Based on the results of the study, what changes would you recommend to persons to help them reduce their anger?
The Nature of Probability and Statistics
CHAPTER 1
The Nature of Probability and Statistics
Objectives
After completing this chapter, you should be able to
1Demonstrate knowledge of statistical terms.
2Differentiate between the two branches of statistics.
3Identify types of data.
4Identify the measurement level for each variable.
5Identify the four basic sampling techniques.
6Explain the difference between an observational and an experimental study.
7Explain how statistics can be used and misused.
8Explain the importance of computers and calculators in statistics.
Outline
Introduction
1–1Descriptive and Inferential Statistics
1–2Variables and Types of Data
1–3Data Collection and Sampling Techniques
1–4Observational and Experimental Studies
1–5Uses and Misuses of Statistics
1–6Computers and Calculators
Summary
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Statistics Today
Are We Improving Our Diet?
It has been determined that diets rich in fruits and vegetables are associated with a lower risk of chronic diseases such as cancer. Nutritionists recommend that
Americans consume five or more servings of fruits and vegetables each day. Several researchers from the Division of Nutrition, the National Center for Chronic Disease
Control and Prevention, the National Cancer Institute, and the National Institutes of Health decided to use statistical procedures to see how much progress is being
made toward this goal.
The procedures they used and the results of the study will be explained in this chapter. See Statistics Today—Revisited at the end of this chapter.
Introduction
You may be familiar with probability and statistics through radio, television, newspapers, and magazines. For example, you may have read statements like the following
found in newspapers.
•In Massachusetts, 36% of adults aged 25 and older have at least a bachelor’s degree. (Source: U.S. Census Bureau.)
•In 1995 there were 926,621 bankruptcy filings, while in 2005 there were 2,078,415 bankruptcy filings. (Source: Administrative Office of the U.S. Courts, Washington,
D.C.)
•Toddlers need an average of 13 hours of sleep per day.
•The average in-state college tuition and fees for 4-year public college is $5836. (Source: The College Board.)
•There is a 3.8% probability of selecting a briefcase containing $1 million on the television show “Deal or No Deal.”
•The back-to-school student plans to spend, on average, $114.38 on electronics and computer-related items. (Source: National Retail Federation.)
Unusual Stat
Of people in the United States, 14% said that they feel happiest in June, and 14% said that they feel happiest in December.
Statistics is used in almost all fields of human endeavor. In sports, for example, a statistician may keep records of the number of yards a running back gains during a
football game, or the number of hits a baseball player gets in a season. In other areas, such as public health, an administrator might be concerned with the number of
residents who contract a new strain of flu virus during a certain year. In education, a researcher might want to know if new methods of teaching are better than old
ones. These are only a few examples of how statistics can be used in various occupations.
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Interesting Fact
Every day in the United States about 120 golfers claim that they made a hole-in-one.
Furthermore, statistics is used to analyze the results of surveys and as a tool in scientific research to make decisions based on controlled experiments. Other uses of
statistics include operations research, quality control, estimation, and prediction.
Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.
Students study statistics for several reasons:
1.Like professional people, you must be able to read and understand the various statistical studies performed in your fields. To have this understanding, you must be
knowledgeable about the vocabulary, symbols, concepts, and statistical procedures used in these studies.
2.You may be called on to conduct research in your field, since statistical procedures are basic to research. To accomplish this, you must be able to design
experiments; collect, organize, analyze, and summarize data; and possibly make reliable predictions or forecasts for future use. You must also be able to communicate
the results of the study in your own words.
3.You can also use the knowledge gained from studying statistics to become better consumers and citizens. For example, you can make intelligent decisions about what
products to purchase based on consumer studies, about government spending based on utilization studies, and so on.
These reasons can be considered the goals for studying statistics.
It is the purpose of this chapter to introduce the goals for studying statistics by answering questions such as the following:
What are the branches of statistics?
What are data?
How are samples selected?
Objective 1
Demonstrate knowledge of statistical terms.
1–1Descriptive and Inferential Statistics
To gain knowledge about seemingly haphazard situations, statisticians collect information for variables, which describe the situation.
A variable is a characteristic or attribute that can assume different values.
Data are the values (measurements or observations) that the variables can assume. Variables whose values are determined by chance are called random variables.
Suppose that an insurance company studies its records over the past several years and determines that, on average, 3 out of every 100 automobiles the company insured
were involved in accidents during a 1-year period. Although there is no way to predict the specific automobiles that will be involved in an accident (random
occurrence), the company can adjust its rates accordingly, since the company knows the general pattern over the long run. (That is, on average, 3% of the insured
automobiles will be involved in an accident each year.)
Objective 2
Differentiate between the two branches of statistics.
A collection of data values forms a data set. Each value in the data set is called a data value or a datum.
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Data can be used in different ways. The body of knowledge called statistics is sometimes divided into two main areas, depending on how data are used. The two areas are
1.Descriptive statistics
2.Inferential statistics
Descriptive statistics consists of the collection, organization, summarization, and presentation of data.
In descriptive statistics the statistician tries to describe a situation. Consider the national census conducted by the U.S. government every 10 years. Results of this
census give you the average age, income, and other characteristics of the U.S. population. To obtain this information, the Census Bureau must have some means to
collect relevant data. Once data are collected, the bureau must organize and summarize them. Finally, the bureau needs a means of presenting the data in some
meaningful form, such as charts, graphs, or tables.
The second area of statistics is called inferential statistics.
Inferential statistics consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables,
and making predictions.
Historical Note
The origin of descriptive statistics can be traced to data collection methods used in censuses taken by the Babylonians and Egyptians between 4500 and 3000 B.C. In
addition, the Roman Emperor Augustus (27 B.C–A.D. 17) conducted surveys on births and deaths of the citizens of the empire, as well as the number of livestock each
owned and the crops each citizen harvested yearly.
Here, the statistician tries to make inferences from samples to populations. Inferential statistics uses probability, i.e., the chance of an event occurring. You may
be familiar with the concepts of probability through various forms of gambling. If you play cards, dice, bingo, and lotteries, you win or lose according to the laws of
probability. Probability theory is also used in the insurance industry and other areas.
It is important to distinguish between a sample and a population.
A population consists of all subjects (human or otherwise) that are being studied.
Unusual Stat
Twenty-nine percent of Americans want their boss’s job.
Most of the time, due to the expense, time, size of population, medical concerns, etc., it is not possible to use the entire population for a statistical study;
therefore, researchers use samples.
A sample is a group of subjects selected from a population.
Historical Note
Inferential statistics originated in the 1600s, when John Graunt published his book on population growth, Natural and Political Observations Made upon the Bills of
Mortality. About the same time, another mathematician/astronomer, Edmund Halley, published the first complete mortality tables. (Insurance companies use mortality
tables to determine life insurance rates.)
If the subjects of a sample are properly selected, most of the time they should possess the same or similar characteristics as the subjects in the population. The
techniques used to properly select a sample will be explained in Section 1–3.
An area of inferential statistics called hypothesis testing is a decision-making process for evaluating claims about a population, based on information obtained from
samples. For example, a researcher may wish to know if a new drug will reduce the number of heart attacks in men over 70 years of age. For this study, two groups of
men over 70 would be selected. One group would be given the drug, and the other would be given a placebo (a substance with no medical benefits or harm). Later, the
number of heart attacks occurring in each group of men would be counted, a statistical test would be run, and a decision would be made about the effectiveness of the
drug.
Statisticians also use statistics to determine relationships among variables. For example, relationships were the focus of the most noted study in the 20th century,
“Smoking and Health,” published by the Surgeon General of the United States in 1964. He stated that after reviewing and evaluating the data, his group found a definite
relationship between smoking and lung cancer. He did not say that cigarette smoking actually causes lung cancer, but that there is a relationship between smoking and
lung cancer. This conclusion was based on a study done in 1958 by Hammond and Horn. In this study, 187,783 men were observed over a period of 45 months. The death rate
from lung cancer in this group of volunteers was 10 times as great for smokers as for nonsmokers.
Finally, by studying past and present data and conditions, statisticians try to make predictions based on this information. For example, a car dealer may look at past
sales records for a specific month to decide what types of automobiles and how many of each type to order for that month next year.
Page 5
Speaking of Statistics
Statistics and the New Planet
In the summer of 2005, astronomers announced the discovery of a new planet in our solar system. This planet, as of this writing, has not yet been named; however,
astronomers have dubbed it Xena. They also discovered that it has a moon that is larger than Pluto.1 Xena is about 9 billion miles from the Sun. (Some sources say 10
billion.) Its diameter is about 4200 miles. Its surface temperature has been estimated at –400°F, and it takes 560 years to circle the Sun.
How does Xena compare to the other planets? Let’s look at the statistics.
Source: NASA.
1Some astronomers no longer consider Pluto a planet.
With these statistics, we can make some comparisons. For example, Xena is about the size of the planet Mars, but it is over 21 times the size of Pluto. (Compare the
volumes.) It takes about twice as long to circle the Sun as Pluto. What other comparisons can you make?
Applying the Concepts 1–1
Attendance and Grades
Read the following on attendance and grades, and answer the questions.
A study conducted at Manatee Community College revealed that students who attended class 95 to 100% of the time usually received an A in the class. Students who
attended class 80 to 90% of the time usually received a B or C in the class. Students who attended class less than 80% of the time usually received a D or an F or
eventually withdrew from the class.
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Based on this information, attendance and grades are related. The more you attend class, the more likely you will receive a higher grade. If you improve your
attendance, your grades will probably improve. Many factors affect your grade in a course. One factor that you have considerable control over is attendance. You can
increase your opportunities for learning by attending class more often.
Unusual Stat
Only one-third of crimes committed are reported to the police.
1.What are the variables under study?
2.What are the data in the study?
3.Are descriptive, inferential, or both types of statistics used?
4.What is the population under study?
5.Was a sample collected? If so, from where?
6.From the information given, comment on the relationship between the variables.
See page 33 for the answers.
Objective 3
Identify types of data.
1–2Variables and Types of Data
As stated in Section 1–1, statisticians gain information about a particular situation by collecting data for random variables. This section will explore in greater
detail the nature of variables and types of data.
Variables can be classified as qualitative or quantitative. Qualitative variables are variables that can be placed into distinct categories, according to some
characteristic or attribute. For example, if subjects are classified according to gender (male or female), then the variable gender is qualitative. Other examples of
qualitative variables are religious preference and geographic locations.
Quantitative variables are numerical and can be ordered or ranked. For example, the variable age is numerical, and people can be ranked in order according to the value
of their ages. Other examples of quantitative variables are heights, weights, and body temperatures.
Quantitative variables can be further classified into two groups: discrete and continuous. Discrete variables can be assigned values such as 0, 1, 2, 3 and are said to
be countable. Examples of discrete variables are the number of children in a family, the number of students in a classroom, and the number of calls received by a
switchboard operator each day for a month.
Discrete variables assume values that can be counted.
Continuous variables, by comparison, can assume an infinite number of values in an interval between any two specific values. Temperature, for example, is a continuous
variable, since the variable can assume an infinite number of values between any two given temperatures.
Continuous variables can assume an infinite number of values between any two specific values. They are obtained by measuring. They often include fractions and
decimals.
The classification of variables can be summarized as follows:
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Since continuous data must be measured, answers must be rounded because of the limits of the measuring device. Usually, answers are rounded to the nearest given unit.
For example, heights might be rounded to the nearest inch, weights to the nearest ounce, etc. Hence, a recorded height of 73 inches could mean any measure from 72.5
inches up to but not including 73.5 inches. Thus, the boundary of this measure is given as 72.5–73.5 inches. Boundaries are written for convenience as 72.5–73.5 but
are understood to mean all values up to but not including 73.5. Actual data values of 73.5 would be rounded to 74 and would be included in a class with boundaries of
73.5 up to but not including 74.5, written as 73.5–74.5. As another example, if a recorded weight is 86 pounds, the exact boundaries are 85.5 up to but not including
86.5, written as 85.5–86.5 pounds. Table 1–1 helps to clarify this concept. The boundaries of a continuous variable are given in one additional decimal place and
always end with the digit 5.
Unusual Stat
Fifty-two percent of Americans live within 50 miles of a coastal shoreline.
Table 1–1 Recorded Values and Boundaries
Variable Recorded value Boundaries
Length 15 centimeters (cm) 14.5–15.5 cm
Temperature 86 degrees Fahrenheit (°F) 85.5–86.5°F
Time 0.43 second (sec) 0.425–0.435 sec
Mass 1.6 grams (g) 1.55–1.65 g
Objective 4
Identify the measurement level for each variable.
In addition to being classified as qualitative or quantitative, variables can be classified by how they are categorized, counted, or measured. For example, can the
data be organized into specific categories, such as area of residence (rural, suburban, or urban)? Can the data values be ranked, such as first place, second place,
etc.? Or are the values obtained from measurement, such as heights, IQs, or temperature? This type of classification—i.e., how variables are categorized, counted, or
measured—uses measurement scales, and four common types of scales are used: nominal, ordinal, interval, and ratio.
The first level of measurement is called the nominal level of measurement. A sample of college instructors classified according to subject taught (e.g., English,
history, psychology, or mathematics) is an example of nominal-level measurement. Classifying survey subjects as male or female is another example of nominal-level
measurement. No ranking or order can be placed on the data. Classifying residents according to zip codes is also an example of the nominal level of measurement. Even
though numbers are assigned as zip codes, there is no meaningful order or ranking. Other examples of nominal-level data are political party (Democratic, Republican,
Independent, etc.), religion (Christianity, Judaism, Islam, etc.), and marital status (single, married, divorced, widowed, separated).
The nominal level of measurement classifies data into mutually exclusive (nonoverlapping), exhausting categories in which no order or ranking can be imposed on the
data.
The next level of measurement is called the ordinal level. Data measured at this level can be placed into categories, and these categories can be ordered, or ranked.
For example, from student evaluations, guest speakers might be ranked as superior, average, or poor. Floats in a homecoming parade might be ranked as first place,
second place, etc. Note that precise measurement of differences in the ordinal level of measurement does not exist. For instance, when people are classified according
to their build (small, medium, or large), a large variation exists among the individuals in each class.
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Other examples of ordinal data are letter grades (A, B, C, D, F).
Unusual Stat
Sixty-three percent of us say we would rather hear the bad news first.
The ordinal level of measurement classifies data into categories that can be ranked; however, precise differences between the ranks do not exist.
The third level of measurement is called the interval level. This level differs from the ordinal level in that precise differences do exist between units. For example,
many standardized psychological tests yield values measured on an interval scale. IQ is an example of such a variable. There is a meaningful difference of 1 point
between an IQ of 109 and an IQ of 110. Temperature is another example of interval measurement, since there is a meaningful difference of 1°F between each unit, such as
72 and 73°F. One property is lacking in the interval scale: There is no true zero. For example, IQ tests do not measure people who have no intelligence. For
temperature, 0°F does not mean no heat at all.
The interval level of measurement ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero.
The final level of measurement is called the ratio level. Examples of ratio scales are those used to measure height, weight, area, and number of phone calls received.
Ratio scales have differences between units (1 inch, 1 pound, etc.) and a true zero. In addition, the ratio scale contains a true ratio between values. For example, if
one person can lift 200 pounds and another can lift 100 pounds, then the ratio between them is 2 to 1. Put another way, the first person can lift twice as much as the
second person.
The ratio level of measurement possesses all the characteristics of interval measurement, and there exists a true zero. In addition, true ratios exist when the same
variable is measured on two different members of the population.
There is not complete agreement among statisticians about the classification of data into one of the four categories. For example, some researchers classify IQ data as
ratio data rather than interval. Also, data can be altered so that they fit into a different category. For instance, if the incomes of all professors of a college are
classified into the three categories of low, average, and high, then a ratio variable becomes an ordinal variable. Table 1–2 gives some examples of each type of data.
Table 1–2 Examples of Measurement Scales
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Applying the Concepts 1–2
Safe Travel
Read the following information about the transportation industry and answer the questions.
Transportation Safety
The chart shows the number of job-related injuries for each of the transportation industries for 1998.
Industry Number of injuries
Railroad 4520
Intercity bus 5100
Subway 6850
Trucking 7144
Airline 9950
1.What are the variables under study?
2.Categorize each variable as quantitative or qualitative.
3.Categorize each quantitative variable as discrete or continuous.
4.Identify the level of measurement for each variable.
5.The railroad is shown as the safest transportation industry. Does that mean railroads have fewer accidents than the other industries? Explain.
6.What factors other than safety influence a person’s choice of transportation?
7.From the information given, comment on the relationship between the variables.
See page 33 for the answers.
Objective 5
Identify the four basic sampling techniques.
1–3Data Collection and Sampling Techniques
In research, statisticians use data in many different ways. As stated previously, data can be used to describe situations or events. For example, a manufacturer might
want to know something about the consumers who will be purchasing his product so he can plan an effective marketing strategy. In another situation, the management of a
company might survey its employees to assess their needs in order to negotiate a new contract with the employees’ union. Data can be used to determine whether the
educational goals of a school district are being met. Finally, trends in various areas, such as the stock market, can be analyzed, enabling prospective buyers to make
more intelligent decisions concerning what stocks to purchase. These examples illustrate a few situations where collecting data will help people make better decisions
on courses of action.
Data can be collected in a variety of ways. One of the most common methods is through the use of surveys. Surveys can be done by using a variety of methods. Three of
the most common methods are the telephone survey, the mailed questionnaire, and the personal interview.
Telephone surveys have an advantage over personal interview surveys in that they are less costly. Also, people may be more candid in their opinions since there is no
face-to-face contact. A major drawback to the telephone survey is that some people in the population will not have phones or will not answer when the calls are made;
hence, not all people have a chance of being surveyed. Also, many people now have unlisted numbers and cell phones, so they cannot be surveyed. Finally, even the tone
of the voice of the interviewer might influence the response of the person who is being interviewed.
Mailed questionnaire surveys can be used to cover a wider geographic area than telephone surveys or personal interviews since mailed questionnaire surveys are less
expensive to conduct. Also, respondents can remain anonymous if they desire. Disadvantages of mailed questionnaire surveys include a low number of responses and
inappropriate answers to questions. Another drawback is that some people may have difficulty reading or understanding the questions.
Page 10
Historical Note
A pioneer in census taking was Pierre-Simon de Laplace. In 1780, he developed the Laplace method of estimating the population of a country. The principle behind his
method was to take a census of a few selected communities and to determine the ratio of the population to the number of births in these communities. (Good birth
records were kept.) This ratio would be used to multiply the number of births in the entire country to estimate the number of citizens in the country.
Personal interview surveys have the advantage of obtaining in-depth responses to questions from the person being interviewed. One disadvantage is that interviewers
must be trained in asking questions and recording responses, which makes the personal interview survey more costly than the other two survey methods. Another
disadvantage is that the interviewer may be biased in his or her selection of respondents.
Data can also be collected in other ways, such as surveying records or direct observation of situations.
As stated in Section 1–1, researchers use samples to collect data and information about a particular variable from a large population. Using samples saves time and
money and in some cases enables the researcher to get more detailed information about a particular subject. Samples cannot be selected in haphazard ways because the
information obtained might be biased. For example, interviewing people on a street corner during the day would not include responses from people working in offices at
that time or from people attending school; hence, not all subjects in a particular population would have a chance of being selected.
To obtain samples that are unbiased—i.e., that give each subject in the population an equally likely chance of being selected—statisticians use four basic methods of
sampling: random, systematic, stratified, and cluster sampling.
Random Sampling
Random samples are selected by using chance methods or random numbers. One such method is to number each subject in the population. Then place numbered cards in a
bowl, mix them thoroughly, and select as many cards as needed. The subjects whose numbers are selected constitute the sample. Since it is difficult to mix the cards
thoroughly, there is a chance of obtaining a biased sample. For this reason, statisticians use another method of obtaining numbers. They generate random numbers with a
computer or calculator. Before the invention of computers, random numbers were obtained from tables.
Some two-digit random numbers are shown in Table 1–3. To select a random sample of, say, 15 subjects out of 85 subjects, it is necessary to number each subject from 01
to 85. Then select a starting number by closing your eyes and placing your finger on a number in the table. (Although this may sound somewhat unusual, it enables us to
find a starting number at random.) In this case suppose your finger landed on the number 12 in the second column. (It is the sixth number down from the top.) Then
proceed downward until you have selected 15 different numbers between 01 and 85. When you reach the bottom of the column, go to the top of the next column. If you
select a number greater than 85 or the number 00 or a duplicate number, just omit it. In our example, we will use the subjects numbered 12, 27, 75, 62, 57, 13, 31, 06,
16, 49, 46, 71, 53, 41, and 02.
Page 11
Speaking of Statistics
Commuting Times
This graph shows the highest average commuting times for cities with a population of 250,000 or more.
This graph shows the cities with the lowest average commuting times.
Source: U.S. Census Bureau.
By looking at the locations of the cities, what conclusions can you draw?
Systematic Sampling
Researchers obtain systematic samples by numbering each subject of the population and then selecting every kth subject. For example, suppose there were 2000 subjects
in the population and a sample of 50 subjects were needed. Since 2000 ÷ 50 = 40, then k = 40, and every 40th subject would be selected; however, the first subject
(numbered between 1 and 40) would be selected at random. Suppose subject 12 were the first subject selected; then the sample would consist of the subjects whose
numbers were 12, 52, 92, etc., until 50 subjects were obtained. When using systematic sampling, you must be careful about how the subjects in the population are
numbered. If subjects were arranged in a manner such as wife, husband, wife, husband, and every 40th subject were selected, the sample would consist of all husbands.
Numbering is not always necessary. For example, a researcher may select every tenth item from an assembly line to test for defects.
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Table 1–3 Random Numbers
Stratified Sampling
Researchers obtain stratified samples by dividing the population into groups (called strata) according to some characteristic that is important to the study, then
sampling from each group. Samples within the strata should be randomly selected. For example, suppose the president of a two-year college wants to learn how students
feel about a certain issue. Furthermore, the president wishes to see if the opinions of the first-year students differ from those of the second-year students. The
president will select students from each group to use in the sample.
Historical Note
In 1936, the Literary Digest, on the basis of a biased sample of its subscribers, predicted that Alf Landon would defeat Franklin D. Roosevelt in the upcoming
presidential election. Roosevelt won by a landslide. The magazine ceased publication the following year.
Cluster Sampling
Researchers also use cluster samples. Here the population is divided into groups called clusters by some means such as geographic area or schools in a large school
district, etc. Then the researcher randomly selects some of these clusters and uses all members of the selected clusters as the subjects of the samples. Suppose a
researcher wishes to survey apartment dwellers in a large city. If there are 10 apartment buildings in the city, the researcher can select at random 2 buildings from
the 10 and interview all the residents of these buildings. Cluster sampling is used when the population is large or when it involves subjects residing in a large
geographic area. For example, if one wanted to do a study involving the patients in the hospitals in New York City, it would be very costly and time-consuming to try
to obtain a random sample of patients since they would be spread over a large area. Instead, a few hospitals could be selected at random, and the patients in these
hospitals would be interviewed in a cluster.
The four basic sampling methods are summarized in Table 1–4.
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Table 1–4 Summary of Sampling Methods
Random Subjects are selected by random numbers.
Systematic Subjects are selected by using every kth number after the first subject is randomly selected from 1 through k.
Stratified Subjects are selected by dividing up the population into groups (strata), and subjects are randomly selected within groups.
Cluster Subjects are selected by using an intact group that is representative of the population.
Other Sampling Methods
In addition to the four basic sampling methods, researchers use other methods to obtain samples. One such method is called a convenience sample. Here a researcher uses
subjects that are convenient. For example, the researcher may interview subjects entering a local mall to determine the nature of their visit or perhaps what stores
they will be patronizing. This sample is probably not representative of the general customers for several reasons. For one thing, it was probably taken at a specific
time of day, so not all customers entering the mall have an equal chance of being selected since they were not there when the survey was being conducted. But
convenience samples can be representative of the population. If the researcher investigates the characteristics of the population and determines that the sample is
representative, then it can be used.
Interesting Fact
Older Americans are less likely to sacrifice happiness for a higherpaying job. According to one survey, 38% of those aged 18–29 said they would choose more money over
happiness, while only 3% of those over 65 would.
Applying the Concepts 1–3
American Culture and Drug Abuse
Assume you are a member of the Family Research Council and have become increasingly concerned about the drug use by professional sports players. You set up a plan and
conduct a survey on how people believe the American culture (television, movies, magazines, and popular music) influences illegal drug use. Your survey consists of
2250 adults and adolescents from around the country. A consumer group petitions you for more information about your survey. Answer the following questions about your
survey.
1.What type of survey did you use (phone, mail, or interview)?
2.What are the advantages and disadvantages of the surveying methods you did not use?
3.What type of scores did you use? Why?
4.Did you use a random method for deciding who would be in your sample?
5.Which of the methods (stratified, systematic, cluster, or convenience) did you use?
6.Why was that method more appropriate for this type of data collection?
7.If a convenience sample were obtained, consisting of only adolescents, how would the results of the study be affected?
See page 33 for the answers.
Objective 6
Explain the difference between an observational and an experimental study.
1–4Observational and Experimental Studies
There are several different ways to classify statistical studies. This section explains two types of studies: observational studies and experimental studies.
In an observational study, the researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations.
Page 14
For example, data from the Motorcycle Industry Council (USA TODAY) stated that “Motorcycle owners are getting older and richer.” Data were collected on the ages and
incomes of motorcycle owners for the years 1980 and 1998 and then compared. The findings showed considerable differences in the ages and incomes of motorcycle owners
for the two years.
In this study, the researcher merely observed what had happened to the motorcycle owners over a period of time. There was no type of research intervention.
In an experimental study, the researcher manipulates one of the variables and tries to determine how the manipulation influences other variables.
Interesting Fact
The safest day of the week for driving is Tuesday.
For example, a study conducted at Virginia Polytechnic Institute and presented in Psychology Today divided female undergraduate students into two groups and had the
students perform as many sit-ups as possible in 90 sec. The first group was told only to “Do your best,” while the second group was told to try to increase the actual
number of sit-ups done each day by 10%. After four days, the subjects in the group who were given the vague instructions to “Do your best” averaged 43 sit-ups, while
the group that was given the more specific instructions to increase the number of sit-ups by 10% averaged 56 sit-ups by the last day’s session. The conclusion then was
that athletes who were given specific goals performed better than those who were not given specific goals.
This study is an example of a statistical experiment since the researchers intervened in the study by manipulating one of the variables, namely, the type of
instructions given to each group.
In a true experimental study, the subjects should be assigned to groups randomly. Also, the treatments should be assigned to the groups at random. In the sit-up study,
the article did not mention whether the subjects were randomly assigned to the groups.
Sometimes when random assignment is not possible, researchers use intact groups. These types of studies are done quite often in education where already intact groups
are available in the form of existing classrooms. When these groups are used, the study is said to be a quasi-experimental study. The treatments, though, should be
assigned at random. Most articles do not state whether random assignment of subjects was used.
Statistical studies usually include one or more independent variables and one dependent variable.
The independent variable in an experimental study is the one that is being manipulated by the researcher. The independent variable is also called the explanatory
variable. The resultant variable is called the dependent variable or the outcome variable.
The outcome variable is the variable that is studied to see if it has changed significantly due to the manipulation of the independent variable. For example, in the
sit-up study, the researchers gave the groups two different types of instructions, general and specific. Hence, the independent variable is the type of instruction.
The dependent variable, then, is the resultant variable, that is, the number of sit-ups each group was able to perform after four days of exercise. If the differences
in the dependent or outcome variable are large and other factors are equal, these differences can be attributed to the manipulation of the independent variable. In
this case, specific instructions were shown to increase athletic performance.
In the sit-up study, there were two groups. The group that received the special instruction is called the treatment group while the other is called the control group.
The treatment group receives a specific treatment (in this case, instructions for improvement) while the control group does not.
Both types of statistical studies have advantages and disadvantages. Experimental studies have the advantage that the researcher can decide how to select subjects and
how to assign them to specific groups. The researcher can also control or manipulate the independent variable. For example, in studies that require the subjects to
consume a certain amount of medicine each day, the researcher can determine the precise dosages and, if necessary, vary the dosage for the groups.
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Interesting Fact
The number of potholes in the United States is about 56 million.
There are several disadvantages to experimental studies. First, they may occur in unnatural settings, such as laboratories and special classrooms. This can lead to
several problems. One such problem is that the results might not apply to the natural setting. The age-old question then is, “This mouthwash may kill 10,000 germs in a
test tube, but how many germs will it kill in my mouth?”
Another disadvantage with an experimental study is the Hawthorne effect. This effect was discovered in 1924 in a study of workers at the Hawthorne plant of the Western
Electric Company. In this study, researchers found that the subjects who knew they were participating in an experiment actually changed their behavior in ways that
affected the results of the study.
Another problem is called confounding of variables.
A confounding variable is one that influences the dependent or outcome variable but was not separated from the independent variable.
Researchers try to control most variables in a study, but this is not possible in some studies. For example, subjects who are put on an exercise program might also
improve their diet unbeknownst to the researcher and perhaps improve their health in other ways not due to exercise alone. Then diet becomes a confounding variable.
Observational studies also have advantages and disadvantages. One advantage of an observational study is that it usually occurs in a natural setting. For example,
researchers can observe people’s driving patterns on streets and highways in large cities. Another advantage of an observational study is that it can be done in
situations where it would be unethical or downright dangerous to conduct an experiment. Using observational studies, researchers can study suicides, rapes, murders,
etc. In addition, observational studies can be done using variables that cannot be manipulated by the researcher, such as drug users versus nondrug users and right-
handedness versus left-handedness.
Observational studies have disadvantages, too. As mentioned previously, since the variables are not controlled by the researcher, a definite cause-and-effect situation
cannot be shown since other factors may have had an effect on the results. Observational studies can be expensive and time-consuming. For example, if one wanted to
study the habitat of lions in Africa, one would need a lot of time and money, and there would be a certain amount of danger involved. Finally, since the researcher may
not be using his or her own measurements, the results could be subject to the inaccuracies of those who collected the data. For example, if the researchers were doing
a study of events that occurred in the 1800s, they would have to rely on information and records obtained by others from a previous era. There is no way to ensure the
accuracy of these records.
When you read the results of statistical studies, decide if the study was observational or experimental. Then see if the conclusion follows logically, based on the
nature of these studies.
Unusual Stat
Of people in the United States, 66% read the Sunday paper.
No matter what type of study is conducted, two studies on the same subject sometimes have conflicting conclusions. Why might this occur? An article entitled “Bottom
Line: Is It Good for You?” (USA TODAY Weekend) states that in the 1960s studies suggested that margarine was better for the heart than butter since margarine contains
less saturated fat and users had lower cholesterol levels. In a 1980 study, researchers found that butter was better than margarine since margarine contained trans-
fatty acids, which are worse for the heart than butter’s saturated fat. Then in a 1998 study, researchers found that margarine was better for a person’s health. Now,
what is to be believed? Should one use butter or margarine?
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The answer here is that you must take a closer look at these studies. Actually, it is not a choice between butter or margarine that counts, but the type of margarine
used. In the 1980s, studies showed that solid margarine contains trans-fatty acids, and scientists believe that they are worse for the heart than butter’s saturated
fat. In the 1998 study, liquid margarine was used. It is very low in trans-fatty acids, and hence it is more healthful than butter because trans-fatty acids have been
shown to raise cholesterol. Hence, the conclusion is to use liquid margarine instead of solid margarine or butter.
Before decisions based on research studies are made, it is important to get all the facts and examine them in light of the particular situation.
Applying the Concepts 1–4
Just a Pinch Between Your Cheek and Gum
As the evidence on the adverse effects of cigarette smoke grew, people tried many different ways to quit smoking. Some people tried chewing tobacco or, as it was
called, smokeless tobacco. A small amount of tobacco was placed between the cheek and gum. Certain chemicals from the tobacco were absorbed into the bloodstream and
gave the sensation of smoking cigarettes. This prompted studies on the adverse effects of smokeless tobacco. One study in particular used 40 university students as
subjects. Twenty were given smokeless tobacco to chew, and twenty given a substance that looked and tasted like smokeless tobacco, but did not contain any of the
harmful substances. The students were randomly assigned to one of the groups. The students’ blood pressure and heart rate were measured before they started chewing and
20 minutes after they had been chewing. A significant increase in heart rate occurred in the group that chewed the smokeless tobacco. Answer the following questions.
1.What type of study was this (observational, quasi-experimental, or experimental)?
2.What are the independent and dependent variables?
3.Which was the treatment group?
4.Could the students’ blood pressures be affected by knowing that they are part of a study?
5.List some possible confounding variables.
6.Do you think this is a good way to study the effect of smokeless tobacco?
See page 33 for the answers.
Objective 7
Explain how statistics can be used and misused.
1–5Uses and Misuses of Statistics
As explained previously, statistical techniques can be used to describe data, compare two or more data sets, determine if a relationship exists between variables, test
hypotheses, and make estimates about population characteristics. However, there is another aspect of statistics, and that is the misuse of statistical techniques to
sell products that don’t work properly, to attempt to prove something true that is really not true, or to get our attention by using statistics to evoke fear, shock,
and outrage.
There are two sayings that have been around for a long time that illustrate this point:
“There are three types of lies—lies, damn lies, and statistics.”
“Figures don’t lie, but liars figure.”
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Just because we read or hear the results of a research study or an opinion poll in the media, this does not mean that these results are reliable or that they can be
applied to any and all situations. For example, reporters sometimes leave out critical details such as the size of the sample used or how the research subjects were
selected. Without this information, you cannot properly evaluate the research and properly interpret the conclusions of the study or survey.
It is the purpose of this section to show some ways that statistics can be misused. You should not infer that all research studies and surveys are suspect, but that
there are many factors to consider when making decisions based on the results of research studies and surveys. Here are some ways that statistics can be
misrepresented.
Suspect Samples
The first thing to consider is the sample that was used in the research study. Sometimes researchers use very small samples to obtain information. Several years ago,
advertisements contained such statements as “Three out of four doctors surveyed recommend brand such and such.” If only 4 doctors were surveyed, the results could have
been obtained by chance alone; however, if 100 doctors were surveyed, the results might be quite different.
Not only is it important to have a sample size that is large enough, but also it is necessary to see how the subjects in the sample were selected. Studies using
volunteers sometimes have a built-in bias. Volunteers generally do not represent the population at large. Sometimes they are recruited from a particular socioeconomic
background, and sometimes unemployed people volunteer for research studies to get a stipend. Studies that require the subjects to spend several days or weeks in an
environment other than their home or workplace automatically exclude people who are employed and cannot take time away from work. Sometimes only college students or
retirees are used in studies. In the past, many studies have used only men, but have attempted to generalize the results to both men and women. Opinion polls that
require a person to phone or mail in a response most often are not representative of the population in general, since only those with strong feelings for or against
the issue usually call or respond by mail.
Another type of sample that may not be representative is the convenience sample. Educational studies sometimes use students in intact classrooms since it is
convenient. Quite often, the students in these classrooms do not represent the student population of the entire school district.
When results are interpreted from studies using small samples, convenience samples, or volunteer samples, care should be used in generalizing the results to the entire
population.
Ambiguous Averages
In Chapter 3, you will learn that there are four commonly used measures that are loosely called averages. They are the mean, median, mode, and midrange. For the same
data set, these averages can differ markedly. People who know this can, without lying, select the one measure of average that lends the most evidence to support their
position.
Changing the Subject
Another type of statistical distortion can occur when different values are used to represent the same data. For example, one political candidate who is running for
reelection might say, “During my administration, expenditures increased a mere 3%.” His opponent, who is trying to unseat him, might say, “During my opponent’s
administration, expenditures have increased a whopping $6,000,000.” Here both figures are correct; however, expressing a 3% increase as $6,000,000 makes it sound like
a very large increase. Here again, ask yourself, Which measure better represents the data?
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Detached Statistics
A claim that uses a detached statistic is one in which no comparison is made. For example, you may hear a claim such as “Our brand of crackers has one-third fewer
calories.” Here, no comparison is made. One-third fewer calories than what? Another example is a claim that uses a detached statistic such as “Brand A aspirin works
four times faster.” Four times faster than what? When you see statements such as this, always ask yourself, Compared to what?
Implied Connections
Many claims attempt to imply connections between variables that may not actually exist. For example, consider the following statement: “Eating fish may help to reduce
your cholesterol.” Notice the words may help. There is no guarantee that eating fish will definitely help you reduce your cholesterol.
“Studies suggest that using our exercise machine will reduce your weight.” Here the word suggest is used; and again, there is no guarantee that you will lose weight by
using the exercise machine advertised.
Another claim might say, “Taking calcium will lower blood pressure in some people.” Note the word some is used. You may not be included in the group of “some” people.
Be careful when you draw conclusions from claims that use words such as may, in some people, and might help.
Misleading Graphs
Statistical graphs give a visual representation of data that enables viewers to analyze and interpret data more easily than by simply looking at numbers. In Chapter 2,
you will see how some graphs are used to represent data. However, if graphs are drawn inappropriately, they can misrepresent the data and lead the reader to draw false
conclusions. The misuse of graphs is also explained in Chapter 2.
Faulty Survey Questions
When analyzing the results of a survey using questionnaires, you should be sure that the questions are properly written since the way questions are phrased can often
influence the way people answer them. For example, the responses to a question such as “Do you feel that the North Huntingdon School District should build a new
football stadium?” might be answered differently than a question such as “Do you favor increasing school taxes so that the North Huntingdon School District can build a
new football stadium?” Each question asks something a little different, and the responses could be radically different. When you read and interpret the results
obtained from questionnaire surveys, watch out for some of these common mistakes made in the writing of the survey questions.
To restate the premise of this section, statistics, when used properly, can be beneficial in obtaining much information, but when used improperly, can lead to much
misinformation. It is like your automobile. If you use your automobile to get to school or work or to go on a vacation, that’s good. But if you use it to run over your
neighbor’s dog because it barks all night long and tears up your flower garden, that’s not so good!
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Objective 8
Explain the importance of computers and calculators in statistics.
1–6Computers and Calculators
In the past, statistical calculations were done with pencil and paper. However, with the advent of calculators, numerical computations became much easier. Computers do
all the numerical calculation. All one does is to enter the data into the computer and use the appropriate command; the computer will print the answer or display it on
the screen. Now the TI-83 Plus or TI-84 Plus graphing calculator accomplishes the same thing.
There are many statistical packages available; this book uses MINITAB and Microsoft Excel. Instructions for using MINITAB, the TI-83 Plus or TI-84 Plus graphing
calculator, and Excel have been placed at the end of each relevant section, in subsections entitled Technology Step by Step.
You should realize that the computer and calculator merely give numerical answers and save the time and effort of doing calculations by hand. You are still responsible
for understanding and interpreting each statistical concept. In addition, you should realize that the results come from the data and do not appear magically on the
computer. Doing calculations using the procedure tables will help you reinforce this idea.
The author has left it up to instructors to choose how much technology they will incorporate into the course.
Technology Step by Step
MINITAB
Step by Step
General Information
MINITAB statistical software provides a wide range of statistical analysis and graphing capabilities.
Take Note
In this text you will see captured screen images from computers running MINITAB Release 14. If you are using an earlier or later release of MINITAB, the screens you
see on your computer may bear slight visual differences from the screens pictured in this text. But don’t be alarmed! All the Step by Step operations described in this
text, including the commands, the menu options, and the functionality, will work just fine on your computer.
Start the Program
1.Click the Windows XP Start Menu, then All Programs.
2.Click the MINITAB 14 folder and then click , the program icon. The program screen will look similar to the one shown here. You will see the Session Window, the
Worksheet Window, and perhaps the Project Manager Window.
3.Click the Project Manager icon on the toolbar to bring the project manager to the front.
For Vista, click the start button, then “All Programs.” Next click “MINITAB Solutions” and then “MINITAB Statistical Software English.”
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To use the program, data must be entered from the keyboard or from a file.
Entering Data in MINITAB
In MINITAB, all the data for one variable are stored in a column. Step by step instructions for entering these data follow.
Data
213208203215222
1.Click in row 1 of Worksheet 1***. This makes the worksheet the active window and puts the cursor in the first cell. The small data entry arrow in the upper left-hand
corner of the worksheet should be pointing down. If it is not, click it to change the direction in which the cursor will move when you press the [Enter] key.
2.Type in each number, pressing [Enter] after each entry, including the last number typed.
3.Optional: Click in the space above row 1 to type in Weight, the column label.
Save a Worksheet File
4.Click on the File Menu. Note: This is not the same as clicking the disk icon .
5.Click Save Current Worksheet As …
6.In the dialog box you will need to verify three items:
a)Save in:Click on or type in the disk drive and directory where you will store your data. For a CD this would be A:.
b)File Name:Type in the name of the file, such as MyData.
c)Save as Type:The default here is MINITAB. An extension of mtw is added to the name.
Click [Save]. The name of the worksheet will change from Worksheet 1*** to MyData.MTW.
Open the Databank File
The raw data are shown in Appendix D. There is a row for each person’s data and a column for each variable. MINITAB data files comprised of data sets used in this
book, including the Databank, are available on the accompanying CD-ROM or at the Online Learning Center (www.mhhe.com/bluman). Here is how to get the data from a file
into a worksheet.
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1.Click File>Open Worksheet. A sequence of menu instructions will be shown this way.
Note: This is not the same as clicking the file icon . If the dialog box says Open Project instead of Open Worksheet, click [Cancel] and use the correct menu item.
The Open Worksheet dialog box will be displayed.
2.You must check three items in this dialog box.
a)The Look In: dialog box should show the directory where the file is located.
b)Make sure the Files of Type: shows the correct type, MINITAB [*.mtw].
c)Double-click the file name in the list box Databank.mtw. A dialog box may inform you that a copy of this file is about to be added to the project. Click on the
checkbox if you do not want to see this warning again.
3.Click the [OK] button. The data will be copied into a second worksheet. Part of the worksheet is shown here.
a)You may maximize the window and scroll if desired.
b)C12-T Marital Status has a T appended to the label to indicate alphanumeric data. MyData.MTW is not erased or overwritten. Multiple worksheets can be available;
however, only the active worksheet is available for analysis.
4.To switch between the worksheets, select Window>MyData.MTW.
5.Select File>Exit to quit. To save the project, click [Yes].
6.Type in the name of the file, Chapter01. The Data Window, the Session Window, and settings are all in one file called a project. Projects have an extension of mpj
instead of mtw.
Clicking the disk icon on the menu bar is the same as selecting File>Save Project.
Clicking the file icon is the same as selecting File>Open Project.
7.Click [Save]. The mpj extension will be added to the name. The computer will return to the Windows desktop. The two worksheets, the Session Window results, and
settings are saved in this project file. When a project file is opened, the program will start up right where you left off.
TI-83 Plus or TI-84 Plus
Step by Step
The TI-83 Plus or TI-84 Plus graphing calculator can be used for a variety of statistical graphs and tests.
General Information
To turn calculator on:
Press ON key.
To turn calculator off:
Press 2nd [OFF].
To reset defaults only:
1.Press 2nd, then [MEM].
2.Select 7, then 2, then 2.
Optional. To reset settings on calculator and clear memory: (Note: This will clear all settings and programs in the calculator’s memory.)
Press 2nd, then [MEM]. Then press 7, then 1, then 2.
(Also, the contrast may need to be adjusted after this.)
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To adjust contrast (if necessary):
Press 2nd. Then press and hold ? to darken or ? to lighten contrast.
To clear screen:
Press CLEAR.
(Note: This will return you to the screen you were using.)
To display a menu:
Press appropriate menu key. Example: STAT.
To return to home screen:
Press 2nd, then [QUIT].
To move around on the screens:
Use the arrow keys.
To select items on the menu:
Press the corresponding number or move the cursor to the item, using the arrow keys. Then press ENTER.
(Note: In some cases, you do not have to press ENTER, and in other cases you may need to press ENTER twice.)
Entering Data
To enter single-variable data (if necessary, clear the old list):
1.Press STAT to display the Edit menu.
2.Press ENTER to select 1:Edit.
3.Enter the data in L1 and press ENTER after each value.
4.After all data values are entered, press STAT to get back to the Edit menu or 2nd [QUIT] to end.
Example TI1–1
Enter the following data values in L1: 213, 208, 203, 215, 222.
To enter multiple-variable data:
The TI-83 Plus or TI-84 Plus will take up to six lists designated L1, L2, L3, L4, L5, and L6.
1.To enter more than one set of data values, complete the preceding steps. Then move the cursor to L2 by pressing the ? key.
2.Repeat the steps in the preceding part.
Editing Data
To correct a data value before pressing ENTER, use ? and retype the value and press ENTER.
To correct a data value in a list after pressing ENTER, move cursor to incorrect value in list and type in the correct value. Then press ENTER.
To delete a data value in a list:
Move cursor to value and press DEL.
To insert a data value in a list:
1.Move cursor to position where data value is to be inserted, then press 2nd [INS].
2.Type data value; then press ENTER.
To clear a list:
1.Press STAT, then 4.
2.Enter list to be cleared. Example: To clear L1, press 2nd [L1]. Then press ENTER.
(Note: To clear several lists, follow step 1, but enter each list to be cleared, separating them with commas. To clear all lists at once, follow step 1 then press
ENTER.)
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Sorting Data
To sort the data in a list:
1.Enter the data in L1.
2.Press STAT 2 to get SortA to sort the list in ascending order.
3.Then press 2nd [L1] ENTER.
The calculator will display Done.
4.Press STAT ENTER to display sorted list.
(Note: The SortD or 3 sorts the list in descending order.)
Example TI1–2
Sort in ascending order the data values entered in Example TI1–1.
Excel
Step by Step
Excel’s Analysis ToolPak Add-In
General Information
Microsoft Excel 2007 has two different ways to solve statistical problems. First, there are built-in functions, such as STDEV and CHITEST, available from the standard
toolbar by clicking
Formulas, then selecting the Insert Function icon . Another feature of Excel that is useful for calculating multiple statistical measures and performing statistical
tests for a set of data is the Data Analysis command found in the Analysis Tool-Pak Add-in.
To load the Analysis Tool-Pak:
Click the Microsoft Office button , then select Excel Options.
1.Click Add-Ins, and select Add-ins from the list of options on the left side of the options box.
2.Select the Analysis Tool-Pak, then click the Go button at the bottom of the options box.
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3.After loading the Analysis Tool-Pak, the Data Analysis command is available in the Analysis group on the Data tab.
MegaStat
Later in this text you will encounter a few Excel Technology Step by Step operations that will require the use of the MegaStat Add-in for Excel. MegaStat can be
downloaded from the CD that came with your textbook as well as from the text’s Online Learning Center at www.mhhe.com/bluman.
1.Save the Zip file containing the MegaStat Excel Add-in file (MegaStat.xls) and the associated help file on your computer’s hard drive.
2.After opening the Zip file, double-click the MegaStat Add-in file, then Extract the MegaStat program to your computer’s hard drive. After extracting the file, you
can load the MegaStat Add-in to Excel by double-clicking the MegaStat.xls file. When the Excel program opens to load the Add-in, choose the Enable Macros option.
3.After installation of the add-in, you will be able to access MegaStat by selecting the Add-ins tab on the Excel toolbar.
4.If MegaStat is not listed under Add-ins when you reopen the Excel program, then you can access MegaStat by double-clicking the MegaStat.xls file at any time.
Entering Data
1.Select a cell at the top of a column on an Excel worksheet where you want to enter data. When working with data values for a single variable, you will usually want
to enter the values into a single column.
2.Type each data value and press [Enter] or [Tab] on your keyboard.
You can also add more worksheets to an Excel workbook by clicking the Insert Worksheet icon located at the bottom of an open workbook.
Example XL1–1: Opening an existing Excel workbook/worksheet
1.Open the Microsoft Office Excel 2007 program.
2.Click the Microsoft Click Office button , then click the Open file function. The Open dialog box will be displayed.
3.In the Look in box, click the folder where the Excel workbook file is located.
4.Double-click the file name in the list box. The selected workbook file will be opened in Excel for editing.
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Summary
The two major areas of statistics are descriptive and inferential. Descriptive statistics includes the collection, organization, summarization, and presentation of
data. Inferential statistics includes making inferences from samples to populations, estimations and hypothesis testing, determining relationships, and making
predictions. Inferential statistics is based on probability theory.
Since in most cases the populations under study are large, statisticians use subgroups called samples to get the necessary data for their studies. There are four basic
methods used to obtain samples: random, systematic, stratified, and cluster.
Data can be classified as qualitative or quantitative. Quantitative data can be either discrete or continuous, depending on the values they can assume. Data can also
be measured by various scales. The four basic levels of measurement are nominal, ordinal, interval, and ratio.
There are two basic types of statistical studies: observational studies and experimental studies. When conducting observational studies, researchers observe what is
happening or what has happened and then draw conclusions based on these observations. They do not attempt to manipulate the variables in any way.
Unusual Stat
The chance that someone will attempt to burglarize your home in any given year is 1 in 20.
When conducting an experimental study, researchers manipulate one or more of the independent or explanatory variables and see how this manipulation influences the
dependent or outcome variable.
Finally, 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, or watching television. Since statistics is used in almost every field of endeavor, the educated individual should be knowledgeable about the vocabulary,
concepts, and procedures of statistics.
Today, computers and calculators are used extensively in statistics to facilitate the computations.
Source: © 1993 King Features Syndicate, Inc. World Rights reserved. Reprinted with special permission of King Features Syndicate.
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Important Terms
cluster sample
confounding variable
continuous variables
control group
convenience sample
data
data set
data value or datum
dependent variable
descriptive statistics
discrete variables
experimental study
explanatory variable
Hawthorne effect
hypothesis testing
independent variable
inferential statistics
interval level of measurement
measurement scales
nominal level of measurement
observational study
ordinal level of measurement
outcome variable
population
probability
qualitative variables
quantitative variables
quasi-experimental study
random sample
random variable
ratio level of measurement
sample
statistics
stratified sample
systematic sample
treatment group
variable
Review Exercises
Note: All odd-numbered problems and even-numbered problems marked with “ans” are included in the answer section at the end of this book.
1.Name and define the two areas of statistics.
2.What is probability? Name two areas where probability is used.
3.Suggest some ways statistics can be used in everyday life.
4.Explain the differences between a sample and a population.
5.Why are samples used in statistics?
6.(ans) In each of these statements, tell whether descriptive or inferential statistics have been used.
a.In the year 2010, 148 million Americans will be enrolled in an HMO (Source: USA TODAY).
b.Nine out of ten on-the-job fatalities are men (Source: USA TODAY Weekend).
c.Expenditures for the cable industry were $5.66 billion in 1996 (Source: USA TODAY).
d.The median household income for people aged 25–34 is $35,888 (Source: USA TODAY).
e.Allergy therapy makes bees go away (Source: Prevention).
f.Drinking decaffeinated coffee can raise cholesterol levels by 7% (Source: American Heart Association).
g.The national average annual medicine expenditure per person is $1052 (Source: The Greensburg Tribune Review).
h.Experts say that mortgage rates may soon hit bottom (Source: USA TODAY).
7.Classify each as nominal-level, ordinal-level, interval-level, or ratio-level measurement.
a.Pages in the city of Cleveland telephone book.
b.Rankings of tennis players.
c.Weights of air conditioners.
d.Temperatures inside 10 refrigerators.
e.Salaries of the top five CEOs in the United States.
f.Ratings of eight local plays (poor, fair, good, excellent).
g.Times required for mechanics to do a tune-up.
h.Ages of students in a classroom.
i.Marital status of patients in a physician’s office.
j.Horsepower of tractor engines.
8.(ans) Classify each variable as qualitative or quantitative.
a.Number of bicycles sold in 1 year by a large sporting goods store.
b.Colors of baseball caps in a store.
c.Times it takes to cut a lawn.
d.Capacity in cubic feet of six truck beds.
e.Classification of children in a day care center (infant, toddler, preschool).
f.Weights of fish caught in Lake George.
g.Marital status of faculty members in a large university.
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9.Classify each variable as discrete or continuous.
a.Number of doughnuts sold each day by Doughnut Heaven.
b.Water temperatures of six swimming pools in Pittsburgh on a given day.
c.Weights of cats in a pet shelter.
d.Lifetime (in hours) of 12 flashlight batteries.
e.Number of cheeseburgers sold each day by a hamburger stand on a college campus.
f.Number of DVDs rented each day by a video store.
g.Capacity (in gallons) of six reservoirs in Jefferson County.
10.Give the boundaries of each value.
a.42.8 miles.
b.1.6 milliliters.
c.5.36 ounces.
d.18 tons.
e.93.8 ounces.
f.40 inches.
11.Name and define the four basic sampling methods.
12.(ans) Classify each sample as random, systematic, stratified, or cluster.
a.In a large school district, all teachers from two buildings are interviewed to determine whether they believe the students have less homework to do now than in
previous years.
b.Every seventh customer entering a shopping mall is asked to select her or his favorite store.
c.Nursing supervisors are selected using random numbers to determine annual salaries.
d.Every 100th hamburger manufactured is checked to determine its fat content.
e.Mail carriers of a large city are divided into four groups according to gender (male or female) and according to whether they walk or ride on their routes. Then 10
are selected from each group and interviewed to determine whether they have been bitten by a dog in the last year.
13.Give three examples each of nominal, ordinal, interval, and ratio data.
14.For each of these statements, define a population and state how a sample might be obtained.
a.The average cost of an airline meal is $4.55 (Source: Everything Has Its Price, Richard E. Donley, Simon and Schuster).
b.More than 1 in 4 United States children have cholesterol levels of 180 milligrams or higher (Source: The American Health Foundation).
c.Every 10 minutes, 2 people die in car crashes and 170 are injured (Source: National Safety Council estimates).
d.When older people with mild to moderate hypertension were given mineral salt for 6 months, the average blood pressure reading dropped by 8 points systolic and 3
points diastolic (Source: Prevention).
e.The average amount spent per gift for Mom on Mother’s Day is $25.95 (Source: The Gallup Organization).
15.Select a newspaper or magazine article that involves a statistical study, and write a paper answering these questions.
a.Is this study descriptive or inferential? Explain your answer.
b.What are the variables used in the study? In your opinion, what level of measurement was used to obtain the data from the variables?
c.Does the article define the population? If so, how is it defined? If not, how could it be defined?
d.Does the article state the sample size and how the sample was obtained? If so, determine the size of the sample and explain how it was selected. If not, suggest a
way it could have been obtained.
e.Explain in your own words what procedure (survey, comparison of groups, etc.) might have been used to determine the study’s conclusions.
f.Do you agree or disagree with the conclusions? State your reasons.
16.Information from research studies is sometimes taken out of context. Explain why the claims of these studies might be suspect.
a.The average salary of the graduates of the class of 1980 is $32,500.
b.It is estimated that in Podunk there are 27,256 cats.
c.Only 3% of the men surveyed read Cosmopolitan magazine.
d.Based on a recent mail survey, 85% of the respondents favored gun control.
e.A recent study showed that high school dropouts drink more coffee than students who graduated; therefore, coffee dulls the brain.
f.Since most automobile accidents occur within 15 miles of a person’s residence, it is safer to make long trips.
17.Identify each study as being either observational or experimental.
a.Subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. After 6 months, the numbers of respiratory tract
infections each group had were compared.
b.A researcher stood at a busy intersection to see if the color of the automobile that a person drives is related to running red lights.
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c.A researcher finds that people who are more hostile have higher total cholesterol levels than those who are less hostile.
d.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 diet and
high-fish diet, and a regular diet. After 6 months, the blood pressures of the groups are compared to see if diet has any effect on blood pressure.
18.Identify the independent variable(s) and the dependent variable for each of the studies in Exercise 17.
19.For each of the studies in Exercise 17, suggest possible confounding variables.
20.Beneficial Bacteria According to a pilot study of 20 people conducted at the University of Minnesota, daily doses of a compound called arabinogalactan over a period
of 6 months resulted in a significant increase in the beneficial lactobacillus species of bacteria. Why can’t it be concluded that the compound is beneficial for the
majority of people?
21.Comment on the following statement, taken from a magazine advertisement: “In a recent clinical study, Brand ABC (actual brand will not be named) was proved to be
1950% better than creatine!”
22.In an ad for women, the following statement was made: “For every 100 women, 91 have taken the road less traveled.” Comment on this statement.
23.In many ads for weight loss products, under the product claims and in small print, the following statement is made: “These results are not typical.” What does this
say about the product being advertised?
24.In an ad for moisturizing lotion, the following claim is made: “… it’s the number 1 dermatologist-recommended brand.” What is misleading about this claim?
25.An ad for an exercise product stated: “Using this product will burn 74% more calories.” What is misleading about this statement?
26.“Vitamin E is a proven antioxidant and may help in fighting cancer and heart disease.” Is there anything ambiguous about this claim? Explain.
27.“Just 1 capsule of Brand X can provide 24 hours of acid control.” (Actual brand will not be named.) What needs to be more clearly defined in this statement?
28.“… Male children born to women who smoke during pregnancy run a risk of violent and criminal behavior that lasts well into adulthood.” Can we infer that smoking
during pregnancy is responsible for criminal behavior in people?
29.Caffeine and Health In the 1980s, a study linked coffee to a higher risk of heart disease and pancreatic cancer. In the early 1990s, studies showed that drinking
coffee posed minimal health threats. However, in 1994, a study showed that pregnant women who drank 3 or more cups of tea daily may be at risk for spontaneous
abortion. In 1998, a study claimed that women who drank more than a half-cup of caffeinated tea every day may actually increase their fertility. In 1998, a study
showed that over a lifetime, a few extra cups of coffee a day can raise blood pressure, heart rate, and stress (Source: “Bottom Line: Is It Good for You? Or Bad?” by
Monika Guttman, USA TODAY Weekend). Suggest some reasons why these studies appear to be conflicting.
Extending the Concepts
30.Find an article that describes a statistical study, and identify the study as observational or experimental.
31.For the article that you selected in Exercise 30, suggest some confounding variables that may have an effect on the results of the study.
32.For the article that you used in Exercise 30, identify the independent variable(s) and dependent variable for the study.
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Statistics Today
Are We Improving Our Diet?—Revisited
Researchers selected a sample of 23,699 adults in the United States, using phone numbers selected at random, and conducted a telephone survey. All respondents were
asked six questions:
1.How often do you drink juices such as orange, grapefruit, or tomato?
2.Not counting juice, how often do you eat fruit?
3.How often do you eat green salad?
4.How often do you eat potatoes (not including french fries, fried potatoes, or potato chips)?
5.How often do you eat carrots?
6.Not counting carrots, potatoes, or salad, how many servings of vegetables do you usually eat?
Researchers found that men consumed fewer servings of fruits and vegetables per day (3.3) than women (3.7). Only 20% of the population consumed the recommended 5 or
more daily servings. In addition, they found that youths and less-educated people consumed an even lower amount than the average.
Based on this study, they recommend that greater educational efforts are needed to improve fruit and vegetable consumption by Americans and to provide environmental
and institutional support to encourage increased consumption.
Source: Mary K. Serdula, M.D., et al., “Fruit and Vegetable Intake Among Adults in 16 States: Results of a Brief Telephone Survey,” American Journal of Public Health
85, no. 2. Copyright by the American Public Health Association.
Chapter Quiz
Determine whether each statement is true or false. If the statement is false, explain why.
1.Probability is used as a basis for inferential statistics.
2.The height of President Lincoln is an example of a variable.
3.The highest level of measurement is the interval level.
4.When the population of college professors is divided into groups according to their rank (instructor, assistant professor, etc.) and then several are selected from
each group to make up a sample, the sample is called a cluster sample.
5.The variable age is an example of a qualitative variable.
6.The weight of pumpkins is considered to be a continuous variable.
7.The boundary of a value such as 6 inches would be 5.9–6.1 inches.
Select the best answer.
8.The number of absences per year that a worker has is an example of what type of data?
a.Nominal
b.Qualitative
c.Discrete
d.Continuous
9.What are the boundaries of 25.6 ounces?
a.25–26 ounces
b.25.55–25.65 ounces
c.25.5–25.7 ounces
d.20–39 ounces
10.A researcher divided subjects into two groups according to gender and then selected members from each group for her sample. What sampling method was the researcher
using?
a.Cluster
b.Random
c.Systematic
d.Stratified
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11.Data that can be classified according to color are measured on what scale?
a.Nominal
b.Ratio
c.Ordinal
d.Interval
12.A study that involves no researcher intervention is called
a.An experimental study.
b.A noninvolvement study.
c.An observational study.
d.A quasi-experimental study.
13.A variable that interferes with other variables in the study is called
a.A confounding variable.
b.An explanatory variable.
c.An outcome variable.
d.An interfering variable.
Use the best answer to complete these statements.
14.Two major branches of statistics are ________ and ________.
15.Two uses of probability are ________ and ________.
16.The group of all subjects under study is called a(n) ________.
17.A group of subjects selected from the group of all subjects under study is called a(n) ________.
18.Three reasons why samples are used in statistics are a. ________ b. ________ c. ________.
19.The four basic sampling methods are a. ________ b. ________ c. ________ d. ________.
20.A study that uses intact groups when it is not possible to randomly assign participants to the groups is called a(n) ________ study.
21.In a research study, participants should be assigned to groups using ________ methods, if possible.
22.For each statement, decide whether descriptive or inferential statistics is used.
a.The average life expectancy in New Zealand is 78.49 years. Source: World Factbook 2004.
b.A diet high in fruits and vegetables will lower blood pressure. Source: Institute of Medicine.
c.The total amount of estimated losses from hurricane Hugo was $4.2 billion. Source: Insurance Service Office.
d.Researchers stated that the shape of a person’s ears is related to the person’s aggression. Source: American Journal of Human Biology.
e.In 2013, the number of high school graduates will be 3.2 million students. Source: National Center for Education.
23.Classify each as nominal-level, ordinal-level, interval-level, or ratio-level measurement.
a.Rating of movies as G, PG, and R.
b.Number of candy bars sold on a fund drive.
c.Classification of automobiles as subcompact, compact, standard, and luxury.
d.Temperatures of hair dryers.
e.Weights of suitcases on a commercial airline.
24.Classify each variable as discrete or continuous.
a.Ages of people working in a large factory.
b.Number of cups of coffee served at a restaurant.
c.The amount of a drug injected into a guinea pig.
d.The time it takes a student to drive to school.
e.The number of gallons of milk sold each day at a grocery store.
25.Give the boundaries of each.
a.48 seconds.
b.0.56 centimeter.
c.9.1 quarts.
d.13.7 pounds.
e.7 feet.
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Critical Thinking Challenges
1.World’s Busiest Airports A study of the world’s busiest airports was conducted by Airports Council International. Describe three variables that one could use to
determine which airports are the busiest. What units would one use to measure these variables? Are these variables categorical, discrete, or continuous?
2.Smoking and Criminal Behavior The results of a study published in Archives of General Psychiatry stated that male children born to women who smoke during pregnancy
run a risk of violent and criminal behavior that lasts into adulthood. The results of this study were challenged by some people in the media. Give several reasons why
the results of this study would be challenged.
3.Piano Lessons Improve Math Ability The results of a study published in Neurological Research stated that second-graders who took piano lessons and played a computer
math game more readily grasped math problems in fractions and proportions than a similar group who took an English class and played the same math game. What type of
inferential study was this? Give several reasons why the piano lessons could improve a student’s math ability.
4.ACL Tears in Collegiate Soccer Players A study of 2958 collegiate soccer players showed that in 46 anterior cruciate ligament (ACL) tears, 36 were in women.
Calculate the percentages of tears for each gender.
a.Can it be concluded that female athletes tear their knees more often than male athletes?
b.Comment on how this study’s conclusion might have been reached.
5.Anger and Snap Judgments Read the article entitled “Anger Can Cause Snap Judgments” and answer the following questions.
a.Is the study experimental or observational?
b.What is the independent variable?
c.What is the dependent variable?
d.Do you think the sample sizes are large enough to merit the conclusion?
e.Based on the results of the study, what changes would you recommend to persons to help them reduce their anger?
6.Hostile Children Fight Unemployment Read the article entitled “Hostile Children Fight Unemployment” and answer the following questions.
a.Is the study experimental or observational?
b.What is the independent variable?
c.What is the dependent variable?
d.Suggest some confounding variables that may have influenced the results of the study.
e.Identify the three groups of subjects used in the study.
Source: Reprinted with permission from Psychology Today, Copyright © (2004) Sussex Publishers, Inc.
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Source: Reprinted with permission from Psychology Today, Copyright © (2001) Sussex Publishers, Inc.
Data Projects
1.Business and Finance Investigate the types of data that are collected regarding stock and bonds, for example, price, earnings ratios, and bond ratings. Find as many
types of data as possible. For each, identify the level of measure as nominal, ordinal, interval, or ratio. For any quantitative data, also note if they are discrete
or continuous.
2.Sports and Leisure Select a professional sport. Investigate the types of data that are collected about that sport, for example, in baseball, the level of play (A,
AA, AAA, Major League), batting average, and home-run hits. For each, identify the level of measure as nominal, ordinal, interval, or ratio. For any quantitative data,
also note if they are discrete or continuous.
3.Technology Music organization programs on computers and music players maintain information about a song, such as the writer, song length, genre, and your personal
rating. Investigate the types of data collected about a song. For each, identify the level of measure as nominal, ordinal, interval, or ratio. For any quantitative
data, also note if they are discrete or continuous.
4.Health and Wellness Think about the types of data that can be collected about your health and wellness, things such as blood type, cholesterol level, smoking status,
and BMI. Find as many data items as you can. For each, identify the level of measure as nominal, ordinal, interval, or ratio. For any quantitative data, also note if
they are discrete or continuous.
5.Politics and Economics Every 10 years since 1790, the federal government has conducted a census of U.S. residents. Investigate the types of data that were collected
in the 2000 census. For each, identify the level of measure as nominal, ordinal, interval, or ratio. For any quantitative data, also note if they are discrete or
continuous. Use the library or a genealogy website to find a census form from 1860. What types of data were collected? How do the types of data differ?
6.Your Class Your school probably has a database that contains information about each student, such as age, county of residence, credits earned, and ethnicity.
Investigate the types of student data that your college collects and reports. For each, identify the level of measure as nominal, ordinal, interval, or ratio. For any
quantitative data, also note if they are discrete or continuous.
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Answers to Applying the Concepts
Section 1–1Attendance and Grades
1.The variables are grades and attendance.
2.The data consist of specific grades and attendance numbers.
3.These are descriptive statistics; however, if an inference is made to all students, then that would be inferential statistics.
4.The population under study is students at Manatee Community College (MCC).
5.While not specified, we probably have data from a sample of MCC students.
6.Based on the data, it appears that, in general, the better your attendance the higher your grade.
Section 1–2Safe Travel
1.The variables are industry and number of job-related injuries.
2.The type of industry is a qualitative variable, while the number of job-related injuries is quantitative.
3.The number of job-related injuries is discrete.
4.Type of industry is nominal, and the number of job-related injuries is ratio.
5.The railroads do show fewer job-related injuries; however, there may be other things to consider. For example, railroads employ fewer people than the other
transportation industries in the study.
6.A person’s choice of transportation might also be affected by convenience issues, cost, service, etc.
7.Answers will vary. One possible answer is that the railroads have the fewest job-related injuries, while the airline industry has the most job-related injuries (more
than twice those of the railroad industry). The numbers of job-related injuries in the subway and trucking industries are fairly comparable.
Section 1–3American Culture and Drug Abuse
Answers will vary, so this is one possible answer.
1.I used a telephone survey. The advantage to my survey method is that this was a relatively inexpensive survey method (although more expensive than using the mail)
that could get a fairly sizable response. The disadvantage to my survey method is that I have not included anyone without a telephone. (Note: My survey used a random
dialing method to include unlisted numbers and cell phone exchanges.)
2.A mail survey also would have been fairly inexpensive, but my response rate may have been much lower than what I got with my telephone survey. Interviewing would
have allowed me to use follow-up questions and to clarify any questions of the respondents at the time of the interview. However, interviewing is very labor- and
cost-intensive.
3.I used ordinal data on a scale of 1 to 5. The scores were 1 = strongly disagree, 2 = disagree, 3 = neutral, 4 = agree, 5 = strongly agree.
4.The random method that I used was a random dialing method.
5.To include people from each state, I used a stratified random sample, collecting data randomly from each of the area codes and telephone exchanges available.
6.This method allowed me to make sure that I had representation from each area of the United States.
7.Convenience samples may not be representative of the population, and a convenience sample of adolescents would probably differ greatly from the general population
with regard to the influence of American culture on illegal drug use.
Section 1–4Just a Pinch Between Your Cheek and Gum
1.This was an experiment, since the researchers imposed a treatment on each of the two groups involved in the study.
2.The independent variable is whether the participant chewed tobacco or not. The dependent variables are the students’ blood pressures and heart rates.
3.The treatment group is the tobacco group—the other group was used as a control.
4.A student’s blood pressure might not be affected by knowing that he or she was part of a study. However, if the student’s blood pressure were affected by this
knowledge, all the students (in both groups) would be affected similarly. This might be an example of the placebo effect.
5.Answers will vary. One possible answer is that confounding variables might include the way that the students chewed the tobacco, whether or not the students smoked
(although this would hopefully have been evened out with the randomization), and that all the participants were university students.
6.Answers will vary. One possible answer is that the study design was fine, but that it cannot be generalized beyond the population of university students (or people
around that age).
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