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statistics informed decisions using data

Questions and Answers of Statistics Informed Decisions Using Data

Amethodofstatisticalinferencehasprobability0.05ofyieldinganincorrectresult.Howmany independenttimescanthemethodbeuseduntiltheprobabilityofalltheinferencesbeing correct islessthan0.50?
Aquizhastenmultiple-choicequestions,withfivepossibleanswersforeach.Astudentwho is completelyunpreparedrandomlyguessestheanswerforeachquestion.Let Y denote the numberofcorrectresponses.(a)
Eachtimeapersonshopsatagrocerystore,theeventofcatchingacoldorsomeothervirus from anothershopperisindependentfromvisittovisitandhasaconstantprobabilityoverthe year,equalto0.01.(a) In100 trips
Forthesimulationattheendof Section 2.3.1, explainwhyyoucouldalsosimulatethemean with asinglebinomialexperimentof30millionobservationsandprobability0.50ofaheadfor
Let Y denote thenumberofpeopleknownpersonallyinone’slifetimewhocommittedsuicide.AccordingtoarecentGeneralSocialSurvey,forarandomlychosenpersonintheU.S.,the probabilitydistributionof Y is
Supposethatapersonisequallylikelytobebornonanyof365daysoftheyear.(a) Forthreepeopleselectedrandomly,explainwhytheprobabilitythattheyallhavedifferent birthdaysis [(365)(364)(363)]~3653.(b)
Awineconnoisseurisaskedtomatchfiveglassesofredwinewiththebottlesfromwhichthey came, representingfivedifferentgrapetypes.(a) Setupasamplespaceforthefiveguesses.(b)
AccordingtorecentdataattheFBIwebsite,ofallBlacksslainintheU.S.,85%areslain byBlacks,andofallWhitesslain,93%areslainbyWhites.Let Y = victim’s raceand X =offender’s race(a)
Dataanalystsoftenimplementstatisticalinferencemethodsbysettingtheprobabilityofa correct inferenceequalto0.95.Let A denote theeventthataninferenceforthepopulation aboutmeniscorrect.Let B
For therainsimulationexamplein Section 2.1.1, butwithprobabilityofrain0.30onany givenday,simulatetheoutcome(a) onthenextday,(b) thenext10days.(c) Simulatethe
+1.06 x
andpredicted y =
x(d) Correlation =
−
andpredicted y =
+1.06 x(c) Correlation =
x(b) Correlation = −0.85 andpredicted y =
−
is ascatterplotofU.S.statewidedatacompiledbetween x = per-centagewearingmasksand y = percentageknowingsomeonewithCovid-19symptoms.Whichdoyouthinkbestdescribesthescatterplot?(a) Correlation = −0.85
TheDelphigroupatCarnegie-MellonUniversityhastrackedstatisticsaboutcoron-avirus. Figure
Forasample {yi} of size n, Σi Syi − cS is minimizedat c = median. Explainwhythis propertyholds.(Hint:Startingat c = median, whathappensto Σi Syi − cS as youmove awayfromitineitherdirection?)
The leastsquares propertyofthemeanstatesthatthedatafallcloserto ¯y than toany other numberc, inthesensethatΣi(yi − ¯y)2
The R output in Section 1.5.2 showsa mosaicplot function. Implementitforthe PartyID data. DoanInternetsearchandlookatthe R Appendixtothisbooktolearn about mosaic plots,
FindtheChebyshevinequalityupperboundfortheproportionofobservationsfalling at least(a) 1,(b) 2,(c) 3standarddeviationsfromthemean.Comparethistothe
Supposethesampledatadistributionof {yi} = {y1, ...,yn} is veryhighlyskewedtothe right,andwetakelogsandanalyze {xi = log(yi)}.(a) Is ¯x = log(¯y)? Whyorwhynot?(b) Ismedian({xi}) = log[median({yi})]?
Forasamplewithmean ¯y, showthataddingaconstant c to eachobservationchanges the meanto ¯y +c, andthestandarddeviation s is unchanged.Showthatmultiplying eachobservationby c changesthemeanto c¯y and
TheInternetsite www.artofstat.com/web-apps has usefulapps 20 for illustrating data analyses andpropertiesofstatisticalmethods.(a) Usingthe ExploreQuantitativeData app,
Toinvestigatehow ¯y can varyfromsampletosampleofsize n, forthesimulationfrom a bell-shapedpopulationshownattheendof Section 1.5.3, take (a) 10,000 random samples ofsize n = 30 each; (b) 10,000
Thelargestvaluein a sampleismovedupwardssothatitisanextremeoutlier.Explain how,ifatall,thisaffectsthemean,median,range,andinterquartilerange.
Tomeasurevariability,whyisthe (a) standard deviation s usually preferredoverthe range? (b) interquartilerangeoftenpreferredovertherange?
Tomeasurecenter,whyisthe (a) median sometimespreferredoverthemean? (b) mean sometimes preferredoverthemedian?(Hint: Awidevarietyofhighlydiscretefrequency distributions
SupposeyouestimatethemeannumberoffriendsthatmembersofFacebookhaveby randomly sampling100membersofFacebookand(i)averagingthenumbersoffriends that
Constructasetofdataforwhichthemeanandmedianareidentical.
Supposethatgrade-pointaveragesatyouruniversityarebell-shapedwithmean3.0and standard deviation0.3.Randomlysample n studentsseveraltimesfor n = 20 (using a functionsuchas rnorm in R),
AresearchstudyfundedbyWobegonSpringsMineralWater,Inc.,discoversthatchil-dren withdentalproblemsarelesscommoninfamiliesthatregularlybuybottledwater than
Anarticle19 in the New EnglandJournalofMedicine (October12,2012)observeda correlation of0.79for23countriesbetweenpercapitaannualchocolateconsumptionand the
WithanInternetsearch,findastudythatusedan(a) experiment;(b) observational study.Ineachcase,describehowthesamplewasobtainedandsummarizeresults.
Ifweuserandomnumberstotakeasimplerandomsampleof50studentsfromthe6500 undergraduate studentsattheUniversityofRochester:(a) Wewouldnevergettherandomnumber1111,becauseitisnotarandomsequence.(b)
Asimplerandomsampleofsize n is oneinwhich:(a) Every nth memberisselectedfromthepopulation.(b) Eachpossiblesampleofsize n has thesamechanceofbeingselected.(c)
A systematic randomsample of n subjectsfromapopulationofsize N selects asubject at randomfromthefirst k = N~n in thepopulationlistandthenselectsevery kth
mentionedapotentialsurveytoobservecharacteristics suchasopinionaboutthelegalizationofsame-sexmarriage,politicalpartyaffiliation, frequency
Thebeginningof Section
Astudyofsheep18 analyzed whetherthesheepsurvivedforayearfromtheoriginal observationtime(1 = yes,0 = no) asafunctionoftheirweight(kg) attheoriginal observation.Using Sheep data
Refertothepreviousexercise.Explanatoryvariableslistedinthedatafilearethe distance oftheraceandtheclimbinelevation.Usegraphicalandnumericaldescriptive statistics
The ScotsRaces data fileatthebook’swebsiteshowstherecordtimesformenandfor womenforseveralhillracesinScotland.Usegraphicalandnumericaldescriptivestatis-tics
The UN data fileatthebook’swebsitehasUnitedNationsdatafor42nationsonper capita grossdomesticproduct(GDP,inthousandsofdollars),ahumandevelopment index
Forthe Students data fileintroducedinExercise1.2,constructandsummarizeacon-tingency tablerelatingreligiosityandopinionaboutlegalizedabortion.
Usingthe Happy data file,constructthecontingencytablerelatingmaritalstatusand happiness. Whichvariableisthenaturalresponsevariable?Reporttheproportionsin its
Forthe Students data fileintroducedinExercise1.2,summarizetherelationshipbe-tween hsgpa and cogpa using correlationandregression.FindthepredictedcollegeGPA of astudentwhohadahighschoolGPAof4.0.
Refertothepreviousexercise.Let y = selling priceand x = size ofhome.(a) Constructascatterplot.Interpret.Identifyanyobservationthatseemstofallapart from theothers.(b) Findthecorrelation.Interpret.(c)
The Houses data fileatthebook’swebsiteliststhesellingprice(thousandsofdollars), size (squarefeet),taxbill(dollars),numberofbathrooms,numberofbedrooms,and whether thehouseisnew(1 = yes,0 = no)
The Income data fileatthebook’swebsitereportsannualincomevaluesintheU.S.,in thousands ofdollars.(a) Usingsoftware,constructahistogram.Describeitsshape.(b)
Fromthe Murder data fileatthebook’swebsite,usethevariable murder, whichisthe murderrate(per100,000population)foreachstateintheU.S.in2017accordingtothe FBI
AccessthemostrecentGeneralSocialSurveyat https://sda.berkeley.edu/archive.htm. EnteringTVHOURSfortherowvariableandyear(2018)intheselectionfilter,you obtain
Accordingto www.salary.com, themeansalary(indollars)ofsecondaryschoolteachers in theUnitedStatesin2019variedamongstateswithafive-numbersummaryofmax-imum = 67,600 (California),upperquartile = 64,700,
In2017,accordingtotheKaiserFamilyFoundation(www.kff.org), the five-number summary fortheU.S.statewidepercentageofpeoplewithouthealthinsurancehad minimum = 3% (Massachusetts),lowerquartile = 6%,
Areportindicatesthatpublicschoolteacher’sannualsalariesinNewYorkcityhavean approximatemeanof$69,000andstandarddeviationof$6,000.Ifthedistributionhas
Giveanexampleofavariablethatisnonnegativebuthasthemajorityofitssample valuesat0,sothemedianisnotespeciallyinformativedespitetheskew.
AccordingtoStatisticsCanada, for theCanadianpopulationhavingincomein2019, annualincomehadamedianof$35,000andmeanof$46,700.Whatwouldyoupredict abouttheshapeofthedistribution?Why?
Analyzethe Carbon_West data fileatthebook’swebsiteby(a) constructingafrequency distribution andahistogram,(b) findingthemean,median,andstandarddeviation.Interpreteach.
FortheGSSdataonnumberofgoodfriends(searchat https://sda.berkeley.edu/sdaweb/analysis/?dataset=gss18 for variable NUMFREND), theresponses(1,2,3,4,5, 6, 7,8,9, . .. ,
Explainwhetheranexperimentoranobservationalstudywouldbemoreappropriate to investigatethefollowing:(a) Whethercitieswithhigherunemploymentratestendtohavehighercrimerates.(b)
Thestudentdirectoryforalargeuniversityhas400pageswith130namesperpage,a total of52,000names.Usingsoftware,showhowtoselectasimplerandomsampleof 10 names.
Giveanexampleofavariablethatis(a) technicallydiscretebutessentiallycontinuous for purposesofdataanalysis;(b) potentiallycontinuousbuthighlydiscreteintheway it ismeasuredinpractice.
InanalyzingdataaboutpatientswhodevelopedCovid-19fromcoronavirus,many researchstudiesusedthescale(1.Death;2.Hospitalizedwithinvasiveventila-tion;
Giveanexampleofavariablethatis (a) categorical; (b) quantitative; (c) discrete; (d)continuous.
Identifyeachofthefollowingvariablesascategoricalorquantitative: (a) Numberof smartphones thatyouown; (b) Countyofresidence; (c) Choice ofdiet(vegetarian, nonvegetarian); (d) Distance,
The Students data fileat http://stat4ds.rwth-aachen.de/data showsresponsesofa class of60socialsciencegraduatestudentsattheUniversityofFloridatoaquestionnaire that askedabout gender (1 = female, 0 =
Inthe 2018 electionforSenateinCalifornia,aCNNexitpollof1882votersstatedthat52.5% votedfortheDemocraticcandidate,DianeFeinstein.Ofall11.1millionvoters,54.2% votedforFeinstein.(a)
Which of the following constitute continuous variables?(a) Number of times a score of 180 is achieved in a darts match(b) Gender(c) Temperature(d) All of the above
Experimental designs are characterised by:(a) Fewer than two conditions(b) No control condition(c) Random allocation of participants to conditions(d) None of the above
In a study with gender as the manipulated variable, the IV is:(a) Within participants(b) Correlational(c) Between participants(d) None of the above
Which of the following are true of correlational designs?(a) They have no IV or DV(b) They look at relationships between variables(c) You cannot infer causation from correlations(d) All of the above
Which of the following could be considered as categorical variables?(a) Gender(b) Brand of baked beans(c) Hair colour(d) All of the above
Between-participants designs can be:(a) Either quasi-experimental or experimental(b) Only experimental(c) Only quasi-experimental(d) Only correlational
Which of the following statements are true of experiments?(a) The IV is manipulated by the experimenter(b) The DV is assumed to be dependent upon the IV(c) They are difficult to conduct(d) (a) and
Quasi-experimental designs have:(a) An IV and a DV(b) Non-random allocation of participants to conditions(c) No IV or DV(d) (a) and (b) above
A continuous variable can be described as:(a) Able to take only certain discrete values within a range of scores(b) Able to take any value within a range of scores(c) Being made up of categories(d)
Which of the following are problems associated with within-participants designs?(a) There is an increased likelihood of practice or fatigue effects(b) Participants are more likely to guess the nature
According to Streiner (2002) how efficient are studies that dichotimise continuous variables when compared with studies that do not?(a) 100%(b) 95%(c) 67%(d) 50%
A researcher has just conducted a correlational study investigating the relationship between amount of alcohol drunk by fans of the home team before a football match and the number of goals scored by
In a within-participants design with two conditions, if you do not use counterbalancing of the conditions then your study is likely to suffer from:(a) Order effects(b) Effects of time of day(c) Lack
You have conducted a study that shows that the earlier people get up, the more work they get done. Which of the following are valid conclusions?(a) There is not necessarily a causal relationship
Which of the following designs is least likely to enable us to establish causal relationships between variables?(a) Experimental design(b) Quasi-experimental design(c) Correlational design(d)
Demand effects are possible confounding variables where:(a) Participants behave in the way they think the experimenter wants them to behave(b) Participants perform poorly because they are tired or
Suppose you wanted to conduct a study to see if depressed individuals bite their nails more than non-depressed individuals. Which of the following would be the best way to proceed?(a) Measure
Which of the following might be suitable IVs in a quasi-experimental study?(a) Gender(b) Whether or not someone had Generalised Anxiety Disorder(c) Students versus non-students(d) All of the above
In within-participant designs order effects occur when:(a) Participants get tired in later conditions(b) Participants perform equally well in all conditions(c) Participants have trouble obtaining
Which of the following are problems associated with dichotomising continuous variables?(a) Loss of experimental power(b) Spurious effects may occur(c) There is a serious loss of information(d) All of
Dr Genius has conducted a study comparing memory for adjectives with that for nouns.She randomly allocates 20 participants to two conditions. She then presents to one of the groups of 10 participants
Using the data from Exercise 1:■ If you input the data as a within-participants design, then input it now as a betweenparticipants design.■ If you input the data as a between-participants design,
You are given the job of finding out whether or not changing the lighting in an office from normal fluorescent lighting to red lighting will increase the alertness of data inputters and thereby
A group of final-year students decides to see if the lecture material in Dr Boering’s lectures can be made more memorable. They decide that the best way to do this would be to take hallucinogenic
Which one of the following represents the best estimate of the population mean?(a) The sample mean(b) The mean of several sample means(c) The mode of several sample means(d) The median of several
If you obtained a sample of data that was relatively normally distributed and had no extreme scores, which measure of central tendency would you opt for?(a) Mode(b) Median(c) Mean(d) None of the above
Which of the following measures of central tendency are sensitive to extreme scores?(a) Mode(b) Median(c) Mean(d) None of the above
Given the following graph, how would you describe the distribution?(a) Normal (b) Positively skewed (c) Negatively skewed (d) Bimodal
The standard deviation is equal to:(a) The variance(b) The square-root of the variance(c) The variance squared(d) The variance divided by the number of scores
What is the relationship between sample size and sampling error?(a) The larger the sample size, the larger the sampling error(b) The larger the sample size, the smaller the sampling error(c) Sample
The mode is:(a) The frequency of the most common score divided by the total number of scores(b) The middle score after all the scores have been ranked(c) The most frequently occurring score(d) The

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