Copyright © 2008 Pearson Education, Inc.

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Chapter 1The Nature of

StatisticsSection 1.1

Statistics Basics

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IntroductionWhat is Statistics? A branch of mathematics devoted to the collection,

description, analysis and interpretation of data.

The science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.

In what occupations might we use statistics?

Education: Which method of teaching is best the old or the new?

Sports: Number of hits a baseball player gets in one season.

Public Health: Number of residents that contracted a new strain of flu.

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What are the two branches of Statistics?

Descriptive statistics includes the construction of graphs, charts, and tables and the calculation of various descriptive measures such as averages, measures of variation, and percentiles.

Descriptive Statistics consists of methods for organizing and summarizing information.

Consists of the collection, organization, summarization, and presentation of data.

The statistician tries to describe a situation.

The goal is simply to describe a set of data that has been collected, whether the data represents an entire population or a sample. (Chapters 2 and 3)

Descriptive Statistics

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Descriptive Statistics

The 1948 Baseball Season In 1948, the Washington Senators played 153 games, winning 56 and losing 97. They finished seventh in the American League and were led in hitting by Bud Stewart, whose batting average was .279

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Inferential Statistics

Statisticians analyze the information obtained from a sample of the voting population to make inferences (draw conclusions) about the preferences of the entire voting population. Inferential statistics provides methods for drawing such conclusions.

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.

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Inferential Statistics

consists of generalizing from samples to

populations, performing estimations hypothesis

testing, determining relationships among variables,

and making predictions.

The statistician tries to make conclusions from

samples and populations.

The goal is to reach a conclusion about a

population based only on knowledge obtained by

studying a sample drawn from that population.

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Classifying Statistical StudiesIn each of these statements, tell whether descriptive or

inferential statistics have been used.

Inferential – making predictionsDescriptive – values that can be counted

•In the year 2010, 148 million Americans will be enrolled in an HMO (Source: USA TODAY)

Inferential

•Nine out of ten on-the-job fatalities are men. (Source: USA TODAY Weekend)

Descriptive

•Expenditures for the cable industry were $5.66 billion in 1996 (Source: USA TODAY)

Descriptive

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Classifying Statistical Studies•The median household income for people aged 25 – 34 is

$35,888 (Source: USA TODAY)

Descriptive

•Allergy therapy makes bees go away (Source: Prevention) Inferential

•Drinking decaffeinated coffee can raise cholesterol levels by 7% (Source: American Heart Association)

Inferential

•The national average annual medicine expenditure per person is $1052 (Source: The Greensburg Tribune review)

Descriptive

•Experts say that mortgage rates may soon hit bottom (Source: USA TODAY)

Inferential

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Population and Sample

Political polling provides an example of inferential statistics.

Interviewing everyone of voting age in the United States on their voting preferences would be expensive and unrealistic.

Statisticians who want to gauge the sentiment of the entire population of U.S. voters can afford to interview only a carefully chosen group of a few thousand voters. This group is called a sample of the population.

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Population

When a statistical study is done (meaning data is collected) the set of all objects being studied is called the population. The Population then consists of all the subject (human or otherwise) that are being studied.

Population: The collection of all individuals or items underconsideration in a statistical study.

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Sample

Sample: That part of the population from which informationis obtained.

Population

Sample

In a statistical study the population might be small and easily accessible. However, populations are often very large and, in some cases, theoretical. In such instances, the population is not going to be easily accessible. Here, statisticians have to be content with studying a sample drawn from the population.

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Figure 1.1

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Is a subset or part of a population. In other words, is a group of subjects selected from a population.

Sample:

If a statistician must work with a sample, it is important how the sample is selected. The most desirable characteristic of a sample is that it be representative of the population from which it is drawn.

However, selecting representative samples from a population is a science in itself and is not a topic covered in an elementary statistics course.

We should, however, mention a few of the basic concepts of sampling theory. For example: random sample and stratified random sample.

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What are the two types of studies? Observational study

Researchers observe characteristics and take measurements.

They merely observes what is happening or what has happened in the

past and tries to draw conclusions based on these observations.

Reveals only association

Designed Experiment

Researchers impose treatments and controls and then observe

characteristics and take measurements.

They manipulates one of the variables and tries to determine how the

manipulation influences other variables.

Helps establish causation

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Obervational Studies and Designed ExperimentsIdentify each study as being either observational or experimental. Observational – researchers observe characteristics and take measurements.

Designed Experiment – researchers impose treatments and controls and then observe characteristics and take measurements.---------------------------------------------------------------------------Subjects are randomly assigned to two groups, and one group was given a herb and the other group a placebo. After 6 months, the number of respiratory tract infections each group had were compared.

Designed Experiment

A research stood at a busy intersection to see if the color of the automobile that a person drives is related to running red lights.

Observational Study

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Obervational Studies and Designed Experiments

A researcher finds that people that are more hostile have higher total cholesterol levels than those who are less hostile.

Observational

Subjects are randomly assigned to four groups. Each group is placed on one of four special diets – a low fat diet, a high fish diet, a combination of low fat and high fish, and a regular diet. After 6 months, the blood pressure of these groups are compared to see if diet has any effect on blood pressure.

Experimental

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Computers and Calculators

In the past, statistical calculations were done with pencil and paper. However, with the advent of calculators, numerical computations became easier.

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Statistical Packages

Microsoft Excel, MINITAB, the TI-83 and TI-84 graphing calculator can be used to perform statistical computations.

Students should realize that the computer and calculator merely give numerical answers and save time and effort of doing calculations by hand. You still have to understand and interpret the statistical concept.

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Summary The two major areas of statistics are

descriptive and inferential.

When the populations to be studied are large, statisticians

use subgroups called

samples.

The two basic types of statistical studies are

observational and designed experiment.

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Conclusion

The applications of statistics are many and varied. People encounter them in everyday life, such as in reading newspapers or magazines, listening to the radio, surfing the Internet, or watching television.

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HOMEWORK – CHAPTER 1.1

Pages 9-11

1, 2, 5, 6, 7, 9, 10, 12, 14, 20, and 23