991,291 45.2 Thurmond-Wright (States Rights) 1,176,125 2.4 Wallace-Taylor (Progressive) 1,157,326 Thomas-Smith (Socialist) 139,572 0.3 9

Example 3b: Classify the following studies as descriptive or inferential. (b) (Example 1.4; Page 7) Testing Baseballs – Major League Baseball used Spalding baseballs until 1976. In 1977, MLB began using Rawlings baseballs (which are still in use today). In 1977, pitchers complained that the baseballs were harder, bounced farther and faster, and gave hitters an unfair advantage. An independent testing company randomly selected a sample of 85 baseballs from the 1977 supplies of various major league clubs. The bounce, weight, and hardness of the baseballs chosen was carefully measured and compared with measurements obtained from similar tests on baseballs used in 1952, 1953, 1961, 1963, 1970, 1973. The conclusion was that “… the 1977 Rawlings ball is livelier than the 1976 Spalding, but not as lively as it could be under big league rules, or as the ball has been in the past.” 10

Example 3c: Classify the following studies as descriptive or inferential. Music Type Expenditure (%) Rock 24.4 Pop 12.1 Rap/Hip hop 11.4 R&B/Urban 10.6 Country 10.5 Religious 6.7 Jazz 3.4 Classical 3.2 Soundtracks 1.4 New Age 1 Oldies 0.8 Children's 0.5 Other 7.9 Unknown 6.1 (c) (Problem 1.12; Page 10) Music People Buy – Results of monthly telephone surveys yielded the percentage estimates of all music expenditures shown in the table at the top of the next column. These statistics were published in 2001 Consumer Profile. 11

Example 3d: Classify the following studies as descriptive or inferential. (d) (Problem 1.11; Page 10) Dow Jones Industrial Averages - The following table provides the closing values of the Dow Jones Industrial Averages as of the end of December for the years 1997-2002. Year Closing Value 1997 7,908.25 1998 9,181.43 1999 11,497.12 2000 10,786.85 2001 10,021.50 2002 8,341.63 12

1.2: Simple Random Sampling

Acquiring Information A census is obtaining information on the entire population of interest. Experimentation is conducting a controlled study to come to conclusions about a topic. Sampling is a method of acquiring information by choosing portions of a population in a particular way to make inferences.

Comments on Sampling A representative sample reflects as closely as possible the relevant characteristics of the population under consideration. If you were interested in the average height of an ASU student, who would you include in your sample?

Probability Sampling In probability sampling, a random device, such as tossing a coin or consulting a table of random numbers, is used to decide which members of the population will constitute the sample instead of leaving such decisions to human judgment. The use of probability sampling guarantees that the techniques of inferential statistics can be applied.

Simple Random Sampling Simple random sampling is a sampling procedure for which each possible sample of a given size is equally likely to be the one obtained. A simple random sample is a sample obtained by simple random sampling. (Unless otherwise specified, assume simple random sampling is done without replacement.)

Example 1: The line of succession for the Presidency is: Vice-President (V), Speaker of the House (H), President pro tempore of the Senate (P), Secretary of State (S), Secretary of the Treasury (T). (a) List the 10 possible samples of size 2 that can be obtained from the population of 5 officials. If a simple random sampling procedure is used to obtain a sample of two officials, what are the chances that it is the first sample on your list from part (a)? What are some ways to obtain an SRS of size 2?

Table of Random Numbers Appendix A Table I or Page 14

How to Use the Random Number Table Number the units of interest Randomly select a starting point Read down the column using the number of digits of interest (i.e. If there are 50 units of interest, use 2 digits. If there are 451 units of interest, use 3 digits.) Record numbers, discarding repeats and numbers outside the list of units.

Example 2: Use the table of random numbers to select eight years between 1950-1999 to study for your sample. Let the two digit random number you select be the year. For example, if you selected ‘62’, study the year 1962. Begin with the digits 79 in row/line 11, columns 07-08 of the random number table.

Example 3: (Problem 1.28; Page 16) In the game of keno, 20 balls are selected at random from 80 balls, numbered 1-80. Use Table I in Appendix A to simulate one game of keno by obtaining 20 random numbers between 1 and 80. Begin with the digits 99 in row/line 07, columns 22-23 of the random number table.

Bibliography Some of the textbook images embedded in the slides were taken from: Elementary Statistics, Sixth Edition; by Weiss; Addison Wesley Publishing Company Copyright © 2005, Pearson Education, Inc.