STATS 8.3 HOMEWORK QUESTIONS AND VERIFIED ANSWERS

STATS 8.3 HOMEWORK QUESTIONS AND
VERIFIED ANSWERS
TheA2histogramA2belowA2representsA2dataA2obtainedA2afterA2theA2censusA2ofA2anA2entireA2
populationA2wasA2conducted.

TheA2samplingA2distributionA2ofA2theA2sampleA2meanA2basedA2onA2samplesA2ofA2sizeA22A2f
orA2theA2populationA2wasA2simulated,A2andA2aA2histogramA2ofA2theA2resultsA2wasA2produce
d.A2WhichA2ofA2theA2followingA2histogramsA2isA2mostA2likelyA2theA2histogramA2ofA2thatA2sa
mplingA2distribution?A2-A2Ans--
reallyA2pointA2inA2middleA2thenA2backA2upA2slightlyA2onA2sides

InA2aA2testA2ofA2H0:A2μA2=A28A2versusA2Ha:A2μA2≠A28,A2aA2sampleA2ofA2sizeA2ofA2220A2leadsA
2toA2aA2p-valueA2ofA20.034.A2WhichA2ofA2theA2followingA2mustA2beA2true?A2-A2Ans--
AA295%A2confidenceA2intervalA2forA2μA2calculatedA2fromA2theseA2dataA2willA2notA2includeA2
μA2=A28.

ZucchiniA2weightsA2areA2approximatelyA2normallyA2distributedA2withA2meanA20.8A2poundA2
andA2standardA2deviationA20.25A2pound.A2WhichA2ofA2theA2followingA2shadedA2regionsA2be
stA2representsA2theA2probabilityA2thatA2aA2randomlyA2selectedA2zucchiniA2willA2weighA2bet
weenA20.55A2poundA2andA21.3A2pounds?A2-A2Ans--
middle,A2biggerA2leftoverA2sectionA2onA2left,A2tinyA2leftoverA2onA2right

AA2medicalA2centerA2conductedA2aA2studyA2toA2investigateA2cholesterolA2levelsA2inA2peopl
eA2whoA2haveA2hadA2heartA2attacks.A2AA2randomA2sampleA2ofA216A2peopleA2wasA2obtaine
dA2fromA2theA2namesA2ofA2allA2patientsA2ofA2theA2medicalA2centerA2whoA2hadA2aA2heartA2att
ackA2inA2theA2previousA2year.A2OfA2theA2peopleA2inA2theA2sample,A2theA2meanA2cholesterol
A2levelA2wasA2264.70A2milligramsA2perA2deciliterA2(mg/
dL)A2withA2standardA2deviationA242.12A2mg/
dl.A2AssumingA2allA2conditionsA2forA2inferenceA2wereA2met,A2whichA2ofA2theA2followingA2isA
2aA290A2percentA2confidenceA2intervalA2forA2theA2meanA2cholesterolA2level,A2inA2mg/
dl.A2ofA2allA2patientsA2ofA2theA2medicalA2centerA2whoA2hadA2aA2heartA2attackA2inA2theA2previ
ousA2year?A2-A2Ans--(246.24,A2283.16)

ResearchersA2areA2investigatingA2theA2effectivenessA2ofA2leg-
strengthA2trainingA2onA2cyclingA2performance.A2AA2sampleA2ofA27A2menA2willA2beA2selected
A2toA2participateA2inA2aA2trainingA2programA2thatA2lastsA2forA2oneA2month.A2PeakA2powerA2d
uringA2cyclingA2willA2beA2recordedA2forA2eachA2manA2bothA2beforeA2trainingA2andA2afterA2tr
aining.A2TheA2meanA2differenceA2inA2timesA2willA2beA2usedA2toA2constructA2aA295A2percentA
2confidenceA2intervalA2forA2theA2meanA2differenceA2inA2theA2population.
WhenA2allA2otherA2thingsA2remainA2theA2same,A2whichA2ofA2theA2followingA2statementsA2ab
outA2theA2widthA2ofA2theA2intervalA2isA2correct?A2-A2Ans--
TheA2intervalA2willA2beA2narrowerA2ifA215A2menA2areA2usedA2inA2theA2sample.

, AA2researcherA2constructedA2aA295A2percentA2confidenceA2intervalA2forA2theA2meanA2num
berA2ofA2alfalfaA2weevilsA2onA2anA2alfalfaA2plantA2withinA2aA2field.A2BasedA2onA280A2random
lyA2selectedA2alfalfaA2plants,A2theA2researcherA2foundA2anA2averageA2ofA22.5A2alfalfaA2wee
vilsA2perA2plantA2andA2computedA2theA295A2percentA2confidenceA2intervalA2toA2beA21.50A2t
oA23.50.A2WhichA2ofA2theA2followingA2statementsA2isA2aA2correctA2interpretationA2ofA2theA29
5A2percentA2confidenceA2level?A2-A2Ans--
IfA2weA2repeatedlyA2sampledA2thisA2field,A2takingA2samplesA2ofA280A2plantsA2andA2construc
tingA295%A2confidenceA2intervals,A2then,A2approximatelyA295A2percentA2ofA2theseA2interval
sA2wouldA2includeA2theA2populationA2meanA2numberA2ofA2alfalfaA2weevilsA2onA2anA2alfalfaA
2plantA2inA2thisA2field.


AA2nationalA2surveyA2askedA21,501A2randomlyA2selectedA2employedA2adultsA2howA2manyA
2hoursA2theyA2workA2perA2week.A2BasedA2onA2theA2collectedA2data,A2aA295A2percentA2confi
denceA2intervalA2forA2theA2meanA2numberA2ofA2hoursA2workedA2perA2weekA2forA2allA2emplo
yedA2adultsA2wasA2givenA2asA2(41.18,A242.63).A2WhichA2ofA2theA2followingA2statementsA2is
A2aA2correctA2interpretationA2ofA2theA2interval?A2-A2Ans--
WeA2areA295%A2confidentA2thatA2theA2meanA2numberA2ofA2hoursA2workedA2perA2weekA2for
A2allA2employedA2adultsA2isA2betweenA241.18A2hoursA2andA242.63A2hours.


ForA2aA2certainA2onlineA2store,A2theA2distributionA2ofA2numberA2ofA2purchasesA2perA2hourA2
isA2approximatelyA2normalA2withA2meanA21,200A2purchasesA2andA2standardA2deviationA22
00A2purchases.A2ForA2whatA2proportionA2ofA2hoursA2willA2theA2numberA2ofA2purchasesA2atA
2theA2onlineA2storeA2exceedA21,400A2?A2-A2Ans--16%


AnA2environmentalA2agencyA2frequentlyA2samplesA2theA2waterA2inA2aA2regionA2toA2ensureA
2thatA2theA2levelsA2ofA2aA2certainA2contaminantA2doA2notA2exceedA230A2partsA2perA2billionA2
(ppb).A2FromA212A2randomlyA2selectedA2samplesA2ofA2theA2water,A2theA2agencyA2construc
tedA2theA299A2percentA2confidenceA2intervalA2(22.5,A228.7).A2-A2Ans--
WeA2areA299A2percentA2confidentA2thatA2theA2meanA2levelA2ofA2theA2contaminantA2inA2allA2t
heA2waterA2inA2theA2regionA2isA2betweenA222.5A2ppbA2andA228.7A2ppb

MonthlyA2rentA2wasA2determinedA2forA2eachA2apartmentA2inA2aA2randomA2sampleA2ofA2100
A2apartments.A2TheA2sampleA2meanA2wasA2$820A2andA2theA2sampleA2standardA2deviation
A2wasA2$25.A2AnA2approximateA295A2percentA2confidenceA2intervalA2forA2theA2trueA2meanA
2monthlyA2rentA2forA2theA2populationA2ofA2apartmentsA2fromA2whichA2thisA2sampleA2wasA2s
electedA2isA2($815,A2$825).A2WhichA2ofA2theA2followingA2statementsA2isA2aA2correctA2interp
retationA2ofA2theA295A2percentA2confidenceA2level?A2-A2Ans--
InA2repeatedA2sampling,A2theA2methodA2producesA2intervalsA2thatA2includeA2theA2populati
onA2meanA2approximatelyA295A2percentA2ofA2theA2time.

AA2readingA2specialistA2wantedA2toA2estimateA2theA2meanA2wordA2length,A2inA2numberA2ofA
2letters,A2forA2anA2elementaryA2schoolA2historyA2textbook.A2TheA2specialistA2tookA2repeate
dA2randomA2samplesA2ofA2sizeA2100A2wordsA2andA2estimatedA2theA2meanA2andA2standard
A2deviationA2ofA2theA2samplingA2distributionA2toA2beA24.9A2lettersA2andA20.15A2letter,A2resp
ectively.