Statistical Methods for the Social Sciences

Alan Agresti, Barbara Finlay

Chapter 2 Sampling and Measurement - all with Video Answers

Educators

Chapter Questions

Problem 1

Expluin the difference between
a) Discrele and continuous variables
b) Qualiative and quantitative vanables
c) Nominal and ordinal varnables
Why do these disunctions inatter fer stalistical analysis

Harsh Gadhiya

Numerade Educator

05:56

Identify each of the following variables as qualitative or quantitative
a) Number of pets in family
b) Counly of residence
c) Choice of auto (donnestic or import)
d) Distance tin priles) commute to work
e) Choice of dier (vegelarian. nonvegetarian)
f) Tiane spent in previous month boowsing the World Widc Wcb
g) Ownership of personal comuputer ()es. no)
h) Namber of people you have known with AlDS ( $0,1,2,3,4$ or mote)

Jennifer Stoner

Numerade Educator

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Problem 3

Which scale of measurement (nominal, ordinal. ol inten al) is most appropiste for
a) Attitude toward legalization of marijuana (favor. neutral, oppose)
b) Gender (male, female)
c) Number of siblings $(0,1,2, \ldots)$
d) Political party affiliation (Democrat. Republican, Independent)
e) Religious affiliation (Roman Catholic, Baptish, Mcthodist. . . )
f) Political philosophy (very liberal. somew hat liberal. moderate, somewhat consen ative. very conservative)
g) Years of school completed $(0,1,2,3, \ldots)$
h) Highest degree obaincd (wone, high school. bachelor's. master's, doctorate
i) College ınajor (education, anthropology, physics. sociolegy. . . .)
j) Scholastic Aptitude Test score (200-800 range for scores)
k) Employmen status (employed, uncmploy cd)

Rashmi Sinha

Numerade Educator

02:47

Problem 4

Which scalc of measurement is most appropnate fot each of the following vanables?
a) Occupation (pluunber. leacirer. secretary; elc.)
b) Oceupational status (blue collar, white collar)
c) Social status (lower middle, upper class)
d) Statewide muider rate (number nurders per 1000 population)
e) Counry population size (number of people)
f) Population growlh rate (in percentages)
g) Coinmunity size (rural. small town, large town, small city: large city)
h) Annual income (dbousands of dollass per year)
i) Altitude towdrd affinmative action (favorable, neutral. unfavorable)

James Kiss

Numerade Educator

01:49

Problem 5

Which scale of measurement is most appropriate for "attained education" when it is measured as
a) Nunber of years $(0.1,2,3, \ldots)$
b) Grade level (elementary school, middle school, hugh school, college, graduate school)
c) School type (public schuol, private school)

Harsh Gadhiya

Numerade Educator

02:16

Problem 6

Give an example of a variable that is
a) Qualitative
b) Quantitative
c) Ordiaal scalc
d) Categorical
e) Discrete
f) Continuous
g) Quanlitative and discrele

Harsh Gadhiya

Numerade Educator

Problem 7

A survey asks habjects to rate five issues acconding to their importance in determining woing intention for U.S. senator, using the scale vory important, somewhat important, wnimportaut. The issues are foreign policy, unemployinent, inflation, the arns race, and civil rights. The evaluations can be ueited as tive varnables: "foreign policy er aluation." "unemployment craluation." and so on These variables repiesent what scale of measurement?

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05:56

Problem 8

Which of the following variables ale continuous when the measurements are as fine as possible?
a) Age of mothel
b) Number of childuen in Eamily
c) Income of epouse
d) Population of cites
e) Latitude and Iongitude of cities
f) Distance of bome from place of employnuent

Jennifer Stoner

Numerade Educator

01:18

Problem 9

Which of the following variables could theoretically be measured on a contunuous scale?
a) Method of contraception used
b) Length of tume of residence in al state
c) Task conlpletion time
d) Intelligcnce
e) Authoritarianism
f) Alienation
g) State of residence

Julian Wong

Numerade Educator

00:35

Problem 10

A class bas 50 stadenth. Use the column of the first two digits in the random nanber table (Tahle 2.1) to select a simple random sainple of three students. If the students are numbered 1 to 50 , what are the numbers of the three students selected?

Nick Johnson

Numerade Educator

00:54

Problem 11

In the 1995 Miss America beauty pasreanh, television viewers could cast their vote on whether lo cancel the swinwear parade by phoning a number the network provided Abour 1 million viewers called and registered their opinion, of whom 79\% said they 4 anted to see the contestants dressed as bathing beauties Is this sample a probability sample of al] vicuers of this program in 1995? Why, or why not?

Sheryl Ezze

Numerade Educator

01:25

Problem 12

In lall 1095. the BBC in Britain requested viewers to call the netu ork and indicale their favorite poein. Of more than 7500 callers, more than twice as inauy voted for Rudyard Kipling 's If than foi any other poem. The BBC then reported that this was the clear favonte. Was theit sample a probability sample": Explain. How might they have obtained a more reliable sample, even if much smaller in size?

Harsh Gadhiya

Numerade Educator

01:19

Problem 13

A local telephone directory has 300 pages with 120 names per page.
a) Explain how you would choose a sumple randoun sample of 5 names. Using the second column of Table 21 , selec. 5 numbers to identify subjects for the sample.
b) Select five nombers to identify subjects for a syslematic sample of five natnes fiom the saune directory

Matt Bremer

Numerade Educator

01:19

Problem 14

Refer to the pieceding problem Is cluster sampling applicable": How could it be carned out, and whal would be the advantages and disadvantages?

Gus Steppen

Numerade Educator

Problem 15

Refer to the data file created in Pioblem 1.7. For each sariable in the data set. indicate whether it is
a) Qualitative or quantitarive
b) Nominal. ordinal. or interval

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03:04

Problem 16

Repeat the pievious exercise for the World Wide Web (K'WW) data set (Problem 1.7).

Cinsy Krehbiel

Numerade Educator

Problem 17

Table 22 shows the result of the 1992 Presidential election along with the vote predicted by several ouganizations in the days before the election The sample sizcs were ty pically about 2000. The percenlages fir cach poll do not sum to 100 because of voters reporting as undecided Whar factors cause the results to sary somewhal anvong organizations? How accurate would you characterize these results, considcring the relative sizes of the sumple and the population?

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00:30

Problem 18

A simple nundont sample of size $n$ is one in which (select the best response)
a) Every ath member is sclecied Irom the population
b) Each possible sample of size $n$ has the same chance of being selected.
c) There is exactly the same proportion of women in the sample as is in the population.
d) One heeps sampling until obtaining a fixed number of people baving various charactenstics (e.g., males, females, or whites, blacks).
(TABLE CAN'T COPY)
c) A pirticulan minonty group inember of the population is less likely to be chosen than a paticular undipity group member.
f) All of the above
g) None of the above

Harsh Gadhiya

Numerade Educator

03:22

Problem 19

You are assigned to direct a study on your campus to dere mine the factors that relate to strong academic perfor mance at the school.
a) Describe fou you might select a sample of 100 srudents for the study.
b) List soine variables that you would mcasue in your study For cacl. piovide the scale yous would use to measure it, and indicate whether statistical andly sis could treat it as (i) qualitative or quantitative, (iif noninal. ondinal, or interval, (iiij continuous or discıete.

Derrick Hanson

Numerade Educator

07:49

Problem 20

Quota samplang is a method used when. for example, an intervicwer stands at a trreed cornes and conducls interviews until obtaining a quota in val ioks categorics representing the relative sizes of various groups in the population of interest For instance, the quota migh be 50 factony workers, 100 housewives, 60 eiderly people, 30 blacks and so forth. a) Is this a poobability of nonprobdbility sainpling method? Explain, and dircuss polcatial advantages or disadvantages of this method. (Even professional pollsters such as Gullup used this method umil 1948. when they incorrecly prediced that Dewey would defeat Truman in a landslide in the presidential electioa )
b) Explain how quota sampling differs from (i) cluster sampling, iii) stratified sampling.

Kelsey Dondelinger

Numerade Educator

Problem 21

In 1995 in the United Kingdomn, the Equality Code used by the legal profession added a section to male members mole aware of the dangers of sexual harassment It states that "iesearch for the Bdt found that over 40 percent of Jemale junior tenamts said they had encounteied scxual harassment dusing their time at the Bar.-" This was based on a study conducted at the University of Sheilield. The academics sent a quectionanire to 774 junior tenants al the Bar, of whom 159 responded OI the 159.67 wete female OI the feinales. 3 said they bud experienced scxual harassinent ds a major pioblem, and 24 had experienced it as a slight ptohien. Comment on ways in which the quolod statememt migh be mislei|ding

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Problem 22

When the Yankelovich polling organization asked, "Should laws be passed to climiaate all possibilities of special interests giving huge sums of moncy to candidales ${ }^{2+} 805$ of the sainple answered yes. When they posed the question. "Should laws be passed to prollibit interest groups from contributing to campaigns, or do groups have a right to contribute to the candidate they support? only $40 \%$ said yes (Source A Mathematician Reads the Nen spaper, by 1. A Puulos. New York: Basic Books, 1995, p 15). Explan what this example illustrates, and use your answe to diffcrenciate between sampling error and other types of vanability in survey results.

Rashmi Sinha

Numerade Educator

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Problem 23

Crosson (1994, p 168) describes an analysis of published medical studies involving treatments for heart attacks. In the studics having randomuzation and strong coutrols for bias. the new therapy piov ided improved treatment $9 \%$ of the time. In studies withoul randomization or othei controls for bias, the new therapy provided inproved treatment $58 \%$ of the time. Sclect the correcl response(s).
a) This result suggests it is better not to use randomzation in medical sudies, because it is harder to show that new ideas are beneficial.
b) Many newspaper articles that suggest that a particular lood, drug. or environmental agent is hannful or benelicial should be view'ed skeptically, unless we leam more about the statistical design and analysis for the study.
c) This result suggests that you should be skcptical about published ıesulis of medical studies that are not randomized, controlled studies.
d) Controlling for hiases, both suspected and unsuspected. is necessary in medical research but not in social research, hecause the social sciences deal in suhjccrive 1athe than objective truth

Victor Salazar

Numerade Educator

05:38

Problem 24

In each of the following situations, evaluate whether the method of sample sclection is appropriate for obtaining information about the population of interest Hou would you improve the sample design?
a) A newspaper wants to determine whether its ıcaders believe that governincut expendirures slould be reduced by cutting welfare programs. They provide a telephone number for readers to call to give their opinons Based on 1434 calls that they receive, they report that $93 \%$ of the city's residents believe that welfare payments should be reduced b) A congresswoman reports that letters to her office are running 3 to 1 in oppositon to the passage of stricter gun contiol laws. She concludes that approxumately 75\% of her conslituents oppose stricter gun control laws
c) An anthonology piofessor wanted to compare altitudes toward premantal sex of physical science majors and social science majors She administered a questionnaire to her large class of Anthropology 437, Comparative Ifuulan Sexualiry She found no appreciable difference between her physical science and social science majors in their attitades, so she concluded that the two student groups were about the same in theit relative acceptance of premarital sex.
d) A questionnaire was mailed to a simple random sample of 500 household addresses in a city Ten were ictumed as bad addiesses. 63 were retumed completed. and the rest werc nol returned The researcher analyced the 63 cases and reported that they represent a 'random sample of city households."

Himani Sood

Numerade Educator

19:01

Problem 25

Refer to the previous exercise. Repeal for the following scenanos:
a) A principal in a large high school is interested in student attiludes toward a proposed general achievement test to determine whether a student should goaduate. She lists all of the first-period classes, assigning a number to each Then. using a random number table, she chooses a class at ıandom and itter iews every' student in that class ahout the proposed test
b) A new restaurant opened in January. In June, after six months of operation, the owner applied for a loan to improve the bulding. The loan applicatiou requested au estimale of the yealy gross income of the business. The owner's record book contains receipts for cach day of operation since operung. She decided to calculate the average daily receipt based on a sample of the daily records and multiply thay by the number of days of opera- tion in a ycar. She took a systematic suruple, with $k=7$. sampling e cry Hinday $x$ record. The average daily receipt for this sample was then used to estimate the yearty receipts.

John Lee

Numerade Educator

02:25

Problem 26

You plan to sample from the 5000 students at your college in order to compate the proportions of men and women who believe thas women should have tile right to an aboution. a) Explain how you sould proceed. if you want a sinple random sainple of 100 students b) How would you proceed if you want a systemalic random sample?
c) You use a random number table to select students, but you stop sclecting females as soon as you have 50 , and you stop selecting males as soon as you havc 50 is the resulting sample a simple sandom sample? Why or why not?

Sheryl Ezze

Numerade Educator

01:27

Problem 27

In a sy stematic randorn sample. every subject has the same chance of selection. but the sample is not a simple random samplc. Explan why, by showing that ever) possible saiuple of size $n$ is not equally likcly.

James Kiss

Numerade Educator

07:31

Problem 28

I need to collect data for a sample of residents of registered nui sing homes in my state. 1 obtain from the state a list of all nursing homes. which I number Irom 1 to 317 Beginning landonly, I choose every tench hame on the list. ending up with 31 homes. I then oblain lists of residents from those 31 homes, and I selec1 a simple randon sample from each list What hinds od sanpling have J used?

Jon Southam

Numerade Educator