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84.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
SUSANVILLE—Fewer than 20 percent of college professors consider themselves shy,
according to a new study by two psychologists. "We were surprised by this result because
other studies have reported that almost 50 percent of adult Americans think of themselves
as shy," said Elliot Smalley, professor at Colusa State University. "College professors are
sometimes thought to be an introverted lot, and so we expected perhaps a majority to
think of themselves as shy," he said.
Smalley and his associate, John Mahmoud, interviewed 150 college professors who were
identified by administrators at twenty-five American universities as typical faculty. The
universities were selected by a random procedure from a list of American colleges and
universities, Smalley said.
This is a poor generalization. University administrators might be apt to state the first
professors who come to mind, and professors selected in this manner might tend to be
among the more outspoken faculty. Truly shy, introverted faculty might well be unknown to
most administrators at a large university.
85.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
Gridley has been going to the Silver Dollar Fair every year for the past fifteen years. An
acquaintance suggests they go to the fair, but "For God’s sake, let’s don’t eat there, we’ll
die." Gridley knows better; he’s never even once gotten sick from Silver Dollar food.
No fallacy.
86.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
A random survey of 1,000 callers to a drug hotline number produced the following results:
535 of the callers were heavy users of either cocaine freebase, amphetamines, or heroin;
220 were "recreational" users of cocaine or hashish; 92 were not drug users at all; and the
remainder refused to answer the survey questions. This should put to rest the claim that
most people who take drugs are of the occasional, "recreational" type.
The sample in this argument is badly biased. A typical heavy user of a drug is much more
likely to get into a crisis situation and thus more likely to call a hotline number than a
typical "recreational" user.
87.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
ATLANTA (UPI)—A long-term federal study by the National Centers for Disease Control of
13 million U.S. births shows increases in the rate of eleven different types of birth defects,
including a 17.5 percent yearly average increase in patent ductus arteriosus and a 10.8
percent increase for ventricular septal defects, over a fourteen-year period. The study was
conducted by the Birth Defects Monitoring Program of the CDC, which collected its data
from hospitals across the country. From 1970 to 1983, over 13 million births were
monitored. [An adaptation]
"Hospitals across the country" is vague, but this is almost certainly a reputable scientific
study, and the sample is extremely large. A generalization from these results to the
American population as a whole should be sound.
88.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
FRESNO—In a new study of dangerous Halloween pranks, Fresno State University
sociologist Joel Best has documented the exact number of American children killed or
seriously injured by anonymously given, booby-trapped Halloween treats. Best reviewed
supposedly real Halloween horror stories appearing from 1958 to 2004 in the
New York
Times
, the
Chicago Tribune
, the
Los Angeles Times
, and the
Fresno Bee
. He did not find a
single case in which a Halloween treat anonymously given to a child caused serious harm.
He concluded that the infamous Halloween sadist is an "urban myth."
—Adapted from a McClatchy News Service release
The question is whether the "exact number" of American children killed or seriously
injured by anonymously given Halloween tricks can be determined by looking at the
incidents reported in the four newspapers mentioned. There may have been a few
incidents not reported in these newspapers, but we’d be surprised if there were many.
Events of this type tend to attract too much attention not to be reported in at least one of
these sources.
89.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
Haslett wanted to know what percentage of students at his college vote in local elections.
He asked each of his professors (he was a political science major) to ask for a show of
hands in his classes, so he could make a count. He found that 45 percent of the 120
classmates polled vote in local elections. He concludes that about 45 percent of the
students at his college vote in those elections.
The sample is large enough to be somewhat reliable, although Haslett should not be
surprised by a substantial deviation from his 45 percent projection. A more serious
problem is that Haslett’s poll may have been taken in political science classes (or at least
mainly in political science classes) and that people who take such classes may be more
interested in political matters and hence more likely to vote in any election. The possibility
of bias is substantial.
90.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
A survey was made in 1948 in which a large number of names were randomly selected
from the telephone book of a large city. The individuals called were asked whether they
preferred Truman or Dewey in the presidential race. Over half of the respondents named
Dewey, so the pollsters concluded that Dewey would carry the city and region.
The principal problem with this survey is that in 1948 many voters did not have telephones
and thus had no chance of being selected. Since possession of a telephone was linked
with a person’s economic status, and economic status helps determine political views, the
sample was badly biased.
91.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
As part of his work for NASA, Dr. Murdock was asked to find out what percentage of
Americans saw Halley’s comet when it was last visible. He randomly selected three
cities—Seattle, Cleveland, and Boston—and polled several hundred randomly selected
individuals from these cities. His findings are that fewer than 5 percent of Americans saw
the comet.
It makes no difference whether the cities and the individuals were randomly selected.
Inhabitants of large cities, especially northern big cities, would be less likely to see the
comet because of city lights, clouds, air pollution, and latitude.
92.
In evaluating the following generalization(s), identify sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
Let’s say that according to statewide studies done in Montana and Virginia, the infant
mortality rate for these two states averaged 10.5 per thousand live births. Could this figure
be generalized to the infant mortality rate in the United States? What factors might be
relevant to the generalization?
Montana and Virginia provide a large and reasonably good sample, although there may be
a bias toward rural areas and small towns over large urban areas. We would want to know
about Montana’s and Virginia’s resident-to-doctor ratios, their ratios of residents to
hospital beds, the level of prenatal education available in the two states, and similar
matters. The more similar these possibly relevant factors are in Montana and Virginia to
the remainder of the country, the stronger the argument.
93.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
Osteoporosis is a degeneration of bone tissue that afflicts between fifteen and twenty
million Americans and leads to approximately 1.3 million bone fractures every year. The
condition is found mainly among women. A conference sponsored by the National
Institutes of Health in 1994 reported that calcium was one of the "mainstays of prevention
and management of osteoporosis." In a localized study designed to help predict the future
incidence of osteoporosis in women in a midwestern community, a county hospital did a
survey on calcium intake. It selected five hundred women at random and asked them to
keep a record of their food and dietary supplements for one month. The data were
analyzed to determine the amounts of calcium each woman received. It was determined
that 85 percent of the surveyed women received less calcium than the recommended
amount of 1,000 to 1,500 milligrams per day. County medical authorities concluded that
about 85 percent of the community’s women were getting less than the recommended
intake of calcium. They also concluded that local medical facilities would soon see an
increase in the number of cases of osteoporosis as the calcium deficiency showed its
effects. Given just the information presented here, how much confidence would you have
in these conclusions?
The first conclusion is less solid than it might appear. The survey was done during one
month, and diets change during the course of a year. More dairy products may be
consumed during one time of the year than others; certainly some vegetables are
consumed on a varying seasonal basis. Hence, the study may accurately reflect only the
calcium intake in the population during that month of the year. Another problem with the
11-50
calcium at age twenty-four but who increase their intake by the time they are thirty-five
may be no more likely to suffer osteoporosis than those whose intake is high during their
entire lives.)
The second conclusion does not follow at all. The insufficient intake of calcium may have
been going on for years; so the incidence of osteoporosis may remain exactly the same in
the future.
94.
In evaluating the following generalization(s), identify sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
Seventy-two percent of those interviewed at a luncheon sponsored by the Camellia
Chamber of Commerce favored local tax incentives to attract new businesses. Would this
finding generalize to the Camellia population?
No. This is not likely to be a representative sample.
95.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
A majority of Americans think that tobacco companies should be prohibited from
advertising their products. In a survey of 1,213 adults, 86 percent said that prohibiting
tobacco advertising would lower smoking rates. The results of the nationwide telephone
survey, conducted by American Opinion Research, Inc., were published in this week’s
edition of
Research Fact
. Spokespersons for the American Tobacco Council had no
immediate comment on the findings.
It is not clear from this passage whether a majority of the respondents actually think that
tobacco advertising should be prohibited. The 86 percent said something else: that doing
so would lower smoking rates. Whether they would outlaw tobacco advertising is not
known.
96.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
A poll of fifty weight lifters at a southern California gym determined that thirty-three payed
close attention to their diets as well as to their exercise. Of those thirty-three, twenty-five
(50 percent of the original fifty) made it a point to eat more than the minimum daily
amount of protein for large adults, and twenty (40 percent of the original fifty) took vitamin
pills and other dietary supplements. The chain of health-food stores that took the poll
concluded that weight lifters constitute a substantial market for its products, since it is
likely that 40 percent of all weight lifters across the country take vitamin pills and
supplements and that an additional 10 percent are at least highly conscious of their diets.
The health-food chain had best not invest too much in attracting this new market. The
first flaw in the survey is technical: the sample is too small to give a very detailed picture
of weight lifters’ habits. Even if nothing else were wrong with the survey, strong
confidence (95 percent) would be justified only in the claim that from about 36 to 64
percent of the weight lifters nationwide make sure to eat more than the usual amount of
protein—not a very precise conclusion (see the error margin table [Table 10-1] in the text,
page 360). A more important flaw in the survey is that the interviews are confined to
clients of only one gym. Information is often passed around among people who frequent
the same establishments, and there may be trends or fads or a particular bit of useful
97.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
Thirty percent of American people ages nineteen to thirty-nine diet at least once a month,
according to a news syndicate poll released last November. These findings are based on
telephone interviews with a random sample of people listed in the Los Angeles telephone
directory.
A generalization about the subject based on a sample of people would be unreliable,
especially since people in southern California are more likely to be aspiring models and
actors, beachgoers, and tend to pay more attention to their physiques.
98.
In the following passage, identifying sample, population, attribute of interest, and the
extent to which the claims involved are knowable. Consider carefully the size and
diversification of the sample and the extent to which the population differs or may differ
from the sample; remember, what’s important is that the sample be representative. Do you
find any flaw in our professor’s reasoning about the usefulness of the survey for her own
purposes? Should she believe that the more people who have home offices, the more
likely her own will escape attention from the IRS?
A college professor converted one room of her house into a home office and intended to
deduct her expenses on her federal income tax return. She wondered how many other
college faculty had done the same, thinking that the more who deducted home offices, the
less likely her own return would be noticed by the IRS and hence the less likely she would
be audited. So she decided to do her own informal survey of her colleagues to see how
many of them had home offices. She sent out a questionnaire of three questions to all
1,200 instructors at her campus, and she received 950 responses. (Her promise to share
the results of the survey apparently motivated faculty to respond.)
As it turned out, 32 percent of her respondents answered yes to the question, "Do you
maintain an office at home?" Half of these also answered yes to the question, "Do you
deduct your home office expenses on your federal income tax return?" And 24 percent of
the entire group of respondents answered yes to the question, "Is your campus office
adequate?"
This is not a question about the criteria for evaluating statistical generalizations, but
rather about the assumption that motivated the study. It does us no good to produce
studies to answer questions if they are the wrong questions to begin with. In this case, it
may be that the IRS will turn more attention to home office deductions if there are enough
99.
In the following passage, identifying sample, population, attribute of interest, and the
extent to which the claims involved are knowable. Consider carefully the size and
diversification of the sample and the extent to which the population differs or may differ
from the sample; remember, what’s important is that the sample be representative. Would
our professor’s conclusion, "About 32 percent of college faculty nationwide maintain home
offices," be more likely if she had included faculty from other institutions among her
survey? Why?
A college professor converted one room of her house into a home office and intended to
deduct her expenses on her federal income tax return. She wondered how many other
college faculty had done the same, thinking that the more who deducted home offices, the
less likely her own return would be noticed by the IRS and hence the less likely she would
be audited. So she decided to do her own informal survey of her colleagues to see how
many of them had home offices. She sent out a questionnaire of three questions to all
1,200 instructors at her campus, and she received 950 responses. (Her promise to share
the results of the survey apparently motivated faculty to respond.)
As it turned out, 32 percent of her respondents answered yes to the question, "Do you
maintain an office at home?" Half of these also answered yes to the question, "Do you
deduct your home office expenses on your federal income tax return?" And 24 percent of
the entire group of respondents answered yes to the question, "Is your campus office
adequate?"
It would be much more likely to be accurate. Faculty at different kinds of colleges
(community colleges, state colleges, state universities, and private universities) have
different requirements and hence a different level of need for offices at home—the more
research a faculty does, the more likely the need for home offices.
100.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
Seventeen percent of Winchell State students intend to pursue careers as computer
programmers or analysts. That’s what a recent survey of WSU students conducted by
psychology major Jack Nafarik shows. Nafarik passed out questionnaires to students who
voted in the March student election as they exited from the polling stations in the student
union. "The results didn’t surprise me," Nafarik said. "The figure may seem fairly high, but
you’d expect that in a technical school like Winchell State."
Do student voters constitute a representative sample of the students at Winchell State?
Probably not. Upper-division students may vote in larger numbers than freshmen and
sophomores, and there may be correlations between class standing and career goals.
There may also be a direct correlation between types of major and participation in student
elections. Can you think of any other possible sources of bias?
101.
In the following passage, identifying sample, population, attribute of interest, and the
extent to which the claims involved are knowable. Consider carefully the size and
diversification of the sample and the extent to which the population differs or may differ
from the sample; remember, what’s important is that the sample be representative. Is it
reasonable for our professor to conclude that faculty office space on the campus is
inadequate?
A college professor converted one room of her house into a home office and intended to
deduct her expenses on her federal income tax return. She wondered how many other
college faculty had done the same, thinking that the more who deducted home offices, the
less likely her own return would be noticed by the IRS and hence the less likely she would
be audited. So she decided to do her own informal survey of her colleagues to see how
many of them had home offices. She sent out a questionnaire of three questions to all
1,200 instructors at her campus, and she received 950 responses. (Her promise to share
the results of the survey apparently motivated faculty to respond.)
As it turned out, 32 percent of her respondents answered yes to the question, "Do you
maintain an office at home?" Half of these also answered yes to the question, "Do you
deduct your home office expenses on your federal income tax return?" And 24 percent of
the entire group of respondents answered yes to the question, "Is your campus office
adequate?"
Yes; at least, it is reasonable for her to conclude that her faculty colleagues believe it is
inadequate, and by a large majority. Her sample not only is large enough to guarantee
reliability in such a conclusion, but also includes almost all of the population.
11-58
102.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
Ronald is driving across the country when his car develops a minor mechanical problem.
He can fix the trouble himself, but he’ll need a wrench of a size he doesn’t have. He
resolves to stop at the next Sears retail store he sees to purchase one. He’s been in four
or five Sears retail stores in the past, and all of them have carried automotive tools. So he
is confident that all Sears retail outlets stock them.
His sample is small, but very representative; Ronald has made a sound generalization.
Note that the argument could also be construed as analogical.
103.
In the following passage, identifying sample, population, attribute of interest, and the
extent to which the claims involved are knowable. Consider carefully the size and
diversification of the sample and the extent to which the population differs or may differ
from the sample; remember, what’s important is that the sample be representative. Would
our professor’s conclusion, "Sixteen percent of faculty nationwide deduct home office
expenses on their federal income tax return," be more accurate if she restricted it to
faculty in her own state?
A college professor converted one room of her house into a home office and intended to
deduct her expenses on her federal income tax return. She wondered how many other
college faculty had done the same, thinking that the more who deducted home offices, the
less likely her own return would be noticed by the IRS and hence the less likely she would
be audited. So she decided to do her own informal survey of her colleagues to see how
many of them had home offices. She sent out a questionnaire of three questions to all
1,200 instructors at her campus, and she received 950 responses. (Her promise to share
the results of the survey apparently motivated faculty to respond.)
As it turned out, 32 percent of her respondents answered yes to the question, "Do you
maintain an office at home?" Half of these also answered yes to the question, "Do you
deduct your home office expenses on your federal income tax return?" And 24 percent of
the entire group of respondents answered yes to the question, "Is your campus office
adequate?"
Yes. Different states may have different state income tax rules, and it may be more
worthwhile, for tax reasons, to have a home office in some states than in others. A faculty
member who does not find it worthwhile to have a home office in one state may find it
advantageous in another.
104.
Evaluate the following generalization(s), identifying sample, population, attribute of
interest, and the extent to which the claims involved are knowable. Consider carefully the
size and diversification of the sample and the extent to which the population differs or
may differ from the sample; remember, what’s important is that the sample be
representative.
Well, I did rotten in Algebra I last semester, so I expect I’ll do poorly in the rest of the math
classes I’ll have to take.
There may be enough differences between last semester and the rest—we’d like to
think—to make the argument a weak one: different instructor, new study habits, and so
on. Still, we’d bet against his doing well before we’d bet against somebody who did well in
Algebra I.
