Tải bản đầy đủ - 0 (trang)
ACTIVITY 1.2: Head Sizes: Understanding Variability

# ACTIVITY 1.2: Head Sizes: Understanding Variability

Tải bản đầy đủ - 0trang

Activities

27

FIGURE 1.9

Shapes for Activity 1.3.

3

2

1

6

5

4

9

8

7

10

5. Would the sum of the differences tell you if the estimates and actual values were in close agreement?

Does a sum of 0 for the differences indicate that all

the estimates were equal to the actual value?

Explain.

6. Compare your estimates with those of another person in the class by comparing the sum of the absolute values of the differences between estimates and

corresponding actual values. Who was better at estimating shape sizes? How can you tell?

7. Use the last column of the activity sheet to record

the squared differences (for example, if the difference for shape 1 was 23, the squared difference

would be (23)2 5 9. Explain why the sum of the

squared differences can also be used to assess how

8. For this step, work with three or four other students

from your class. For each of the 10 shapes, form a

new size estimate by computing the average of the

size estimates for that shape made by the individuals

in your group. Is this new set of estimates more accurate than your own individual estimates were?

How can you tell?

why or why not.

Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

28

Chapter 1 The Role of Statistics and the Data Analysis Process

AC TI V I TY 1 . 4

A Meaningful Paragraph

Write a meaningful paragraph that includes the following six terms: sample, population, descriptive statistics, bar chart, numerical variable, and dotplot.

A “meaningful paragraph” is a coherent piece of

writing in an appropriate context that uses all of the

listed words. The paragraph should show that you un-

derstand the meanings of the terms and their relationships to one another. A sequence of sentences that just

deﬁne the terms is not a meaningful paragraph. When

choosing a context, think carefully about the terms you

need to use. Choosing a good context will make writing

a meaningful paragraph easier.

Summary of Key Concepts and Formulas

TERM OR FORMULA

COMMENT

Population

The entire collection of individuals or measurements

Sample

A part of the population selected for study.

Descriptive statistics

Numerical, graphical, and tabular methods for

organizing and summarizing data.

Inferential statistics

Methods for generalizing from a sample to a population.

Categorical data

Individual observations are categorical responses

(nonnumerical).

Numerical data

Individual observations are numerical (quantitative) in

nature.

Discrete numerical data

Possible values are isolated points along the number line.

Continuous numerical data

Possible values form an entire interval along the

number line.

Univariate, bivariate and multivariate data

Each observation consists of one (univariate), two (bivariate), or two or more (multivariate) responses or values.

Frequency distribution for categorical data

A table that displays frequencies, and sometimes relative

frequencies, for each of the possible values of a categorical

variable.

Bar chart

A graph of a frequency distribution for a categorical data

set. Each category is represented by a bar, and the area of

the bar is proportional to the corresponding frequency or

relative frequency.

Dotplot

A graph of numerical data in which each observation is

represented by a dot on or above a horizontal measurement scale.

Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Chapter Review Exercises

29

Chapter Review Exercises 1.32 - 1.37

The report “Testing the Waters 2009” (www

.nrdc.org) included information on the water quality at

1.32

the 82 most popular swimming beaches in California.

Thirty-eight of these beaches are in Los Angeles County.

For each beach, water quality was tested weekly and the

data below are the percent of the tests in 2008 that failed

to meet water quality standards.

Los Angeles County

32

4

6

4

19 13 11 19

33 12 29

3

17 26 17 20

Other Counties

0

15

1

0

10

0

8

0

8

40

0

1

2

8

3

2

5

7

8

4

9

11

10

7

11

6

6

4

16

22

14

27

23

18

11

19

19

31

23

16

43

3

0

0

0

7

5

2

0

5

4

2

17

11

1

3

4

5

0

5

3

7

1

3

7

a. Construct a dotplot of the percent of tests failing to

meet water quality standards for the Los Angeles

County beaches. Write a few sentences describing

any interesting features of the dotplot.

b. Construct a dotplot of the percent of tests failing to

meet water quality standards for the beaches in other

counties. Write a few sentences describing any interesting features of the dotplot.

c. Based on the two dotplots from Parts (a) and (b),

describe how the percent of tests that fail to meet

water quality standards for beaches in Los Angeles

county differs from those of other counties.

1.33 The U.S. Department of Education reported that

14% of adults were classiﬁed as being below a basic literacy level, 29% were classiﬁed as being at a basic literacy

level, 44% were classiﬁed as being at an intermediate

literacy level, and 13% were classiﬁed as being at a

proﬁcient level (2003 National Assessment of Adult

Literacy).

a. Is the variable literacy level categorical or numerical?

b. Would it be appropriate to display the given information using a dotplot? Explain why or why not.

c. Construct a bar chart to display the given data on

literacy level.

Data set available online

1.34

The Computer Assisted Assessment Center at

the University of Luton published a report titled “Technical Review of Plagiarism Detection Software.” The

authors of this report asked faculty at academic institutions about the extent to which they agreed with the

statement “Plagiarism is a signiﬁcant problem in academic institutions.” The responses are summarized in the

accompanying table. Construct a bar chart for these data.

Response

Strongly disagree

Disagree

Not sure

Agree

Strongly agree

Frequency

5

48

90

140

39

1.35

The article “Just How Safe Is That Jet?” (USA

Today, March 13, 2000) gave the following relative frequency distribution that summarized data on the type of

violation for ﬁnes imposed on airlines by the Federal

Type of Violation

Relative Frequency

Security

Maintenance

Flight operations

Hazardous materials

Other

.43

.39

.06

.03

.09

Use this information to construct a bar chart for type of

violation, and then write a sentence or two commenting

on the relative occurrence of the various types of

violation.

Each year, U.S. News and World Report publishes a ranking of U.S. business schools. The following

data give the acceptance rates (percentage of applicants

admitted) for the best 25 programs in a recent survey:

1.36

16.3 12.0 25.1 20.3 31.9 20.7 30.1 19.5 36.2

46.9 25.8 36.7 33.8 24.2 21.5 35.1 37.6 23.9

17.0 38.4 31.2 43.8 28.9 31.4 48.9

Construct a dotplot, and comment on the interesting

features of the plot.

Video Solution available

Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

30

Chapter 1 The Role of Statistics and the Data Analysis Process

1.37

Many adolescent boys aspire to be professional

athletes. The paper “Why Adolescent Boys Dream of

Becoming Professional Athletes” (Psychological Reports [1999]:1075–1085) examined some of the reasons.

Each boy in a sample of teenage boys was asked the following question: “Previous studies have shown that more

teenage boys say that they are considering becoming

professional athletes than any other occupation. In your

opinion, why do these boys want to become professional

athletes?” The resulting data are shown in the following

table:

Data set available online

Response

Frequency

Fame and celebrity

Money

Attract women

Like sports

Easy life

Don’t need an education

Other

94

56

29

27

24

19

19

Construct a bar chart to display these data.

Video Solution available

Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

CHAPTER

2

Collecting Data

Sensibly

A primary goal of statistical studies is to collect data that

can then be used to make informed decisions. It should

come as no surprise that the ability to make good decisions depends on the quality of the information available.

The data collection step is critical to obtaining reliable

information; both the type of analysis that is appropriate

and the conclusions that can be drawn depend on how

the data are collected. In this chapter, we ﬁrst consider

two types of statistical studies and then focus on two

widely used methods of data collection: sampling and

experimentation.

Purestock/Kwame Zikomo/SuperStock

Make the most of your study time by accessing everything you need to succeed

online with CourseMate.

Visit http://www.cengagebrain.com where you will find:

• An interactive eBook, which allows you to take notes, highlight, bookmark, search

the text, and use in-context glossary definitions

Step-by-step instructions for Minitab, Excel, TI-83/84, SPSS, and JMP

Video solutions to selected exercises

Data sets available for selected examples and exercises

Online quizzes

Flashcards

Videos

31

Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

32

2.1

Chapter 2 Collecting Data Sensibly

Statistical Studies: Observation

and Experimentation

On September 25, 2009, results from a study of the relationship between spanking

and IQ were reported by a number of different news media. Some of the headlines

that appeared that day were:

“Spanking lowers a child’s IQ” (Los Angeles Times)

“Do you spank? Studies indicate it could lower your kid’s IQ” (SciGuy,

Houston Chronicle)

“Spanking can lower IQ” (NBC4i, Columbus, Ohio)

“Smacking hits kids’ IQ” (newscientist.com)

In the study that these headlines refer to, the investigators followed 806 kids age 2 to

4 and 704 kids age 5 to 9 for 4 years. IQ was measured at the beginning of the study

and again 4 years later. The researchers found that at the end of the study, the average

IQ of kids who were not spanked was 5 points higher than that of kids who were

spanked among the kids who were 2 to 4 years old when the study began, and

2.8 points higher among the kids who were 5 to 9 years old when the study began.

These headlines all imply that spanking was the cause of the observed difference

in IQ. Is this conclusion reasonable? The answer depends in a critical way on the

considering some important aspects of study design.

Observation and Experimentation

Data collection is an important step in the data analysis process. When we set out to

collect information, it is important to keep in mind the questions we hope to answer

on the basis of the resulting data. Sometimes we are interested in answering questions

about characteristics of a single existing population or in comparing two or more

well-deﬁned populations. To accomplish this, we select a sample from each population under consideration and use the sample information to gain insight into characteristics of those populations.

For example, an ecologist might be interested in estimating the average shell thickness of bald eagle eggs. A social scientist studying a rural community may want to determine whether gender and attitude toward abortion are related. These are examples

of studies that are observational in nature. In these studies, we want to observe characteristics of members of an existing population or of several populations, and then use

the resulting information to draw conclusions. In an observational study, it is important to obtain a sample that is representative of the corresponding population.

Sometimes the questions we are trying to answer deal with the effect of certain

explanatory variables on some response and cannot be answered using data from

an observational study. Such questions are often of the form, “What happens

when ... ?” or, “What is the effect of ... ?” For example, an educator may wonder what

would happen to test scores if the required lab time for a chemistry course were increased from 3 hours to 6 hours per week. To answer such questions, the researcher

conducts an experiment to collect relevant data. The value of some response variable

(test score in the chemistry example) is recorded under different experimental conditions (3-hour lab and 6-hour lab). In an experiment, the researcher manipulates one

or more explanatory variables, also sometimes called factors, to create the experimental conditions.

Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

2.1

Statistical Studies: Observation and Experimentation

33

DEFINITION

A study is an observational study if the investigator observes characteristics

of a sample selected from one or more existing populations. The goal of an

observational study is usually to draw conclusions about the corresponding

population or about differences between two or more populations. In a welldesigned observational study, the sample is selected in a way that is designed

to produce a sample that is respresentative of the population.

A study is an experiment if the investigator observes how a response variable

behaves when one or more explanatory variables, also called factors, are manipulated. The usual goal of an experiment is to determine the effect of the

manipulated explanatory variables (factors) on the response variable. In a welldesigned experiment, the composition of the groups that will be exposed to

different experimental conditions is determined by random assignment.

The type of conclusion that can be drawn from a statistical study depends

on the study design. Both observational studies and experiments can be used to

compare groups, but in an experiment the researcher controls who is in which

group, whereas this is not the case in an observational study. This seemingly small

difference is critical when it comes to drawing conclusions based on data from the

study.

A well-designed experiment can result in data that provide evidence for a causeand-effect relationship. This is an important difference between an observational

study and an experiment. In an observational study, it is impossible to draw clear

cause-and-effect conclusions because we cannot rule out the possibility that the observed effect is due to some variable other than the explanatory variable being studied.

Such variables are called confounding variables.

DEFINITION

A confounding variable is one that is related to both group membership and

the response variable of interest in a research study.

Consider the role of confounding variables in the following three studies:

• The article

“Panel Can’t Determine the Value of Daily Vitamins” (San Luis

Obispo Tribune, July 1, 2003) summarized the conclusions of a government

advisory panel that investigated the beneﬁts of vitamin use. The panel looked at

a large number of studies on vitamin use and concluded that the results were

“inadequate or conﬂicting.” A major concern was that many of the studies were

observational in nature and the panel worried that people who take vitamins

might be healthier just because they tend to take better care of themselves in

general. This potential confounding variable prevented the panel from concluding that taking vitamins is the cause of observed better health among those who

take vitamins.

• Studies have shown that people over age 65 who get a ﬂu shot are less likely than

those who do not get a ﬂu shot to die from a ﬂu-related illness during the following year. However, recent research has shown that people over age 65 who get a

ﬂu shot are also less likely than those who don’t to die from any cause during the

following year (International Journal of Epidemiology, December 21, 2005).

Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

### Tài liệu bạn tìm kiếm đã sẵn sàng tải về

ACTIVITY 1.2: Head Sizes: Understanding Variability

Tải bản đầy đủ ngay(0 tr)

×