Expert answer:Statistics in Business
Solved by verified expert:Purpose of Assignment The purpose of this assignment is to have students demonstrate mastery of the foundational concepts that set the stage for the remainder of the course. Students apply those concepts to business research questions or problem situations to focus their thinking on statistical literacy for use in business decision-making. Assignment Steps Resources: Week 1 Readings; Statistics Lab Tutorial help on Excel® and Word functions can be found on the Microsoft® Office® website. There are also additional tutorials via the web that offer support for office products. Develop a 1,050-word response addressing each of the following prompts: Define statistics with citation and reference.Contrast quantitative data and qualitative data. Use two peer reviewed references.Evaluate tables and charts used to represent quantitative and qualitative data.Describe the levels of data measurement.Describe the role of statistics in business decision-making.Provide at least two business research questions, or problem situations, in which statistics was used or could be used.Use two peer reviewed references. Format your assignment consistent with APA guidelines. Click the Assignment Files tab to submit your assignment.Attached is Ch1-3
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CHAPTER 1
Introduction
© Carol Thacker/iStockphoto
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1.1 Statistics and Types of Statistics
Case Study 1–1 2014 Lobbying Spending by Selected Companies
Case Study 1–2 Americans’ Life Outlook, 2014
1.2 Basic Terms
1.3 Types of Variables
1.4 Cross-Section Versus Time-Series Data
1.5 Population Versus Sample
1.6 Design of Experiments
1.7 Summation Notation
Are you, as an American, thriving in your life? Or are you struggling? Or,
even worse, are you suffering? A poll of 176,903 American adults, aged 18
and older, was conducted January 2 to December 30, 2014, as part of the
Gallup-Healthways Well-Being Index survey. The poll found that while
54.1% of these Americans said that they were thriving, 42.1% indicated that
they were struggling, and 3.8% mentioned that they were suffering. (See
Case Study 1–2.)
The study of statistics has become more popular than ever over the past four decades. The
increasing availability of computers and statistical software packages has enlarged the role of
statistics as a tool for empirical research. As a result, statistics is used for research in almost
all professions, from medicine to sports. Today, college students in almost all disciplines are
required to take at least one statistics course. Almost all newspapers and magazines these
days contain graphs and stories on statistical studies. After you finish reading this book, it
should be much easier to understand these graphs and stories.
Every field of study has its own terminology. Statistics is no exception. This introductory
chapter explains the basic terms and concepts of statistics. These terms and concepts will
bridge our understanding of the concepts and techniques presented in subsequent chapters.
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1.1 Statistics and Types of Statistics
In this section we will learn about statistics and types of statistics.
1.1.1 What Is Statistics?
The word statistics has two meanings. In the more common usage, statistics refers to
numerical facts. The numbers that represent the income of a family, the age of a student, the
percentage of passes completed by the quarterback of a football team, and the starting salary
of a typical college graduate are examples of statistics in this sense of the word. A 1988 article
in U.S. News & World Report mentioned that “Statistics are an American obsession.”1 During
the 1988 baseball World Series between the Los Angeles Dodgers and the Oakland A’s, the
then NBC commentator Joe Garagiola reported to the viewers numerical facts about the
players’ performances. In response, fellow commentator Vin Scully said, “I love it when you
talk statistics.” In these examples, the word statistics refers to numbers.
The following examples present some statistics:
1. During March 2014, a total of 664,000,000 hours were spent by Americans watching
March Madness live on TV and/or streaming (Fortune Magazine, March 15, 2015).
2. Approximately 30% of Google’s employees were female in July 2014 (USA TODAY, July
24, 2014).
3. According to an estimate, an average family of four living in the United States needs
$130,357 to live the American dream (USA TODAY, July 7, 2014).
4. Chicago’s O’Hare Airport was the busiest airport in 2014, with a total of 881,933 flight
arrivals and departures.
5. In 2013, author James Patterson earned $90 million from the sale of his books (Forbes,
September 29, 2014).
6. About 22.8% of U.S. adults do not have a religious affiliation (Time, May 25, 2015).
7. Yahoo CEO Marissa Mayer was the highest paid female CEO in America in 2014, with a
total compensation of $42.1 million.
The second meaning of statistics refers to the field or discipline of study. In this sense of
the word, statistics is defined as follows.
Statistics Statistics is the science of collecting, analyzing, presenting, and interpreting
data, as well as of making decisions based on such analyses.
Every day we make decisions that may be personal, business related, or of some other kind.
Usually these decisions are made under conditions of uncertainty. Many times, the situations
or problems we face in the real world have no precise or definite solution. Statistical methods
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help us make scientific and intelligent decisions in such situations. Decisions made by using
statistical methods are called educated guesses. Decisions made without using statistical (or
scientific) methods are pure guesses and, hence, may prove to be unreliable. For example,
opening a large store in an area with or without assessing the need for it may affect its
success.
Like almost all fields of study, statistics has two aspects: theoretical and applied.
Theoretical or mathematical statistics deals with the development, derivation, and proof of
statistical theorems, formulas, rules, and laws. Applied statistics involves the applications of
those theorems, formulas, rules, and laws to solve real-world problems. This text is
concerned with applied statistics and not with theoretical statistics. By the time you finish
studying this book, you will have learned how to think statistically and how to make educated
guesses.
1.1.2 Types of Statistics
Broadly speaking, applied statistics can be divided into two areas: descriptive statistics
and inferential statistics.
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CASE STUDY 1-1
2014 LOBBYING SPENDING BY SELECTED COMPANIES
Data source: Fortune Magazine, June 1, 2015
The accompanying chart shows the lobbying spending by five selected companies during
2014. Many companies spend millions of dollars to win favors in Washington. According
to Fortune Magazine of June 1, 2015, “Comcast has remained one of the biggest
corporate lobbyists in the country.” In 2014, Comcast spent $17 million, Google spent
$16.8 million, AT&T spent $14.2 million, Verizon spent $13.3 million, and Time Warner
Cable spent $7.8 million on lobbying. These numbers simply describe the total amounts
spent by these companies on lobbying. We are not drawing any inferences, decisions, or
predictions from these data. Hence, this data set and its presentation is an example of
descriptive statistics.
Descriptive Statistics
Suppose we have information on the test scores of students enrolled in a statistics class. In
statistical terminology, the whole set of numbers that represents the scores of students is
called a data set, the name of each student is called an element, and the score of each
student is called an observation. (These terms are defined in more detail in Section 1.2.)
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Many data sets in their original forms are usually very large, especially those collected by
federal and state agencies. Consequently, such data sets are not very helpful in drawing
conclusions or making decisions. It is easier to draw conclusions from summary tables and
diagrams than from the original version of a data set. So, we summarize data by constructing
tables, drawing graphs, or calculating summary measures such as averages. The portion of
statistics that helps us do this type of statistical analysis is called descriptive statistics.
Descriptive Statistics Descriptive statistics consists of methods for organizing,
displaying, and describing data by using tables, graphs, and summary measures.
Chapters 2 and 3 discuss descriptive statistical methods. In Chapter 2, we learn how to
construct tables and how to graph data. In Chapter 3, we learn how to calculate numerical
summary measures, such as averages.
Case Study 1-1 presents an example of descriptive statistics.
Inferential Statistics
In statistics, the collection of all elements of interest is called a population. The selection of
a portion of the elements from this population is called a sample. (Population and sample
are discussed in more detail in Section 1.5.)
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CASE STUDY 1-2
AMERICANS’ LIFE OUTLOOK, 2014
Data source: Gallup-Healthways Well-Being Index
A poll of 176,903 American adults, aged 18 and older, was conducted January 2 to
December 30, 2014, as part of the Gallup-Healthways Well-Being Index survey. Gallup
and Healthways have been “tracking Americans’ life evaluations daily” since 2008.
According to this poll, in 2014, Americans’ outlook on life was the best in seven years, as
54.1% “rated their lives highly enough to be considered thriving,” 42.1% said they were
struggling, and 3.8% mentioned that they were suffering. As mentioned in the chart, the
margin of sampling error was ± 1%. In Chapter 8, we will discuss the concept of margin
of error, which can be combined with these percentages when making inferences. As we
notice, the results described in the chart are obtained from a poll of 176,903 adults. We
will learn in later chapters how to apply these results to the entire population of adults.
Such decision making about the population based on sample results is called inferential
statistics.
A major portion of statistics deals with making decisions, inferences, predictions, and
forecasts about populations based on results obtained from samples. For example, we may
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make some decisions about the political views of all college and university students based on
the political views of 1000 students selected from a few colleges and universities. As another
example, we may want to find the starting salary of a typical college graduate. To do so, we
may select 2000 recent college graduates, find their starting salaries, and make a decision
based on this information. The area of statistics that deals with such decision-making
procedures is referred to as inferential statistics. This branch of statistics is also called
inductive reasoning or inductive statistics.
Inferential Statistics Inferential statistics consists of methods that use sample
results to help make decisions or predictions about a population.
Case Study 1-2 presents an example of inferential statistics. It shows the results of a survey
in which American adults were asked about their opinions about their lives.
Chapters 8 through 15 and parts of Chapter 7 deal with inferential statistics.
Probability, which gives a measurement of the likelihood that a certain outcome will
occur, acts as a link between descriptive and inferential statistics. Probability is used to make
statements about the occurrence or nonoccurrence of an event under uncertain conditions.
Probability and probability distributions are discussed in Chapters 4 through 6 and parts of
Chapter 7.
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EXERCISES
CONCEPTS AND PROCEDURES
1.1 Briefly describe the two meanings of the word statistics.
1.2 Briefly explain the types of statistics.
APPLICATIONS
1.3 Which of the following is an example of descriptive statistics and which is an example of
inferential statistics? Explain.
a. In a survey by Fortune Magazine and SurveyMonkey, participants were asked what was
the most important factor when purchasing groceries (Fortune, June 1, 2015). The
following table lists the summary of the responses of these participants. Assume that the
maximum margin of error is ± 1.5%.
Factor
Percent of Respondents
Price
42.4
Nutrition
36.0
Absence of additives 16.4
Number of calories
3.8
Carbon footprint
1.5
b. The following table gives the earnings of the world’s top seven female professional
athletes for the year 2014 (ceoworld.biz).
Female Professional Athlete 2014 Earnings (millions of dollars)
Maria Sharapova
24.4
Li Na
23.6
Serena Williams
22.0
Kim Yuna
16.3
Danica Patrick
15.0
Victoria Azarenka
11.1
Caroline Wozniacki
10.8
1.2 Basic Terms
It is very important to understand the meaning of some basic terms that will be used
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frequently in this text. This section explains the meaning of an element (or member), a
variable, an observation, and a data set. An element and a data set were briefly defined in
Section 1.1. This section defines these terms formally and illustrates them with the help of an
example.
Table 1.1 gives information, based on Forbes magazine, on the total wealth of the world’s
eight richest persons as of March 2015. Each person listed in this table is called an element
or a member of this group. Table 1.1 contains information on eight elements. Note that
elements are also called observational units.
Table 1.1 Total Wealth of the World’s Eight Richest Persons
Element or Member An element or member of a sample or population is a specific
subject or object (for example, a person, firm, item, state, or country) about which the
information is collected.
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The total wealth in our example is called a variable. The total wealth is a characteristic of
these persons on which information is collected.
Variable A variable is a characteristic under study that assumes different values for
different elements. In contrast to a variable, the value of a constant is fixed.
A few other examples of variables are household incomes, the number of houses built in a
city per month during the past year, the makes of cars owned by people, the gross profits of
companies, and the number of insurance policies sold by a salesperson per day during the
past month.
In general, a variable assumes different values for different elements, as illustrated by the
total wealth for the eight persons in Table 1.1. For some elements in a data set, however, the
values of the variable may be the same. For example, if we collect information on incomes of
households, these households are expected to have different incomes, although some of them
may have the same income.
A variable is often denoted by x, y, or z. For instance, in Table 1.1, the total wealth for
persons may be denoted by any one of these letters. Starting with Section 1.7, we will begin to
use these letters to denote variables.
Each of the values representing the total wealths of the eight persons in Table 1.1 is called
an observation or measurement.
Observation or Measurement The value of a variable for an element is called an
observation or measurement.
From Table 1.1, the total wealth of Warren Buffett was $72.7 billion. The value $72.7 billion
is an observation or a measurement. Table 1.1 contains eight observations, one for each of the
eight persons.
The information given in Table 1.1 on the total wealth of the eight richest persons is called
the data or a data set.
Data Set A data set is a collection of observations on one or more variables.
Other examples of data sets are a list of the prices of 25 recently sold homes, test scores of
15 students, opinions of 100 voters, and ages of all employees of a company.
EXERCISES
CONCEPTS AND PROCEDURES
1.4 Explain the meaning of an element, a variable, an observation, and a data set.
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APPLICATIONS
1.5 The following table lists the number of deaths by cause as reported by the Centers for
Disease Control and Prevention on February 6, 2015 (Source: www.cdc.gov).
Cause of Death
Number of Deaths
Heart disease
611,105
Cancer
584,881
Accidents
130,557
Stroke
128,978
Alzheimer’s disease
84,767
Diabetes
75,578
Influenza and Pneumonia 56,979
Suicide
41,149
Briefly explain the meaning of a member, a variable, a measurement, and a data set with
reference to the information in this table.
1.6 The following table lists the number of deaths by cause as reported by the Centers for
Disease Control and Prevention on February 6, 2015 (Source: www.cdc.gov).
Cause of Death
Number of Deaths
Heart disease
611,105
Cancer
584,881
Accidents
130,557
Stroke
128,978
Alzheimer’s disease
84,767
Diabetes
75,578
Influenza and Pneumonia 56,979
Suicide
41,149
a. What is the variable for this data set?
b. How many observations are in this data set?
c. How many elements does this data set contain?
1.3 Types of Variables
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In Section 1.2, we learned that a variable is a characteristic under investigation that assumes
different values for different elements. Family income, height of a person, gross sales of a
company, price of a college textbook, make of the car owned by a family, number of accidents,
and status (freshman, sophomore, junior, or senior) of a student enrolled at a university are
examples of variables.
A variable may be classified as quantitative or qualitative. These two types of variables are
explained next.
1.3.1 Quantitative Variables
Some variables (such as the price of a home) can be measured numerically, whereas others
(such as hair color) cannot. The price of a home is an example of a quantitative variable
while hair color is an example of a qualitative variable.
Quantitative Variable A variable that can be measured numerically is called a
quantitative variable. The data collected on a quantitative variable are called
quantitative data.
Income, height, gross sales, price of a home, number of cars owned, and number of
accidents are examples of quantitative variables because each of them can be expressed
numerically. For instance, the income of a family may be $81,520.75 per year, the gross sales
for a company may be $567 million for the past year, and so forth. Such quantitative variables
may be classified as either discrete variables o …
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