Moore Chapter 2

Samples,Goodand Bad
As discussedin Chapter'1,since 1960
HelenGraceChocolates
hasconducteda
jelly beanpoll to predictthe winnerof the presidential election.Presidentand CEOJim Gracestatedin
an onlinearticlein October2OOOthat the jelly bean
poll had correctlypickedthe electionwinnerfor over
30 years.When first initiatedin 1960,the poll forecastedJohn F.Kennedy'snarrowvictoryover Richard
Nixon.lt accurately
foretoldRonaldReagan's
victory
overJimmyCarterin 1980andGeorgeBush'swin over
MichaelDukakisin 1988.
In October2OOOthe pollshowedGeorgeW. Bush
havinga 2.2o/o
lead over Vice PresidentAl Gore.The
poll was againcorrectin pickingthe electionwinner.
Thepollhasan extraodinary
record,so doesthisimply
poll
produces
good
that the
data?By the end of this
chapteryou will learnhow to assesswhetherthe data
from the jelly bean poll are good or bad.r
s.
B
3
How to samplebadly
For many years in Rapides Parish, Louisiana, only one company had been
allowed to provide ambulance service. In 1999, the local paper, the Town
Talk, asked readers to call in to offer their opinion on whether the company should keep its monopoly. Call-in polls are generally automated: call
one telephone number to vote'Yes" and caII another number to vote "No."
Telephone companies often charge callers to these numbers.
The Town Talk got 3763 calls, which suggestsunusual interest in ambulance service. Investigation showed that 638 calls came from the ambulance
company office or from the homes of its executives. Many more no doubt
came from lower-Ievel employees."We've got employees who are concerned
about this situation, their job stability and their families and maybe called
more than they should have," said a company vice president. Other sources
said employees were told to, as they say in Chicago, "vote early and often."
21
22
CHAPTER2
Samples, Good and Bad
As the Town Talk learned, it is easier to sample badly than to sample well. The paper relied on uoluntary response,allowing people to call in
rather than actively selecting its own sample. The result was biased,-the
sample was overweighted with people favoring the ambulance monopoly.
Voluntary response samples attract people who feel strongly about the
issue in question. These people, like the employees of the ambulance
company, may not fairly represent the opinions of the entire population.
There are other ways to sample badly. Suppose that we sell your company several crates of oranges each week. You examine a sample of oranges
from each crate to determine the quality of our oranges. It is easy to inspect a few oranges from the top of each crate, but these oranges may not
be representative of the entire crate. Those on the bottom are more often
damaged in shipment. If we were less than honest, we might make sure that
the rotten oranges are packed on the bottom with some good ones on top for
you to inspect. If you sample from the top, your sample results are again
biased-the sample oranges are systematically better than the population
they are supposed to represent.
:EFrUl:f:.i!li:i;'i:.l.:1.:Fri.:'!liij!:irii:1':.r:
,ii;:iii:.:i.'i;ii::':.i:.f,i:
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Biasedsamplingmethods
The design of a statistical study is biased if it systematically favors
certain outcomes.
Selection of whichever individuals are easiest to reach is called convenience sampling.
A voluntary response sample choosesitself by responding to a general appeal. Write-in or call-in opinion polls are examples of voluntary
responsesamples.
Conveniencesamples and voluntary response samples are often biased.
o
EXAMPLEI
Interviewing
at the mall
q
q
Squeezing the oranges on the top of the crate is one example of convenience sampling. MalI interviews are another.
Manufacturers and advertising agencies often use interviews at shopping malls to gather information about the
habits of consumers and the effectivenessof ads. A sample
of mall shoppers is fast and cheap. But people contacted
at shopping malls are not representative of the entire U.S.
population. They are richer, for example, and more likely
to be teenagers or retired. Moreover, the interviewers tend
to select neat, safe-looking individuals from the stream of
Simplerandomsamples
23
customers. Mall samples are biased: they systematically overrepresent
some parts of the population (prosperous people, teenagers, and retired
people) and underrepresent others. The opinions of such a convenience
sample may be very different from those of the population as a whole.
EX A MP L E2 Wri te -i no p i n ionpolls
Ann Landers once asked the readers of her advice column, "If you had it
to do over again, would you have children?" She received nearly 10,000
responses, almost 70% saying "NO!" Can it be true that 70o/oof parents
regret having children? Not at all. This is a voluntary response sample.
People who feel strongly about an issue, particularly people with strong
negative feelings, are more likely to take the trouble to respond. Ann
Landers's results are strongly biased-the percentage of parents who
would not have children again is much higher in her sample than in the
population of all parents.
Write-in and callin opinion polls are
almost sure to lead to
strong bias. In fact,
only about I5o/oof the
public have ever responded to a call-in
poll, and these tend to
be the same people
who call radio talk
shows. That's not a
representative sample
of the population as a
"Hey,Pops,whot wosthot letter you sent off to Ann Londersyesterday?"
whole.
Simplerandomsamples
In a voluntary response sample, people choose whether to respond. In a
convenience sample, the interviewer makes the choice. In both cases,personal choice produces bias. The statistician's remedy is to allow impersonal
chance to choose the sample. A sample chosen by chance allows neither
favoritism by the sampler nor self-selection by respondents. Choosing a
sample by chance attacks bias by giving aII individuals an equal chance
24
CHAPTER2
Samples, Good and Bad
to be chosen. Rich and poor, young and old, black and white, all have the
same chance to be in the sample.
The simplest way to use chance to select a sample is to place names in
a hat (the population) and draw out a handful (the sample). This is the idea
of simple random sampling.
Simplerandomsample
A simple random sample (SRS) of size nconsists of nindividuals from
the population chosen in such a way that every set of n individuals has
an equal chance to be the sample actually selected.
An SRS not only gives each individual an equal chance to be chosen
(thus avoiding bias in the choice) but also gives every possible sample an
equal chance to be chosen. Drawing names from a hat does this. Write 100
names on identical slips of paper and mix them in a hat. This is a population. Now draw 10 slips, one after the other. This is an SRS, because any
10 slips have the same chance as any other 10.
2.1 Sampling my class. There arc 20 studentsin my class.
They sit in assignedseats,consistingof four rows of five students each. I want to take a simple random sample consisting of 4 of the
students in my class. To do this I select a single student from each row as
follows. I write the numbers 1 to 5 on identical slips of paper. I mix the slips
in a hat and draw one at random. I count this number of seats in from the
left in the first row and select the student in this seat. For example, if the
number selected is 3, I select the third student in from the left in the first
row. I replace the slip in the hat, again mix the slips, and draw a new number. The student seated this many seats in from the left in the second row
is selected.I repeat this processfor the remaining two rows. Every student
in the class has a 1-in-5 chance of being selected when I come to their row.
Thus, every student has the same chance of being selected.Is the sample a
simple random sample? Explain.
Drawing names from a hat makes clear what it means to give each individual and each possible set of z individuals the same chance to be chosen.
That's the idea of an SRS. Of course, drawing slips from a hat would be a
bit awkward for a sample of the country's 111 million households. In practice, we use computer-generated random digits to choose samples. Many
Simple random samples
:r+l i: 4:'i:+: l: F ii.:lii iti i.: i .;',' ;:i li ii
Choosean SRSin two steps
Step 1: Label. Assign a numerical Iabel to every individual in the population. Be sure that all Iabels have the same number of digits if you
plan to use a table ofrandom digits.
Step 2: Software
random.
or table. Use random digits to select labels at
You can assign labels in any convenient manner, such as alphabetical
order for names of people. When using a table of random digits, as long as
all Iabels have the same number of digits, all individuals will have the same
chance to be chosen.Use the shortest possible labels: one digit for a population of up to 10 members, two digits for 11 to 100 members, three digits for
101 to 1000 members, and so on. As standard practice, we recommend that
you begin with label 1 (or 01 or 001, as needed).You can read digits from Table A in any order-across a row, down a column, and so on-because the table has no order. As standard practice, we recommend reading across rows.
Sample surveys use computer software to choose an SRS, but the software just automates the steps in Example 3. The computer doesn't look in
a table ofrandom digits because it can generate them on the spot.
EXAMPLE4
Howto choosean SRSusingsoftware
To see how software can be used to generate an SRS, go to the Research
Randomizer at www.randomizer.org. Click on "Randomize Now" and fill
in the boxes. You can even ask the Randomizer to arrange your sample in
order.
To repeat Example 3, we asked the Randomizer to generate one set
of numbers with five numbers per set. We specified the number range
as 1 to 30. We requested that each number remain unique and that the
numbers be sorted from least to greatest. We asked to view the outputted
numbers with the place markers off. See Figure 2.1. After clicking on the
"RandomizeNow!" button, we obtained the digits 4,7, 14,16, and 23.
This time, the sampleis the clients labeled 04,07 ,14, \6,23. Theseare
Anderson Construction, Bennett Hardware, Fleisch Realty, JL Records,
and River City Books.
2.2 Evaluating teaching assistants. Toassesshow its teaching assistantsare performing,the statistics department at a
large university randomlyselects3 of its teachingassistantseachweekand
sendsa faculty memberto visit their classes.The current list of 20 teaching
assistants is given below. Use either software (for example, the Research
27
-
28
CHAPTER2
Samples. Good and Bad
mi
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T{) gtncr;llc li s!'t {r1 t;tfirk}nt nultrl^-ts. rirn;th ttttr.r r rirr
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ft qdour nurnbrrs. simFllitll {!ul the !$nn.
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F IGU R E2 .1 U s i n gth e R e searchR andomi zerat w w w .randomi zer.orq.
Randomizer) or Table A at line 116 to choose 3 to be visited this week. Remember to begin by labeling the teaching assistants from 01 to 20.
Bautista
Bolen
Clottey
Counts
Draper
Frazier
Kumar
Lam
Lovesky
Marin
Miller
Podboy
Roy
Schumacher
Tower
Walters
Wang
Weimer
Yu
Zhang
Canyoutrusta sample?
The Town Talh, Ann Landers, and mall interviews produce samples. We
can't trust results from these samples, because they are chosen in ways
Simplerandomsamples
25
statistical software packages have random number generators that generate random digits. Some also allow one to choosean SRS.
If you don't use software, you can use a table of random digits to choose
small samplesby hand.
Randomdigits
A table of random digits is a long string of the digits 0, 1,2,3, 4, 5,
6,7, 8,9 with these two properties:
1. Each entry in the table is equally likely to be any of the 10 digits 0
through 9.
2. The entries are independent ofeach other. That is, knowledge of
one part of the table gives no information about any other part.
Table A at the back of the book is a table of random
digits. You can think of Table A as the result of asking
an assistant (or a computer) to mix the digits 0 to 9 in a
hat, draw one, then replace the digit drawn, mix again,
draw a second digit, and so on. The assistant's mixing
and drawing save us the work of mixing and drawing
when we need to randomize. Table A begins with the
digits 19223950340575628713.To make the table easier
to read, the digits appear in groups of five and in numbered rows. The groups and rows have no meaning-the
table is just a long list of randomly chosen digits. Here's
how to use the table to choosean SRS.
EX A MP L E5 H o wto ch o o sean SRS
Joan's small accounting firm serves 30 business
clients. Joan wants to interview a sample of 5 clients
to find ways to improve client satisfaction. To avoid
bias, she choosesan SRS ofsize 5.
Step 1: Label. Give each client a numerical label,
using as few digits as possible. TWo digits are needed
to label 30 clients, so we use labels
Are theserandomdigits
reallyrandom?
Not a chance.The random digits
in Table A were produced by a
computerprogram.Computerprograms do exactly what you tell
them to do. Givethe programthe
same input and it will produce
exactlythe same "random"digits.
Of course,cleverpeoplehavedevisedcomputerprogramsthat produceoutputthat lookslikerandom
di gi ts.Theseare cal l ed" pseudo randomnumbers,"and that'swhat
TableA contains.Pseudo-random
numberswork fine for statistical
randomizing,
but they havehidden
nonrandompatternsthat can mess
up morerefineduses.
-
26
CHAPTER2
Samples, Good and Bad
It is also correct to use labels 00 to 29 or even another choice of B0 twodigit labels. Here is the list of clients, with labels attached:
01 A-l Plumbing
02 Accent Printing
03 Action Sport Shop
04 Anderson Construction
05 Bailey Tfucking
06 Balloons,Inc.
07 Bennett Hardware
08 Best's Camera Shop
09 Blue Print Specialties
10 Central Ttee Service
11 ClassicFlowers
12 Computer Answers
13 Darlene'sDolls
14 Fleisch Realty
15 HernandezElectronics
16
17
18
19
20
2I
22
23
24
25
26
27
28
29
30
JL Records
JohnsonCommodities
Keiser Construction
Liu's ChineseRestaurant
MagicTan
PeerlessMachine
Photo Arts
River City Books
Riverside Tavern
Rustic Boutique
Satellite Services
ScotchWash
Sewer'sCenter
Tire Specialties
Von's Video Store
step 2: Table. Enter Table A anywhere and read two-digit groups. s.rppose we enter at line 130, which is
69051
64877 87774 09517
84534 06489
87207 97245
The first 10 two-digit groups in this line are
69
05
16
48
r7
87
77
40
95
77
Each two-digit group in Table A is equally rikely to be any of the 100
possible groups, 00, 01, 02, ..., 9g. so two-digit groups choosetwo-digit
labels at random. That's just what we want.
Joan used only labels 01 to 30, so we ignore all other two-digit groups.
The first 5 labels between 01 and B0 that we encounter in the table choose
our sample. of the first 10 labels in line 180, we ignore 5 becausethey are
too high (over 30).The others are 0b, 16, L7,17, and 17.The clients labeled
05, 16, and 17 go into the sample. Ignore the secondand third 1zs because
that client is already in the sample. Now run your finger across line 180
(and continue to line 131 if needed) until b clients are chosen.
The sample is the clients labeled 0b, 16, rr,20,1g. These are Bailey
T[ucking, JL Becords, Johnson commodities, MagicTan, and Liu's
Chinese Restaurant.
using the table of random digits is much quicker than drawing names
from a hat. As Example 3 shows, choosing an SRS has two steps.
Statistics in Summary
29
that invite bias. We have more confidence in results
from an SRS, because it uses impersonal chance to
avoid bias. The first question to ask of any sample is
whether it was chosen at random. Opinion polls and
other sample surveys carried out by people who know
what they are doing use random sampling.
EX A MP L E 5 A Ga l l u p P o l l
A Gallup PolI on sex and violence on television began with the question "In your view, does the entertainment industry need to make a serious effort to
significantly reduce the amount of sex and violence
in its movies, television shows, and music, or don't
you think they need to do this?" The press release
Golfingat random
reported that the poll found "75Yoof Americans sayRandomdrawingsgiveallthe same
ing the entertainment industry should make a serichanceto be chosen,so they ofous effort to reduce the amount of sex and violence
fer a fair way to decidewho gets
in its movies, television shows, and music, whtle 24%
a scarcegood-like a roundof golf.
Lots of golferswant to play the fasay this isn't necessary." Can we trust this claim?
mous Old Courseat St. Andrews.
Ask first how Gallup selectedits sample. Later in the
Scotland.A few can reservein adpress release we read this: "These results are based
vance.Mostmusthopethat chance
on telephone interviews with a randomly selectednafavors them in the daily random
tional sample of 1008 adults, 18 years and older, condrawingfor tee times.At the height
of the summerseason,only I in 6
ducted February 6-8, 2004."
(about
wins the right to pay .C13O
This is a good start toward gaining our confidence.
for
round.
a
$260)
Gallup tells us what population it has in mind (people
at least 18 years old living anywhere in the United
States). We know that the sample from this population was of size 1008
and, most important, that it was chosen at random. There is more to
consider in assessing a poll, and we will soon discuss this, but we have
at least heard the comforting words "randomly selected."
S T AT IS T ICIN
S S U MMA R Y
We select a sample in order to get information about some population.
How can we choose a sample that fairly represents the population?
Convenience samples and voluntary response samples are common
but do not produce trustworthy data. These sampling methods are usually
biased. That is, they systematically favor some parts of the population
over others in choosing the sample.
The deliberate use ofchance in producing data is one ofthe big ideas of
statistics. Random samples use chance to choose a sample, thus avoiding
bias due to personal choice.The basic type of random sample is the simple
30
CHAPTER2
Samples, Good and Bad
random sample, which gives all samples of the same size the same chance
to be the sample we actually choose.To choosean SRS by hand, use a table
of random digits such as Table A in the back of the book.
CASE STUDY To participatein the jelly bean poll, describedin the Case
EVALUATED Studythat openedthe chapter,one mustpurchasejellybeans
at the storeor online.Usewhat you havelearnedin this chapterto assesswhether
the data collectedin the jelly beanpoll are good or bad.Yourassessment
should
be written so that someone who knows no statisticswill understandvour
reasoning.r
C H A P T E R2 E X E RCISES
For Erercise 2.1, seepage 24; for Exercise 2.2, seepage 27.
2.3 Letters to the editor. You work for a local newspaperthat has recently
reported on a bill that would make it easier to create charter schoolsin the
state. You report to the editor that 2Ol letters have been receivedon the issue,
of which 171 opposethe legislation. "I'm surprised that most of our readers
opposethe bill. I thought it would be quite popular," says the editor. Are you
convinced that a majority of the readers opposethe bill? How would you explain
the statistical issue to the editor?
2.4 Instant opinion. The BusinessWeekonline poll can be found at the Web
site indicated in the "Notes and Data Sources,"on page 34. The latest question
appearson the screen,and visitors to the site can simply click buttons to vote.
On March 29,2007, the question was "Do you think Googleis too powerful?"In
all, 1336 (35.9o/o)
said 'Yes," 2O5I (55.L%)said "No," and 335 (9.0%) said "I'm
not sure."
(a) What is the sample size for this poll?
(b) At the Web site, BusinessWeekincludes the following statement about its
online poll. "Note: Theseare surveys,not scientificpolls." Explain why the poll
may give unreliable information.
(c) Just abovethe poII question was the following statement: "Google'saccelerating lead in search and its movesinto software and traditional advertising
are sparking a backlash among rivals." How might this statement affect the
poll results?
2.5 Ann Landers takes a sample. Advice columnist Ann Landers onceasked
her divorced readers whether they regretted their decisionto divorce. She received approximately 30,000 responses,about 23,000 of which came from
women. Nearly 75% said they were glad they divorced, and most of them said
they wished they had done it sooner.Explain why this sample is certainly biprobably higher or
ased.What is the likely direction of the bias?That is, is 75o/o
Iower than the truth about the population of aII adults who have been divorced?
2.6 We don't like one-way streets. Highway planners decided to make a
main street in WestLafayette, Indiana, a one-waystreet. The LafayetteJournal
Chapter2 Exercises
and Courier took a one-daypoll by inviting readers to call a telephonenumber
to record their comments.The next day, the paper reported:
Journal and courier readersouerwhelminglyprefer two-way traffic
flow in
west Lafayette'svllage area to one-waystreets.By nearry a T-1 margin,
callers to the newspdper'sExpress Yourselfopinion rine on wednesdiy
complainedabout the one-waystreetsthat haue beenin place sinceMay.
Of the 98 commentsreceiued,all but 14 said no to one-way.
(a) what population do you think the newspaperwants information about?
(b) Is the proportion of this population who favor one-way streets almost certainly larger or smaller than the proportion 14198in the sample?why?
2.7 Design your own bad sample. Your college wants to gather student
opinion about parking for students on campus. It isn't practical to contact all
students.
(a) Give an exampleof a way to choosea sampleof stud.entsthat is poor practice
becauseit dependson voluntary response.
(b) Give an exampleof a bad way to choosea sample that doesn'tuse voluntarv
response.
2.8 A call-in opinion poll. In 200b the son FranciscoBay Tlmes
.lK
reported on a poll in New zealand that found that New Zealanders
'),i)
opposedthe nation's new gay-inclusivecivil-unions law by a 3-1 ratio.
r',ENiews
This poll was a call-in poll that cost g1 to participate in. The San FranciscoBay
Timesarticle also reported that a scientificpolling organizationfound.that New
Zealandersfavor the law by a margin of b6.4%to Bg.Bo/o.
Explain to someone
who knows no statistics why the two polls can give such widely differing results
and which poll is likely to be more reliable.
2.9 Call-in versus random sample polls. A national survey of rv network
news viewers found that 48%said they would believea phone-inpoll of 800,000
personsrather than a random sampleof 1000persons.Ofthe viewers, 42% said,
they would believethe random sample poll. Explain to someonewho knows no
statistics why the opinions of only 1000 randomly chosen respondentsare a
better guide to what all peoplethink than the opinions of 800,000callers.
2.10 Choose an SRS. A firm wants to understand the attitudes of its minority
managers toward its system for assessingmanagement performance. Below
is a list of all the firm's managers who are members of minority groups. use
TableA at line 137to choose6 to be interviewed in detail about the plrformance
appraisal system.
Agarwal
Aikens
Alfonseca
Baxter
Bowman
Brown
Cortez
Cross
Dewald
Edwaids
Fleming
Fonseca
Gates
Goel
Gomez
Hernandez
Huang
Johnson
Kim
Liao
Mourning
Nunez
Peters
Pliego
Puri
Reynolds
Richards
Rodriguez
Santiago
Shen
Vega
Watanabe
31
32
OHAPTER2
Samples, Good and Bad
2.11 Choose an SRS. Your classin ancient Ugaritic religion is poorly taught
and the classmembershave decidedto complain to the dean. The classdecides
to choose 4 of its members at random to carry the complaint. The class list
appearsbelow.Choosean SRS of 4 using the table of random digits, beginning
at line 140.
Burkett
Damon
Embree
Fossum
Fox
Garciaparra
Giambi
Gonzales
Hillenbrand
Howry
Jackson
Lowe
Lyon
Martinez
Mendoza
Millar
Mirabelli
Mueller
Nixon
Ofiiz
Person
Ramirez
Timlin
Varitek
Vaughan
Williams
Young
2.12 An election day sample. You want to choosean SRS of 20 of a city's 480
voting precincts for special voting-fraud surveillance on election day.
(a) Explain clearly how you would label the 480 precincts. How many digits
make up each of your labels? What is the gteatest number of precincts you
could label using this number of digits?
(b) Use Table A to choosethe SRS, and list the labels of the precincts you selected. Enter Table A at line 107.
2.13 Is this an SRS? A university has 30,000undergraduateand 10,000graduate students. A survey of student opinion concerning health care benefits for
domesticpartners ofstudents selects300 ofthe 30,000undergraduatestudents
at random and then separately selects100 ofthe 10,000graduate students at
random. The 400 students chosenmake up the sample.
(a) Explain why this sampling method gives each student an equal chance to
be chosen.
(b) Nonetheless,this is not an SRS.Why not?
2.14 How much do students pay for rent? A university's housing and residence office wants to know how much students pay per month for rent in offcampus housing. The university does not have enough on-campus housing for
students and this information will be used in a brochure about student housing.
The population contains 12,304 students who live in off-campushousing and
have not yet graduated. The university will send a questionnaireto an SRS of
200 ofthese students, drawn from an alphabetizedlist.
(a) Describehow you'would label the students in order to selectthe sample.
(b) Use Table A, beginning at line t25, to select the first 5 students in the
sample.
2.15 Apartment living. You are planning a report on apartment living in a
college town. You decide to select three apartment complexesat random for indepth interviews with residents. Use Table A, starting at line 117, to select a
Chapter 2 Exercises
simple random sample of three of the following apartment complexes.
Abbington Village
Bayberry Place
Blendon Square
Cabot's Mill
Carlin Manor
Cedar Grove
Creekside
Dartmouth Place
Eaglecrest
Emerald Glen
Fair Oaks
Fox and Hounds
French Run
Glenchester
Grand Haven
Harvest GIen
Highland Terrace
Iuka Park
Jefferson Chase
Kensington Commons
Lantern Square
Laurel Lake
Meadowbrook
Millstream Village
Old Cape Colony
Olentanry Terrace
Peppermill
Pinecrest
RaccoonCreek
Royal James Plaza
Slate Ridge
Summerview
Timber Tlail
Walnut Glen
Williamsburg
Yearling Green
2.16 How do random digits behave? Which of the following statementsare
true of a table of random digits, and which are false? Explain your answers.
(a) Each pair ofdigits has chance 1/100ofbeing 33.
(b) There are exactly four 4s in each row of 40 digits.
(c) The digits 99999 can never appear as a group, becausethis pattern is not
random.
2.17 Ttrition for illegal immigrants. As part of a project for a political science class, a student decided to conduct an online poll asking the following
question: "Do you think that illegal immigrants should be allowed to pay instate tuition, even though they are not legal citizens of that state?" Possible
responseswere 'Yes," "No," and "IJnsure." Of those who responded,81% said
"No," 19%osaid'Yes," and 0% said "IJnsure." Explain why this opinion poll is
almost certainly biased.
2.18 More randomization. Most sample surveys call residential telephone
numbers at random. They do not, however, always ask their questions of the
person who picks up the phone. Instead, they ask about the adults who live in
the residence and chooseone at random to be in the sample. Why is this a good
idea?
2.19 Racial profiling and traffic stops. The Denver Police Department
wants to know if Hispanic residents of Denver believe that the police use racial
profiling when making traffic stops. A sociologist prepares several questions
about the police. The police department chooses an SRS of 200 mailing addressesin predominantly Hispanic neighborhoods and sends a uniformed Hispanic police officer to each address to ask the questions ofan adult living there.
(a) What are the population and the sample?
G) \ryhv are the results likely to be biased even though the sample is an SRS?
2.20 Random selection? Choosing at random is a "fair" way to decide who
gets some scarce good,in the sensethat everyone has the same chance to win.
Random choice isn't always a good idea-sometimes we don't want to treat
everyonethe same, becausesome people have a better claim. In each of the
33
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34
CHAPTER
2 Samples,Goodand Bad
II
I
{
following situations, would you support choosing at random? Give your reasons in each case.
(a) The basketball arena has 4000 student seats, and 7000 etudents want
tickets. Shall we choose4000 of the 7000 at random?
(b) The list of people waiting for liver transplants is much larger than the
number of available livers. Shall we let impersonal chance decide who gets a
transplant?
(c) During the Vietnam War, young men were chosen for army service at random, by a "drafb lottery." Is this the best way to decide who goesand who stays
home?
2.21Web-based exercise. There are several voluntary response polls
available on the Internet. Visit www.misterpoll.com and examine several
of the current polls. What are the sample sizes in these polls? Who can
vote? Is it possible to vote more than once?Do you think you can trust
the results of the polls on www.misterpoll.com? Why?
Z.2?Web-based exercise. Tb see how software speedsup choosing an
SRS, go to the Research Randomizer at www.randomizer.org. Click on
'Bandomize Noq/'and fill in the boxes.You can even ask the Randomizer
to arrange your sample in order.
NOTESAND DATASOURCES
Page 2l
Case Study. A recent search
revealed no information about the Helen
Grace Chocolatesjelly bean poll since 2000.
This may mean that the poll is no longer
conducted by Helen Grace Chocolates or
it may be that the poll was inconect in
2004 and hence no longer a news item.
Helen Grace Chocolates has a Web site at
www.helengrace.com.You can visit the site
to see if there is any information about the
poll in 2008.
'Acadian ambulance officials,
Page 2l
workers flood call-in poII," Baton Rouge Aduocate,January 22, L999.
Page 29 Example 5: 'Most Americans
offended by sex and violence on television,"
Gallup News Service press release by Jeffrey
M. Jones, February t2, 2004; available online at www.gallup.corr/po1V10588/MostAmericans-Offended-Sex-Violence-Television
.aspx.
Page 30
Exercise 2.4: The link (requires a login) to the BusinessWeeft poll is
http://bwnt.businessweek.com/polls/bwliveresults. asp?displayFormat=vote&poll jd
=20O7OBt423225446660.
Page 31 Exercise 2.8: "Clarffication," Son
Francisco Bay Tlmes, November 15, 2005.
I