1.1 What Is/Are Statistics? LEARNING GOAL Understand the two meanings of the term statistics and the basic ideas behind any statistical study, including the relationships among the study’s population, sample, sample statistics, and population parameters. Page 11

Two Definitions of Statistics Statistics is the science of collecting, organizing, and interpreting data. Statistics are the data (numbers or other pieces of information) that describe or summarize something. Page 2

How Statistics Works Definitions What is the Goal of Research? The population in a statistical study is the compete set of people or things being studied. Population parameters are specific characteristics of the population. Pages 2-3

EXAMPLE 1 Populations and Population Parameters For each of the following situations, describe the population being studied and identify some of the population parameters that would be of interest. You work for Farmers Insurance and you’ve been asked to determine the average amount paid to accident victims in cars without side-impact air bags. Solution: The population consists of people who have received insurance payments for accidents in cars that lacked side-impact air bags. The relevant population parameter is the mean (average) amount paid to these people. Page 3

EXAMPLE 1 Populations and Population Parameters For each of the following situations, describe the population being studied and identify some of the population parameters that would be of interest. b. You’ve been hired by McDonald’s to determine the weights of the potatoes delivered each week for french fries. Solution: The population consists of all the potatoes delivered each week for french fires. Relevant population parameters include the mean weight of the potatoes and the variation of the weights (for example, are most of them close to or far from the mean?) Page 3

EXAMPLE 1 Populations and Population Parameters For each of the following situations, describe the population being studied and identify some of the population parameters that would be of interest. c. You are a business reporter covering Genentech Corporation and you are investigation whether their new treatment is effective against childhood leukemia. Solution: The population consists of all children with leukemia. Important population parameters are the percentage of children who recover without the new treatment and the percentage of children who recover with the treatment. Page 3

How Statistics Works What is the Goal of Research? What Actually Gets Studied? Page 3

Definitions A sample is a subset of the population from which data are actually obtained. The actual measurements or observations collected from the sample constitute the raw data. Sample statistics are characteristics of the sample found by consolidating or summarizing the raw data. Page 4

EXAMPLE 2 Unemployment Survey The U.S. Labor Department defines the civilian labor force as all those people who are either employed or actively seeking employment. Each month, the Labor Department reports the unemployment rate, which is the percentage of people actively seeking employment within the entire civilian labor force. To determine the unemployment rate, the Labor Department surveys 60,000 households. For the unemployment reports, describe the Page 4 a. population b. sample c. raw data d. sample statistics e. population parameters

EXAMPLE 2 Unemployment Survey population Solution: The population is the group that the Labor Department wants to learn about, which is all the people who make up the civilian labor force. Page 4

EXAMPLE 2 Unemployment Survey b. sample Solution: The sample consists of all the people among the 60,000 households surveyed. Page 4

The raw data consist of all the information collected in the survey. EXAMPLE 2 Unemployment Survey c. raw data Solution: The raw data consist of all the information collected in the survey. Page 4

EXAMPLE 2 Unemployment Survey d. sample statistics Solution: The sample statistics summarize the raw data for the sample. In this case, the relevant sample statistic is the percentage of people in the sample who are actively seeking employment. Page 4

EXAMPLE 2 Unemployment Survey e. population parameters Solution: The population parameters are the characteristics of the entire population that correspond to the sample statistics. In this case, the relevant population parameter is the actual unemployment rate. Page 4

How Statistics Works What is the Goal of Research? What Actually Gets Studied? How Do Sample Statistics Relate to Population Parameters? Page 4

TIME OUT TO THINK Suppose Nielsen concludes that 30% of Americans watched the Super Bowl. How many people does this represent? (the population of the United States is approximately 300 million. Page 5

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Definition The margin of error in a statistical study is used to describe the range of values, or confidence interval, likely to contain the population parameter. We find this confidence interval by adding and subtracting the margin of error from the sample statistic obtained in the study. That is, the range of values likely to contain the population parameter is from (sample statistic – margin of error) to (sample statistic + margin of error) The margin of error is usually defined to give a 95% confidence interval, meaning that 95% of samples of the size used in the study would contain the actual population parameter (and 5% would not). Page 6

EXAMPLE 3 People on Mars? The Pew Research Center for the People and the Press interviewed 1,546 adult Americans about their attitudes toward the future. Asked whether humans would land on Mars within the next 50 years, 76% of these 1,546 people said either definitely yes or probably yes. The margin of error for the poll was 3 percentage points. Describe the population and the sample for this survey, and explain the meaning of the sample statistic of 76%. What can we conclude about the percentage of the population that thinks humans will land on Mars with in the next 50 years? Page 6

EXAMPLE 3 People on Mars? The population is all adult Americans and the sample consists of the 1,546 people who were interviewed. The sample statistic of 76% is the actual percentage of people in the sample who answered that humans would definitely or probably land on Mars in the next 50 years. The 76% sample statistic and the margin of error of 3 percentage points tell us that the rang of values from 76% – 3% = 73% to 76% + 3% = 79% is likely (with 95% confidence) to contain the population parameter, which in this case is the true percentage of all adult Americans who think humans will definitely or probably land on Mars within the next 50 years. Solution: Page 6

EXAMPLE 4 Cloning Humans The same Pew survey also asked people whether they believed that humans would be cloned within the next 50 years. On this question, 51% answered either definitely yes or probably yes. Again, the margin of error was 3 percentage points. Can we be confident that a majority of adult Americans think that humans will be cloned in the next 50 years? Page 6

EXAMPLE 4 Cloning Humans No. To find the range of values likely to contain the percentage of all adult Americans who think human cloning will definitely or probably occur, we add and subtract the margin of error of 3 percentage points from the sample statistic of 51%. This gives a range of values from 48% to 54%. Because this range includes values on both sides of 50%, we cannot be confident that the majority (that is, greater than 50%) of adult Americans think that humans will be cloned in the next 50 years. Solution: Page 6

TIME OUT TO THINK Look for a report on an opinion poll in this week’s news. Does the report give a margin of error? What does it mean in this case? Page 6

Putting It All Together: The Process of a Statistical Study Page 7

Basic Steps in a Statistical Study Step 1. State the goal of your study precisely; that is, determine the population you want to study and exactly what you’d like to learn about it. Step 2. Choose a sample from the population. (Be sure to use an appropriate sampling technique, as discussed in the next section.) Step 3. Collect raw data from the sample and summarize these data by finding sample statistics of interest. Step 4. Use the sample statistics to make inference about the population. Step 5. Draw conclusions; determine what you learned and whether you achieved your goal. Page 7

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EXAMPLE 5 Identifying the Steps Consider the Pew Research Center survey described in Examples 3 and 4. Identify how researchers applied the five basic steps in a study. Solution: The steps apply as follows. The researchers had a goal of learning about specific attitudes of Americans toward the future. They chose adult Americans as the population, deliberately leaving out children. They chose 1,546 adult Americans for their sample. Although we are not told how the sample was drawn, we will assume that it was drawn so that the 1,546 adult Americans are typical of the entire adult population. Pages 7-8

EXAMPLE 5 Identifying the Steps Solution: The steps apply as follows. They collected the raw data by asking carefully chosen questions of the people in the sample. The raw data are the individual responses to the questions. They summarized these data with sample statistics, such as the overall percentages of people in the sample who answered yes or no to each question. Techniques of statistical science allowed the researchers to infer population characteristics. In this case, the inference consisted of estimating certain population parameters and calculating the margins of error. Pages 7-8

EXAMPLE 5 Identifying the Steps Solution: The steps apply as follows. 5. By making sure that the study was conducted properly and interpreting the estimates of the population parameters, the researchers drew overall conclusions about Americans’ attitudes toward the future. Pages 7-8

Statistics: Decisions for an Uncertain World The Purpose of Statistics Statistics has many uses, but perhaps its most important purpose is to help us make good decisions about issues that involve uncertainty. Pages 8

The End Pages 8 Slide 1.1- 31