Skills Practice Chapter 2 C

451453_IM3_Skills_CH02_257-304.indd 257

c. randomsample being selected every memberofthepopulationhassamechance of a samplethatisselectedfrom thepopulationinsuchawaythat g. experiment treatments onthecharacteristicofinterest a process thatgathersdataontheeffect ofoneormore h. treatment an experimentalconditionusedontreatment groups a. biasedsample a samplethatisnotrepresentative ofthepopulation e. confounding the study the results tohaveoccurred thatwere notidentifiedpriorto a situationthatoccurswhenthere are otherpossiblereasons for d. characteristicofinterest information youare tryingtogather the specificquestionthatyouare tryingtoanswerorthespecific i. experimentalunit members ofthesampleforanexperiment b. samplesurvey of atargeted population a surveythatposesoneormore questionsofinterest toasample f. observationalstudy by simplyobservinganddescribingeventsintheirnaturalsettings a studythatgathersdataaboutcharacteristicofthepopulation 2.1

Skills Practice Chapter 2 c. b. a. i. h. g. f. e. d.

random sample sample survey biased sample experimental unit treatment experiment observational study confounding characteristic ofinterest

Date

Skills Practice

03/12/13 12:49PM 257 2 451453_IM3_Skills_CH02_257-304.indd 258 2 258

Identify thepopulation,sample,andcharacteristicofinterest foreachsituation. Problem Set Lesson

4. 3. 2. 1. 6. 5.

Chapter 2 The populationisalloftheitemsthatcomeoff oftheassemblyline.Thesampleisevery5000 Every or nottakingtheprep courseimproves studentSAT scores. is theSAT scores ofthe145randomlyselectedstudents.Thecharacteristicinterest iswhether The populationisSAT scorescenter. ofstudentswhotakethecourseatlearning Thesample students before takingtheprep courseandtheirSAT scores aftertakingtheprep course. to testtheclaim,anindependentorganization records the SAT scores of145randomlyselected centerclaimsthatstudentscanimproveA learning SAT scores bytakingtheirprep course.Inorder town residents. Thecharacteristic ofinterest isthenumberofyearstheyhavelivedintown. The populationisallofthepeoplewholiveintown.sample100randomlyselected In asurvey, 100randomlyselectedtownresidents were askedhowmanyyearstheyhavelivedthere. characteristic ofinterest iswhetheroreachsickdayoccurred onaFriday. The populationisallemployeesickdays.sample500randomlyselected on Fridays. Fridays. Themanagerrandomlyselects500sickdaysanddetermineshowmanyofthemoccurred A managerofacompanywantedtoknowwhatproportion ofemployeesickdaysoccurred on the amountofsugarincompany’ The populationisallkids.sample435 characteristicofinterest iswhetherornot on itstaste.Thecompanyteststwodifferent yogurts,onewithlesssugar, on435 kids. A yogurtcompanywantstoknowwhethertheamount ofsugarinitsyogurthasasignificanteffect interest isthelinkbetweenBMIandriskofgettingcommoncold. The populationisAmericanadults.sample4565 Americanadults.Thecharacteristicof past yearare recorded. common cold.Asampleof4565Americanadultsissurveyed.TheirBMIandnumbercoldsinthe A studyisbeingdonetoseewhetherbodymassindex(BMI)linkedahigherriskofgettingthe each itemisdefective. item thatcomesoff thelineina24hourperiod.Thecharacteristicofinterest iswhetherornot 5000 2.1

th Skills Practice itemthatcomesoff oftheassemblylineistestedfordefectsduringa24-hourperiod.

Skills Practice s yogurthasasignificanteffect onitstaste.

page 2 th

03/12/13 12:49PM

treatment isthegroup ofstudentsnotlisteningtoclassicalmusic. treatments. Onetreatment isthegroup ofstudentslisteningtoclassicalmusicandtheother This isanexperimentsincetheresearcher imposedatreatment, classicalmusic.There are two classical musicwhiletakingamathtest. students listenedtoclassicalmusicwhiletakingamath testandanothergroup didnotlistento alleviate studentanxiety. Theresearcher gathered datafrom twogroups ofstudents.Onegroup of A researcher wantstodeterminewhetherlisteningclassicalmusicwhiletakingamathtesthelps This isanobservationalstudybecausethedatawasgathered from itsnaturalsetting. A newspaperreporter gathersdataonthelengthof40mostrecently released independentfilms. This isasamplesurveybecausethevoterswere askedtorespond toaspecificquestion. A randomsampleofregistered votersare askedwhethertheywillvoteinthemidtermelections. This isasamplesurveysincethestudentswere askedtorespond toaspecificquestion. school lunch. During lunchintheschoolcafeteria,studentsare randomlysurveyedaboutwhethertheylikethe setting. This isanobservationalstudybecausetheprincipalgathered existingdatafrom itsnatural have aGPA of3.0orhigher. grades. Sheusedtheschool’ Aprincipalataschoolwantstodeterminewhetherplayinginthebandhasanimpactonstudents’ the supplementtocows. two treatments. Onetreatment isgivingthesupplementtocows.Theothertreatment isnotgiving This isanexperimentsincethefarmerimposedatreatment, thenutritionalsupplement.There are of thecowsthatdidnotgetsupplement. output. Then,hecompares themilkoutputofcowsthattooksupplementwith production. Foroneweek, hegivesthesupplementtohalfofhiscowsandthenmeasures theirmilk A farmerwantstodeterminewhetheranutritionalsupplementwillhaveaneffect oncows’milk 2.1

Skills Practice s databasetodeterminetheproportion ofstudentsinthebandwho

Chapter 2

Date

Skills Practice page 3

03/12/13 12:49PM 259 2 451453_IM3_Skills_CH02_257-304.indd 260 2 260

Explain howconfoundingcouldoccurforeachobservationalstudy. Lesson 16. 15. 14. 13. 18. 17.

Chapter 2 as theamountofeducationalcapitalinschool district. Confounding couldoccurbecauseeducationalsuccess couldbeaffected by otherfactors,such success forelementaryschoolstudents. A statewantstodeterminewhetherthere isalinkbetweenfamilyincomelevel andeducational factors, suchaspoornutrition. Confounding couldoccurbecauseaggressive behaviorinchildren couldberelated toother behavior inchildren. There are manystudiesdoneonwhetherornotthere isalinkbetweenviolenceonTVandaggressive the typeofworkperformed. Confounding couldoccurbecauseproductivity couldbedifferent duetoanotherfactor, suchas workers duetothedifferent timeperiods. A factorymanagerwantstoknowwhetherproductivity isdifferent betweenthefirstandsecondshift such asvitamindeficienciesorlackofsleep. Confounding couldoccurbecausethefrequency oflegcrampscouldbeduetoanotherfactor, frequency oflegcramps. A researcher wantstoknowwhetherthere isalinkbetweentheamountofcoffee adultsdrinkandthe the fourmonthperiodduetoanotherfactor, suchasachange ofseasons. Confounding couldoccurbecausethesampleofadultswithdepression couldgetbetterduring depression. Asampleofadults withdepression isgiventhedrugduringafourmonthperiod. A companywantstoknowwhetheritcanclaimthatanallnaturaldrugwillhelppeoplewith having parents whodonot haveallergies. Confounding couldoccurbecausekidshavelessallergiesduetovariousotherreasons, suchas least twoormore petsin the home. A researcher wantstoknowwhetherthere isalinkbetweenkidsdeveloping lessallergies withat 2.1

Skills Practice

page 4 03/12/13 12:49PM

Choose atermfrom thebox thatbestcompleteseachstatement. Vocabulary Sampling MethodsandRandomization Circle Up Name Lesson 7. 4. 5. 2. 3. 6. 1. 8.

statistic cluster simple randomsample convenience sample This typeofsampleisa Acitymanagerrandomlyselectsoneblockinthe andsurveysalloftheresidents ofthatblock. a sample. A qualitycontrol specialisttestsevery an exampleofa In order togetasetofdatagirl’s heights,Risausestheheightsofallgirlsinherclass.Thisis salary isanexampleofa The manageratadiscountstore determinesthemeansalaryofallstore workers.Themean example ofa John isaskedtoselectasampleofhisfavoritefoodsfrom theschoolcafeteria.Thissampleisan the paper. This data collected from the survey results represents a An online newspaper asks its readers to answer a question about their satisfaction with the content of their scores. Themeanofthesetestscores isa A collegerandomlyselects100outofthe600students whohavetakentheGREexamandrecords group. Theprofessor obtainedisa A professor dividedhisclassintofemalesandmales,thenrandomlyselectedasamplefrom each of a

2.2

systematic sample

Skills Practice

subjective sample convenience sample

cluster sample systematic sample stratified randomsample subjective sample parameter . stratified randomsample 100

th tabletthatcomesoff theline.Thissampleisanexample . .

. becauseitdescribesalloftheworkers. statistic

. Chapter 2 parameter cluster sample volunteer sample volunteer sample

becauseitdescribes Date

Skills Practice

03/12/13 12:49PM 261 2 451453_IM3_Skills_CH02_257-304.indd 262 2 262

Explain Select a subjective sample of four Problem Set Lesson 10. 4. 3. 2. 1. 9.

Chapter 2 chooses oneoftheregions tointerviewallofitsresidents. Eachofthe16regions isanexampleofa A researcher wantstocollectdatafrom astate.Hedividesthestateinto16 regions andrandomly entire dataset. I chose7.95,10.00,13.27,and14.75becausethey seemtoberepresentative ofthemean Answers willvary. The prices(dollars)ofDVDsinanelectronics store representative oftheentire dataset. I chose2,1,0,and3becausetheyare thefirstfourvaluesintableandseemtobe Answers willvary. The numberofcrimescommittedeachmonthduringaten-monthperiod values. Two hundred three and215are inthemiddle,betweenminimumandmaximumvalues. I chose130,203,215,and250.Onehundred thirtyand250are theminimumandmaximum Answers willvary. The weights(kilograms)ofwildebeestsinazoo and 76are inthemiddle,betweenminimumandmaximumvalues. I chose54,75,76,and95.Fifty-four95are theminimumandmaximumvalues.Seventy-five Answers willvary. Test scores foramathtest This sampleisa A theaterownerrandomlychooses15different customerstoreceive free ticketstothenextshow. 130 70 5.99 2 your method for selecting the 75 1 242 2.2 7.95

Skills Practice 89 cluster 0 227

10.00 60 Skills Practice 3 186 simple randomsample 95 3 14.75 250 78 4 items from

8.35 . sample. 54 192 5 82 13.95

2 each data 215 91 0 21.99 203

. 76 6 set that best represents the mean of the data set. 232 13.27 175 8.75 11.95 page 2 03/12/13 12:49PM

numbers yougeneratedtocreate arandomsampleoffourfrom thedataset. For eachdataset,useacalculatortogeneratefourrandomnumbersbetween1and10.Thenthe Name Lesson 9. 8. 7. 6. 5.

Answers willvary. Ten studentsrecord thenumberoftimesacoin isflippeduntilitlandsonheads. Answers willvary. Each contestantparticipatinginacontestisassignednumber. Rodriguez, andSiegelman. The calculatorgeneratedthenumbers2,3,4,and10.randomsampleconsistsofEaston,Wu, Answers willvary. Each doctorinatownisgivenphonenumberthatendsthedigits0001through 0010. I chose54,65,48,and85becausetheyare themiddlefourvaluesofordered data. Answers willvary. The heights(feet)oftenbuildingsinacity I chose 0.193, 0.215, 0.220, and 0.240 because they are the middle four values of the ordered data. Answers willvary. The battingaveragesoftenbaseballplayersduringaseason 0.120 Doctor’s 102 Number Contestant Number Number ofFlips Contestant’s Name Phone Name Trial Number 54 2.2 0.215 Thomas 0001

76 0.240 Skills Practice Easton 95 1 1 0002 0.283 Lia 1 1 2 250 0003 Joe Wu 2 0.175 1 3 37 Ariel Rodriguez 2 4 3 0.160

0004 65 3 5 Jess 4 0.220 48 4 6 Pasles 0005 Victor 5 1 7 27 0.302 Farris 0006 Roberto 5 8 85 0.254 6 2 9 Shea 0007 10 Wen 0.193 1 7 Chapter 2 Wong 0008 Anita 8

Date Price 0009

Mia Skills Practice 9 Siegelman Ana 10 0010 page 3

03/12/13 12:49PM 263 2 451453_IM3_Skills_CH02_257-304.indd 264 2 264

makes thesampleunrepresentative. Determine whethereachstudyhasasource ofbias.Ifso,describethebiasandexplainwhy Lesson 16. 15. 14. 13. 12. 11. 10.

Chapter 2 of healthypatients. There isbiasinthisstudybecausesideeffects ofsickpatientscouldbedifferent from sideeffects A medicalcompanyusessickpatientstotesttheircompetitors’ drugsforsideeffects. side effects ofunhealthypatients. There isbiasinthisstudybecausethesideeffects ofhealthypatientscouldbedifferent from the A medicalcompanyuseshealthypatientstotesttheir drugsforsideeffects. not represented. There isbiasinthisstudybecausethevotersAlbanywhomakelessthan$100,000are the upcomingelection?” A surveyismailedtovotersinAlbanywhomakemore than$100,000ayearasking,“Willyouvotein There isnobiasinthisstudy. A surveyismailedtoallvotersinAlbanyasking“Willyouvotetheupcomingelection?” Answers willvary. A coachrecords theheightsofplayersonhersoftballteam,inmeters. Answers willvary. The pricesofcarsattendifferent dealershipsare recorded. Answers willvary. A factoryworkerrecords theweights,inounces,offirsttenboltsthathemanufactured. Dealership Dealership Height Player Bolt Number Price Price Weight 2.2

Skills Practice 1.8 1

66,000 24,500 Skills Practice 6 1 1.5 2 2.1 1 2.2 1.6 2 3 22,750 32,000 7 2 2.3 3 1.6 4

2.4 4 23,650 27,750 2.2 5 8 3 2.2 5 1.3 2.1 6 6 24,735 23,450 9 4 2.3 1.7 7 7 2.1 8 1.8 8 37,500 26,875 10 2.2 5 9 2.0 9 2.1 10 2.1 10 page 4 03/12/13 12:49PM

4 different continents. The datasetbelowdisplaysthehighesttemperature recorded for10different citieson the magazine. There isbiasinthisstudy becausethepeoplewhoread themagazineare more likelytolike like thismagazine?” A surveythatmeasures the popularityofamagazineisinsertedintotheasking,“Doyou have anopportunitytorespond. There isbiasinthisstudy becauseonlypeoplewhovisitthedepartmentofeducation’ at home?” A pollbythedepartmentofeducationisconductedonlineandasks,“Doyouhaveacomputer b. a.

selected twotemperatures from eachcontinent. My sampleconsistsofthe temperatures 92,95,81, 103,94,97,101,and98.Irandomly Answers willvary. Create astratifiedrandomsamplethatcontains8datavalues. temperature from eachcontinent. My sampleconsistsofthetemperatures 81,103,97,and98.Irandomlyselected one Answers willvary. Create astratifiedrandomsamplethatcontains4datavalues. 2.2

Skills Practice North America 104 111 81 92 90 87 76 94 95 89 Highest Temperature Recorded

Europe 102 103 100 95 81 98 87 92 97 96 Asia 107 102 94 86 92 97 91 97 93 88 Africa 101 103 107 112 96 94 98 97 98 96 Chapter 2

Date

Skills Practice s website page 5

03/12/13 12:49PM 265 2 451453_IM3_Skills_CH02_257-304.indd 266 2 266

Lesson 20.

Chapter 2 b. a. English classes. The datasetbelowshowsthenumberofbooksread by10different students in4different

number ofbooksread by4different studentsfrom eachteacher’ My sampleconsistsof2,3,7,11,6,13,8,4,9, 4,8,0,and8.Irandomlyselectedthe Answers willvary. Create astratifiedrandomsamplethatcontains16datavalues. books read by3different studentsfrom eachteacher’ My sampleconsistsof4,11,7,6,8,12,9,0,and14.Irandomlyselectedthenumber Answers willvary. Create astratifiedrandomsamplethatcontains12datavalues. 2.2

Skills Practice

Skills Practice Number ofBooksReadbyStudentsinEachTeacher’s Class Mr. James 11 11 8 0 2 7 2 3 4 2 Ms. Farley

12 13 2 3 3 6 8 2 6 0 Mr. Nguyen 12 0 1 4 9 4 4 8 8 3 s class. Ms. Razali s class. 14 15 6 6 0 8 0 4 0 8 page 6 03/12/13 12:49PM

b. a. 4 different days. The datasetdisplaysthenumberofcarscrossing anintersectionat8different timesduring

at 6different timesfrom eachday. 349, 313,255,192,268,319,368,305,and279.Irandomly selectedthenumberofcarcrossing My sampleconsistsof124,213,302,312,297,251,249,281,342,324,284,264,184,253,279, Answers willvary. Create astratifiedrandomsamplethatcontains24datavalues. and 256.Irandomlyselectedthenumberofcarcrossing at4different timesfrom eachday. My sampleconsistsof213,302,312,251,234,281,324,284,184,279,314,313,192,264,319, Answers willvary. Create astratifiedrandomsamplethatcontains16datavalues. 2.2

Skills Practice Day 1 124 213 276 302 354 312 297 251 Number ofCarsCrossing anIntersection

Day 2 234 249 281 321 342 324 284 264 Day 3 184 253 279 314 349 313 287 255 Day 4 192 268 264 319 368 305 279 256 Chapter 2

Date

Skills Practice page 7

03/12/13 12:49PM 267 2 451453_IM3_Skills_CH02_257-304.indd 268 2 268

Lesson 22.

Chapter 2 b. a. that eachdoctorsawduring8different volunteerperiods. eight days,andthenitisthenextdoctor’s Thedatasetbelowshowsthenumberofpatients turn. A groupvolunteeringatahospital.Eachdoctorvolunteersforperiodof offivedoctorstakes turns

each day. selected 3volunteerdaysforeachdoctorandrecorded thenumberofpatientvisitsfor My sampleconsistsof15,26,27,18,23,13,24, 26,19,18,23,27,and18.Irandomly Answers willvary. Create astratifiedrandomsamplethatcontains15datavalues. doctor andrecorded thenumberofpatientvisitsforthatday. My sampleconsistsof16,23,24,29,and28.Irandomlyselectedonevolunteerdayforeach Answers willvary. Create astratifiedrandomsamplethatcontains5datavalues. 2.2

Skills Practice

Dr. Kim Skills Practice 18 13 27 24 26 21 15 16 Dr. Rodriguez 16 15 28 23 27 23 16 18

Number ofPatients Dr. Lao 14 17 26 19 24 24 17 13 Dr. Woods 17 16 24 26 29 19 18 19 Dr. Morena 18 14 27 23 28 21 16 17 page 8 03/12/13 12:49PM

b. a. neighborhoods during4different months. The datasetdisplaystheamountsofrecycled materialcollected,inpounds,from sixdifferent

My sampleconsistsof426,425,441,482,324,398, 431,425,486,675,573,543,274,184,234, Answers willvary. Create astratifiedrandomsamplethatcontains18datavalues. I randomly selected2amountsofrecycled materialsfrom eachofthe6neighborhoods. My sampleconsistsof426,425,482,398,431,324,543,274,246,134,and176. Answers willvary. Create astratifiedrandomsamplethatcontains12datavalues. 6 neighborhoods. 162, 176,and186.Irandomlyselected3amountsof recycled materialsfrom eachofthe 2.2

Arlington Skills Practice 441 425 435 426 Recycled MaterialCollectedfrom SixNeighborhoods(pounds) Sylvia 436 398 324 482

Burns 486 425 521 431 Beaverton 543 573 675 324 Bayview 246 234 184 274 Chapter 2 Hillsdale

186 176 162 134 Date

Skills Practice page 9

03/12/13 12:49PM 269 2 451453_IM3_Skills_CH02_257-304.indd 270 2 270

Lesson 24.

Chapter 2 b. a. last 8weeks. The datasetdisplaysthenumberofpeoplewhovisitedasoupkitchenonspecificdaysduring

116, and128.Irandomlyselected5valuesfrom eachofthe4daysweek. My sampleconsistsof43,49,48,38,46,56,57,52,86,92,93,96,87,124,126,118, Answers willvary. Create astratifiedrandomsamplethatcontains20datavalues. I randomly selected4valuesfrom eachofthe4daysweek. My sampleconsistsof42,49,38,41,56,52,57,53,86,87,93,112,126,118,and116. Answers willvary. Create astratifiedrandomsamplethatcontains16datavalues. 2.2

Skills Practice

Skills Practice Monday Number ofPeopleWhoVisitaSoupKitchen 42 43 49 48 38 46 41 48

Wednesday 56 57 52 61 57 53 48 52 Friday 86 87 92 93 96 87 86 87 Sunday 112 124 126 118 116 117 128 127 page 10 03/12/13 12:49PM

The attendancenumbersfrom anyoneoftheweekdaysare acceptableasacluster sample. attendance numbersonTuesday, {94,134,213,227}. My twosamplesconsistedoftheattendancenumbers onMonday, {134,142,197,223},andthe Answers willvary. The weightsfrom anyoneofthezoosare acceptableasaclustersample. and thepolarbearweightsfrom thePhiladelphiaZoo,{884,1237,1384}. My twosamplesconsistedofthepolarbearweightsfrom theSanDiegoZoo,{892,1216,1375}, Answers willvary. Bronx Zoo Movie Theatre AttendanceofFourDailyShowings Weights ofPolarBearsatThree Zoos(pounds) Monday 1416 1295 875 134 142 197 223 2.2

San DiegoZoo Skills Practice Tuesday 1375 1216 892 134 213 227 94 Philadelphia Zoo

Wednesday 1384 1237 884 112 141 206 216 Chapter 2

Date

Skills Practice page 11

03/12/13 12:49PM 271 2 451453_IM3_Skills_CH02_257-304.indd 272 2 272

Lesson 28. 27.

Chapter 2 The scores from anyoneofthestudentsare acceptableasaclustersample. 69, 82,73}. My twosamplesconsistedofAnastasia’ Answers willvary. The timesfrom anyoneof theteamsare acceptableasaclustersample. game durationsfortheBulldogs,{108,123,129,128,149}. My twosamplesconsistedofthegamedurationsforA Answers willvary. Hugo 73 82 69 78 85 Scores onLastFiveMathTests Pirates 116 124 137 128 153 2.2

Miriam Duration ofLastFiveBaseballGames(minutes) Skills Practice 75 86 72 76 79

Skills Practice Anastasia 72 78 71 72 82 123 126 136 126 148 A’s Nick 71 84 67 79 83

Rays 124 122 142 127 153 s scores, {82,72,71,78,72},andHugo’ Bulldogs 108 123 129 128 149 ’ s, {123,126,136,148},andthe s scores, {85,78, page 12 03/12/13 12:49PM

30. 29.

The pricesfrom anyoneoftheweeksare acceptableasacluster sample. and theweekdaystockpricesfrom week4,{2.42,1.77,0.96,3.52,0.91}. My twosamplesconsistedoftheweekdaystockprices from week1,{2.89, 3.81,1.48,3.86,2.27}, Answers willvary. The numbersofcustomersfrom anyoneoftheweeksare acceptableasaclustersample. the weekdaycustomersfrom week3,{94,96,93,163,204}. My twosamplesconsistedoftheweekdaycustomersfrom week2,{145,88,104,174,197},and Answers willvary. Week 1 Week 1 123 154 213 2.27 3.86 1.48 3.81 2.89 93 94 Number ofWeekday CustomersataBank 2.2 Week 2 Weekday PricesforaSpecificStock 145 104 174 197 Week 2 88

3.70 0.98 1.82 4.09 2.77 Skills Practice Week 3 163 204 94 96 93 Week 3 2.59 4.56 1.07 4.66 3.21 Week 4 113 102 164 192 97 Week 4

0.91 3.52 0.96 1.77 2.42 Week 5 127 173 216 94 89 Week 5 1.71 3.33 1.10 1.35 0.69 Chapter 2

Date

Skills Practice page 13

03/12/13 12:49PM 273 2 451453_IM3_Skills_CH02_257-304.indd 274 2 274

Estimate eachpopulationmeanusingthedatafrom thesamples. Lesson 34. 33. 32. 31. 36. 35.

Chapter 2 population. I usedthemeantestscore ofthesample,85.6,asanestimateformeantestscore ofthe 77, 94,89,86,90,68,95,91,79,82, 90, 91,86,87,89,90 The testscores ofstudentsinanEnglishclass the population. I usedthemeanfishlengthofsample,18.2inches, asanestimateforthemeanfishlengthof 20, 22,19,14,12,18,21,15, 19, 21,12,20,22 The lengthsininchesoffishanaquarium number ofweeklyhoursthepopulation. I usedthemeannumberofweeklyhourssample,34.5hours,asanestimatefor 22, 35,40,42,24,36,30,38,24 The numberofhoursforrestaurant employeeslastweek population. I usedthemeanheightofsample,65.4inches,asanestimatefor 70, 69,65,60,62,64,73,66,65 The heightsininchesofpeopleanaerobics class population. I usedthemeansalaryofsample,$35,600,asanestimatefor 38, 40,32,41,31,30,39,42,32 The salariesinthousandsofdollarsemployeesacompany home runsofthepopulation. I usedthemeannumberofhomerunssample,16.8,asanestimatefor 17, 12,16,21,19,15,22,18,17 The numberofhomerunshitbybaseballplayers 2.2

Skills Practice

page 14 03/12/13 12:49PM

population parameter. A confidenceintervalisanestimatedrangeofvalues thatwilllikelyincludethevalueofa confidence interval provide agoodestimateforthepopulationmeanorproportion. equal-sized samples.Asamplingdistributionwillbeclosetoanormaland A samplingdistributionisthesetofsamplemeansorproportions forallpossible sampling distribution particular candidateorthepercent ofacompany’ characteristic. Examplesofsampleproportions are thepercent ofasamplewhovotedfor A sampleproportion isthepercentage ofindividuals(oritems)inasamplesharingthesame sample proportion a particularcandidateorthepercent ofacompany’ characteristic. Examplesofpopulationproportions are thepercent ofapopulation whovotedfor A populationproportion is thepercent ofindividuals(oritems)inapopulationsharingthesame population proportion 2.3

Skills Practice

s sampleofproducts thatare defective. s products thatare defective. Chapter 2

Date

Skills Practice

03/12/13 12:49PM 275 2 451453_IM3_Skills_CH02_257-304.indd 276 2 276

your reasoning. Determine whethereachdescriptionrepresents a68%,95%,or99.7%confidenceinterval.Explain Problem Set Lesson 6. 5. 4. 3. 2. 1.

Chapter 2 3(0.193) deviation ofthesamplingdistribution. This isa99.7%confidenceintervalbecausethemargin oferror isthree timesthestandard sampling distributionis0.193. The confidenceintervalforapopulationmeanis7.5 deviation ofthesamplingdistribution. This isa68%confidenceintervalbecausethemargin oferror isthesame as thestandard sampling distributionis0.002. The confidenceintervalforapopulationproportion is6% 2(7.65) the samplingdistribution. This isa95%confidenceintervalbecausethemarginoferror is2timesthestandard deviationof sampling distributionis7.65. The confidenceintervalforapopulationmeanis145.7 3(0.02) =0.06or6% of thesamplingdistribution. This isa99.7%confidenceintervalbecausethemarginoferror is3timesthestandard deviation sampling distributionis0.02. The confidenceintervalforapopulationproportion is22% deviation ofthesamplingdistribution. This isa68%confidenceintervalbecausethemarginoferror isthesameasstandard sampling distributionis20.4. The confidenceintervalforapopulationmeanis245.8 2(0.15) the samplingdistribution. This isa95%confidenceintervalbecausethemarginoferror is2timesthestandard deviationof sampling distributionis0.015. The confidenceintervalforapopulationproportion is45% 5 5 2.3 5 15.3 0.030or3%

0.58 Skills Practice

Skills Practice

6 0.58andthestandard deviationofthe 6 6 20.4andthestandard deviation ofthe 15.3andthestandard deviationofthe 6 6 6 0.2%andthestandard deviationofthe 6%andthestandard deviationofthe 3%andthestandard deviation ofthe page 2 03/12/13 12:49PM

Determine arangeofvaluesforeachpopulationproportion. Usea95%confidenceinterval. Name Lesson 9. 8. 7.

The intervalfrom 3%to5%represents a95%confidenceintervalforthepopulation proportion. A randomsampleof1500calculatorsshippedischeckedand4%are defective. The intervalfrom 84%to90%represents a95%confidenceintervalforthepopulationproportion. A surveyof500schoolsreports that87%lockalltheirdoorsafterthefirstbell.

population proportion. The intervalfrom 72.2% to 83.8%represents a95%confidenceinterval for the A surveyof200adultsreports that78%believeinextraterrestrial life. √

87 87 4 4 √ 78 78 ______√ ______p ______ p ˆ (1 1 2 ˆ (1 ______ ______

pˆ 1 2 2

1 2(0.5) 2(0.5) (1 2(1.5) 2(1.5) n 2 n 2(2.9) 2

2(2.9) n 2

p p 2.3 ˆ

ˆ )

)

ˆp

5 5 < 5 5

) 5 5 5 < 5

5 5 < 5 5 3 0.005

5 √ √

84 0.015

90 √ √ 83.8 72.2 0.029

______ ______ ______0.04(1 0.04(0.96)

√ √ ______ ______ ______0.87(0.13) 0.87(1 ______ ______ ______0.78(0.22) 0.78(1 1500 Skills Practice 500 1500 200 500 2 200

2 0.04) 0.87)

0.78)

Chapter 2

Date

Skills Practice page 3

03/12/13 12:49PM 277 2 451453_IM3_Skills_CH02_257-304.indd 278 2 278

Lesson 12. 10. 11

Chapter 2 population proportion. The intervalfrom 12.2%to15.8%represents a95%confidenceintervalforthe A randomsampleof1400bottleswaterischeckedand14%are notfilledallthewaytotop. population proportion. The intervalfrom 57.4%to72.6%represents a95%confidenceintervalforthe A surveyof160teenagersreports that65%havehomeworkeverydayoftheweek.

The intervalfrom 72%to 78%represents a95%confidenceintervalfor the population proportion. A surveyof850doctorsreports that75%stillhavemedicalschoolloans.

14 14 65 65 75 75 √ √ √ ______ ______p ˆ ______ ______p ______p

1 2 1 2 1 2 ˆ (1 ˆ

(1 (1 2(0.9) 2(0.9) 2(3.8) 2(3.8) 2(1.5) 2(1.5) 2 n n n 2 2

2.3 p pˆ

ˆ ˆ

) ) )

Skills Practice 5 5 5 < 5 5 5 5 5 < 5 5 < 5 5

0.009

72.6 57.4 0.038 72 0.015

15.8 12.2 78 √ √ √ √ √ √

______ ______ ______ ______ ______ 0.14(1 0.14(0.86) 0.65(0.35) 0.65(1 0.75(0.25) 0.75(1 Skills Practice 1400 160 850 1400 160 850 2 2 2

0.14) 0.65) 0.04)

page 4 03/12/13 12:49PM

3.5 3.5 population mean. The intervalfrom 3.46hoursto3.54represents a95%confidenceintervalforthe 0.25 hours. meetings eachday. Thesamplemeanwas3.5hoursandthestandard deviationwas A sampleof150professionals responded toasurveyabouttheamountoftimetheyspendin 6.10 6.10 population mean. The intervalfrom 6.082lbsto6.118represents a95%confidenceintervalforthe 6.10 lbs andthesamplestandard deviationwas0.15lbs. A sampleof300sockeyesalmonwastakenandeachfishweighed.Themean population mean. The intervalfrom 34.32minutes to34.68minutesrepresents a95%confidence intervalforthe each day. Thesamplemeanwas34.5minutesandthestandard deviationwas1.7minutes. A sampleof350adultsresponded toasurveyabouttheamountoftimespentcommutingwork 34.5 34.5 ___ √ S ___ __ √ n S 1 2

___ √ __ n

S 1 2 1 2

5 __ n 2(0.02) 2(0.02)

5 2(0.009) 2(0.009) 2(0.09) 2(0.09)

5 _____ √ 0.25

2.3 _____ ____ √ 150

_____ 1.7 √ ____ 350 0.15 ____ 300

< 5 5

5 5 <

0.02 3.54 3.46 < 5 5 34.68 34.32 0.09 Skills Practice 0.009 6.118 6.082

Chapter 2

Date

Skills Practice page 5

03/12/13 12:49PM 279 2 451453_IM3_Skills_CH02_257-304.indd 280 2 280

Lesson 17. 16. 18.

Chapter 2 22 22 The intervalfrom $21.60to$22.40represents a95%confidenceintervalforthepopulationmean. was $1.75. outside foodvendorseachweek.Thesamplemeanwas$22andthestandard deviation A sampleof80collegestudentsresponded toasurveyabouttheamountofmoneytheyspendon population mean. The intervalfrom 93.54kWhto94.46represents a95%confidenceintervalforthe The samplemeanwas94kWhandthestandard deviationwas2.8kWh. A sampleof150householdswasselectedandtheirmonthlyelectricityusage(kWh)recorded. population mean. The intervalfrom 20.54inches to21.06inchesrepresents a95%confidence intervalforthe the samplestandard deviation was1.8inches. babieswascollected.Thesamplemean20.8inchesand A sampleofthelength200newborn 20.8 20.8 94 94 ___ √ S ___ √ __ n S ___ √ 1 2 1 2 __ n

__ n 5

2(0.20) 2(0.20) 1 2 2(0.23) 2(0.23)

2(0.13) 2(0.13) _____ √

_____ 1.75 √ 2.8

____ 150 2.3 _____ √ ___

80 1.8 ____ 200

Skills Practice

< 5 5 5 5 <

0.20 22.40 21.60 5 5 <

94.64 93.54 0.23 21.06 20.54 0.13 Skills Practice

page 6 03/12/13 12:49PM

© Carnegie Learning sampling distribution.Then,determinewhatsampleproportions wouldbestatisticallysignificant. Label thehorizontalaxisofnormalcurveusingsampleproportion andstandard deviationofthe Problem Set significant. more thantwostandard deviationsbelowthemeanistypicallyconsidered tobestatistically reason astowhyitoccurred. Anyresult thatismore than2standard deviationsabovethemeanor If aresult isstatisticallysignificant, thenitisa result thatisunlikelytooccurandinsteadmusthavea Define statisticalsignificanceinyourownwords. Vocabulary Using StatisticalSignificancetoMakeInferencesAboutPopulations How MuchDifferent? Name Lesson 1.

because thosevaluesare outsideofthe95%confidenceinterval. Sample proportion valueslessthan54.4%andgreater than71.6%are statisticallysignificant standard deviationofthesamplingdistributionis0.043. A sampleproportion ofteenagerswhoattendedamusementparksoverthesummeris0.63and 2.4

Skills Practice

50.1 54.4

58.7 63 67.3 71.6 75.9 Chapter 2

Date

Skills Practice

03/12/13 12:49PM 281 2 451453_IM3_Skills_CH02_257-304.indd 282 2 282

Lesson 4. 3. 2.

Chapter 2 because thosevaluesare outsideofthe95%confidence interval. Sample proportion valueslessthan78%andgreater than92%are statisticallysignificant deviation ofthesamplingdistributionis0.035. A sampleofadultdriverswhoare opposedtoared-light camerainthetownis0.85andstandard because thosevaluesare outsideofthe95%confidenceinterval. Sample proportion valueslessthan68.6%andgreater than77.4%are statisticallysignificant standard deviationofthesamplingdistributionis0.022. A sampleproportion ofcollegestudentswhowantthecampustobesmokefree is0.73andthe because thosevaluesare outsideofthe95%confidenceinterval. Sample proportion values lessthan38.2%andgreater than67.8%are statistically significant deviation ofthesamplingdistributionis0.074. A sampleproportion ofstudents whoatebreakfast before comingtoschool is0.53andthestandard 2.4

Skills Practice

Skills Practice 30.8 74.5 66.4 38.2 68.6

78 45.6 81.5 70.8 53 85 73 60.4 88.5 75.2 67.8 77.4 92 75.2 95.5 79.6 page 2 03/12/13 12:49PM

because thosevaluesare outsideofthe95%confidenceinterval. Sample proportion valueslessthan7.8%andgreater than14.2%are statisticallysignificant is 0.016. A sampleofadultswhoare vegetarianis0.11andthestandard deviationofthesamplingdistribution because thosevaluesare outsideofthe95%confidenceinterval. Sample proportion valueslessthan83.8%andgreater than94.2%are statisticallysignificant distribution is0.026. A sampleofteendriverswhowearseatbeltsis0.89andthestandard deviationofthesampling 2.4

Skills Practice 81.2 6.2 83.8

7.8 86.4 9.4 89 11 91.6 12.6 94.2 14.2 96.8 15.8 Chapter 2

Date

Skills Practice page 3

03/12/13 12:49PM 283 2 451453_IM3_Skills_CH02_257-304.indd 284 2 284

significant. Usea95%confidenceinterval.Explainyour reasoning. Determine whetherthedifference betweeneachpairofpopulationproportion estimatesisstatistically Lesson 8. 7.

Chapter 2 ranges from 49.2%to54.8%.Themarginoferror isapproximately The 95%confidenceintervalforthepopulationproportion oftheThursday nightviewership from 41.8%to48.2%.Themarginoferror isapproximately The 95%confidenceintervalforthepopulationproportion ofthe Tuesday nightviewershipranges significant becausethetwo95%confidenceintervalsdonot overlap. The difference betweenthetwopopulationproportion estimatesofviewersisstatistically Thursday nightanditiswatchedby650outof1250peoplesurveyed. A TVshowiswatchedonaTuesday nightby450outof1000peoplesurveyed.Itismovedtoa statistically significantandtheirclaimisunlikelytooccur. Because themanufacturer’s claim,5%,isnotwithinthe95%confidenceinterval, results are 0.09 0.09 45 45 √ proportion ofuserswho experienced constantheadacheswhenusingthenosespray. The intervalfrom 6.4%to 11.6%represents a95%confidenceintervalfor thepopulation constant headaches. Thirty-nine outof450meansthatapproximately 9%oftheusersinsampleexperienced estimate. Theresults show statisticalsignificance. The manufacturer’s claimisnotwithinthe95%confidence intervalofthepopulationproportion sample of450usersthenosespray, 39oftheusersexperiencedconstantheadaches. A nosespraymanufacturer claimsthatlessthan5%ofusersexperienceconstantheadaches.Ina

√ ____ 450 ______39 ______ ______ ______pˆ pˆ (1 1 2 (1

2(1.6) 2(1.6) 1 1 < n n 2 2

2(0.013) 2(0.013) 0.09

p pˆ ˆ ) 2.4

)

5 < < 5 5 5 Skills Practice 5 5

0.013 0.016

√ √ √ √ 48.2 41.8 ______

______ ______ ______ ______0.09(0.91) 0.45(1 0.45(0.55) 0.09(1 5 5 1000 Skills Practice 0.116 0.064 450 1000 450

2 2

0.45) 0.09)

52 52

√ ______ ______p ˆ (1 1 2 2(1.4) 2(1.4) n 2 6

0.032. pˆ

)

5 < 5 5 5

0.014

6 √ √ 54.8 49.2 ______ ______ ______0.52(1 0.52(0.48) 0.028. 1250 1250 2

0.52)

page 4 03/12/13 12:49PM

Name Lesson 10. 9.

68 68 TV adayrangesfrom 70.2%to79.8%.Themarginoferror isapproximately The 95%confidenceintervalforthepopulationproportion boyswhowatchmore than2hoursof of TVadayrangesfrom 62.8%to73.2%.Themarginoferror isapproximately The 95%confidenceintervalforthepopulationproportion ofgirlswhowatchmore than2hours significant becausethetwo95%confidenceintervalsoverlap. The difference betweenthetwopopulationproportion estimatesofTVviewersisnotstatistically same school,235ofthemwatchmore than2hoursofTVaday. In apollof330girlsatschool,225watchmore than2hoursofTVaday. Inapollof314boysatthe 36 36 √ is runrangesfrom 35.4% to40.6%.Themarginoferror isapproximately The 95%confidenceintervalforthepopulationproportion ofvoterssupportingJohnafterthead ad isrunrangesfrom 33.6% to38.4%.Themarginoferror isapproximately The 95%confidenceintervalforthepopulationproportion ofvoterssupportingJohnbefore the significant becausethetwo95%confidenceintervalsoverlap. The difference betweenthetwopopulationproportion estimatesofvoters isnotstatistically was runforaweek,fourteenhundred peoplewere polledand38%ofthemsupportJohnformayor. Fifteen hundred peoplewere polledand36%ofthemsupportJohnformayor. Afteracommercial ad √

______ ______ ______pˆ p ˆ

(1 (1 1 2 1 2 2(2.6) 2(2.6) 2(1.2) n n 2 2 2(1.2)

pˆ pˆ 2.4

) )

< < 5 5 5 5 5 5 5 5 0.026 0.012

√ √ √ √ 33.6 73.2 62.8 38.4 ______ ______ ______ ______0.68(0.32) 0.36(0.64) ______0.36(1 0.68(1

1500 Skills Practice 330 1500 330

2 2

0.36) 0.68)

75 75 38 38 √

√ ______ ______pˆ ______pˆ

(1 1 2 1 2 (1 2(2.4) 2(2.4) 2(1.3) 2(1.3) n n 2 2

pˆ pˆ

) )

< 5 5 5 < 5 5 5 5 5 0.024

0.013

√ √ √ √ 79.8 70.2 40.6 35.4 ______ ______ 0.75(0.25) ______0.75(1 ______ ______0.38(1 0.38(0.62) Chapter 2 1400 314 1400 6 314 0.026.

2 2

6 6 0.75) 0.38)

0.024.

0.048.

6 Date

0.052. Skills Practice

page 5

03/12/13 12:49PM 285 2 451453_IM3_Skills_CH02_257-304.indd 286 2 286

Lesson 12. 11.

Chapter 2 73 73 method rangesfrom 70.6%to77.4%.Themarginoferror isapproximately The 95%confidenceintervalforthepopulationproportion ofpassingtestscores forthesecond method rangesfrom 69.2%to76.8%.Themarginoferror isapproximately The 95%confidenceintervalforthepopulationproportion ofpassingtestscores forthefirst statistically significantbecausethetwo95%confidenceintervalsoverlap. The difference betweenthetwopopulationproportion estimatesofpassingtestscores isnot method and515outof700studentspassedwiththesecondmethod. A sample oftestscores from bothmethodsshowsthat400outof550studentspassedwiththefirst A stateeducatorasksteacherstotrytwodifferent teachingmethodsforaparticularmathtopic. confidence interval,the results are statisticallysignificant. Because thepercent ofcitycollegestudentswhocommute,22%,isnotwithinthe95% 0.16 0.16 √ proportion ofruralcollege studentswhocommute. The intervalfrom 14.6% to 17.4%represents a95%confidenceinterval for thepopulation _____ are commuters. Four hundred twenty-five outof2700meansthatapproximately 16%oftheruralcollegestudents interval ofthepopulationproportion ofstudentswhocommutetotheruralcollege. percent ofstudentswho commutetothecitycollege,22%,isnotwithin95%confidence The percent ofcommuting studentstoeachofthecollegesisstatisticallysignificantbecause rural townpollsasampleof2700itsstudentsanddeterminesthat425themare commuters. Twenty-two percent ofstudentsattendingcollegeinacityare commuters.Acollegeinaneighboring

√ 2700 425 ______ ______ pˆ pˆ

(1 (1 1 2

2(1.9) 2(1.9) 1 2

n n 2 2 <

2(0.007) 2(0.007)

0.16 pˆ pˆ 2.4

) )

5 5 < 5 < 5 Skills Practice 5 5

0.019

0.007

√ √ √ √ 76.8 69.2 ______ ______ ______ ______0.16(1 0.73(0.27) 0.73(1

______0.16(0.84) 5 5 2700 Skills Practice 0.174 0.146 550 2700 550 2 2

0.16) 0.73)

74 74 √ ______ ______p ˆ

(1 1 2 2(1.7) 2(1.7) n 2

p ˆ

)

< 5 5 5 5 0.017

√ √ 77.4 70.6 ______ ______0.74(0.26) ______0.74(1 700 700

2 6 6 0.74) 0.034. 0.038.

page 6 03/12/13 12:49PM

Determine arangeofvaluesforthepopulationmeanusing95%confidenceinterval.Explainyourwork. Name Lesson 15. 14. 13.

3550 3550 The marginoferror isapproximately population mean. The intervalfrom $3376.40to$3723.60represents a95%confidenceintervalforthe was $800. average monthlysalesforthestore. Thesamplemeanwas$3550andthestandard deviation During onemonth,asampleof85hardware store transactionswascollectedinorder todetermine 2.3 2.3 The marginoferror isapproximately The intervalfrom 1.82to2.78yearsrepresents a95%confidenceintervalforthepopulationmean. store. Thesamplemeanwas2.3yearsandthestandard deviationwas1.5years. takes asampleof38 cashiersfrom theirstores anddeterminehowlongtheyhaveworkedatthe A grocery store managementteamwantstostudytheemploymentdurationoftheirworkers.They 23.75 23.75 ______ ___ The marginoferror isapproximately The intervalfrom $23.47 to $24.03represents a95%confidenceinterval forthepopulationmean. the samplestandard deviation was$1.20. A sampleof75taxiriderswere askedhowmuchtheirtripcost.Thesamplemeanwas$23.75and √ √ √ S S S ______n n n

5 5 5 1 2

2(0.24) 2(0.24) 1 2 ______ √ 1.50 1.20 1 2 800 √ √ ___ 2(86.8) 2(86.8) 85 ______38 75 2(0.14) 2(0.14) 2.4

< < < 86.8 0.24 0.14 5 5

2.78 1.82 5 5 5 5 3723.60 3376.40 Skills Practice 24.03 23.47 6 6 6

173.6. 0.48. 0.28. Chapter 2

Date

Skills Practice page 7

03/12/13 12:49PM 287 2 451453_IM3_Skills_CH02_257-304.indd 288 2 288

Lesson 18. 17. 16.

Chapter 2 7.5 18 18 The marginoferror isapproximately The intervalfrom $15.74to$20.26represents a95%confidenceintervalforthepopulationmean. customers. Thesamplemeanwas$18andthestandard deviationwas$8. In order tolookathealthcosts,theprescription co-paymentamountwasrecorded forfifty 850 850 The marginoferror isapproximately mean. The intervalfrom $825.94to$874.06represents a95%confidenceintervalforthepopulation The samplemeanwas$850andthestandard deviationwas $125. A realtor sampled108apartmentownerstodetermineanaveragerental amountfortheirproperties. 7.5 ______ ___ The marginoferror isapproximately The interval from 6.98 to 8.02 hours represents a 95% confidence interval for the population mean. deviation was1.4hours. sleep theygottheprevious night.Thesamplemeanwas7.5hoursandthestandard classrespondedA sampleof30studentstakinganearlymorning toasurveyabouttheamount √ √ √ S S S ______n n n

1 2 5 5 5 1 2 1 2 2(1.13) 2(1.13)

2(0.26) 2(0.26) ______ √ √ √ 2(12.03) 2(12.03) 1.4 125 ______108 30 50 8 2.4

< <

Skills Practice < 0.26 1.13 5 5 5 5 12.03 20.26 15.74

8.02 6.98 5 5 874.06 825.94 Skills Practice 6 6 6

2.26. 24.06. 0.52. page 8 03/12/13 12:49PM

test score andtimeoftheclass. cause thestudentstodoworseontest,butthere isstatisticalevidence ofalinkbetweenthe the twoconfidenceintervalsdonotoverlap.Itcannot bestatedthathavingtogetupearlierwill The datadoessuggestapossiblelinkbetweenthe timeoftheclassandtestscores because attending thelaterclass? mean testscore forthe9amclasses.Doesattendingearlierclasscauselower testscores than 8 am classes.Theintervalfrom 78.1to83.9represents a95%confidenceintervalforthepopulation from 70.8to77.5represents a95%confidenceintervalforthepopulationmeantestscore forthe A professor tooksamplesoftestscores from his8amclassesand9classes.Theinterval shorter deliverytimes. methods becausethetwoconfidenceintervalsoverlap.ItislikelythatMethodAlinkedto The datasuggeststhatthere isastatisticallysignificantdifference betweenthetwoshipping difference betweenthetwoshippingmethods? confidence intervalforthepopulationmeantimeofdeliveries. population meantimeofdeliveries.AftermethodB,theintervalfrom 22.5to24.8represents a95% After samplingmethodA,theintervalfrom 17.5to22represents a95%confidenceintervalforthe Method Auseslongerhoursandlessdrivers,Bshorterbutmore drivers. A large companyistryingtodecidebetweentwodifferent shippingmethodsfortheirproducts. additive andincreasing gas mileage. statistical significancetothe results. Itisnotlikelythatthere isacorrelation betweenusingthe The rangeofvaluesforthepopulationmeaneachdifference overlapsothere isnotany that acargets? conclusion canyoustateaboutwhetherornottheadditiveeffectively increases themilespergallon represents a95%confidenceintervalforthepopulationmeandifference inmilespergallon.What difference inmilespergallon.Forthecarsthatdidnotgetadditive,intervalfrom additive, theintervalfrom 1.7to4.4represents a95%confidenceinterval for thepopulationmean additive putintotheirfueltankswhiletheotherfifty didnotgetanadditive.Forthecarsthatgot A product testerrandomly selected100cars.Fiftyofthecarswere randomlyselectedtohavean 2.4

Skills Practice

Is there astatisticallysignificant Chapter 2

Date

Skills Practice 2 0.3 to2.3 page 9

03/12/13 12:49PM 289 2 451453_IM3_Skills_CH02_257-304.indd 290 2 290

Lesson 23. 22. 24.

Chapter 2 for adultsisunlikely. because thetwoconfidenceintervalsoverlap.Acorrelation betweengender andamountofsleep The datadoesnotsuggestapossiblelinkbetween genderandamountofsleepforadults sleep forwomen.Isgenderlinkedtotheamountof foradults? The intervalfrom 6.9to7.5represents a95%confidenceintervalforthepopulationmeanamountof 8.7 hoursrepresents a95%confidenceintervalforthepopulationmeanamountofsleepmen. The sleeptimesofarandomsample63menand74womenare recorded. Theintervalfrom 6.5to lost more weightthanthosewhodidnotworkwithahealthcoach. because thetwoconfidenceintervalsdonotoverlap.Theadultswhoworkedwithahealthcoach The datadoessuggestapossiblelinkbetweenweightlossandworkingwithhealthcoach mean weightloss.Is there alinkbetweenweightlossandworkingwithhealthcoach? health coach, the interval from a 95%confidenceintervalforthepopulationmeanweightloss.Foradultswhoworkedwith coach. Fortheadultswhodidnotworkwithahealthcoach,intervalfrom One-hundred ofthemwere askedtodietontheirown,whiletheother100workedwithahealth Two-hundred adultswere testedforthedifference intheirweightsovera3monthperiod. Some adultsaretohealthcoacheshelpthemmaintainabetterlifestyleandloseweight. turning intervals overlap.Thetypeofmethoddoesnotappeartobelinkedthewaittimeforriders. The newmethoddoesnotseemtodecrease thewaittimeforridersbecausetwoconfidence the newmethodseemtodecrease thewaittimeforriders? represents a95%confidenceintervalforthepopulationmeanwaittime interval forthepopulationmeanwaittimeusingoriginalmethod.Thefrom 44.4to46.0 whether averagewaittimedecreases. Theintervalfrom 45.7to51.8represents a95%confidence An amusementparkwantstotestadifferent methodofloadingridersonapopularridetosee 2.4

Skills Practice

Skills Practice 2 12.7 to

2 4.9 represents a 95% confidence interval for the population using thenewmethod.Does 2 3.5 to8.7represents page 10 03/12/13 12:49PM

© Carnegie Learning scenario. Describehowtoobtainarandomsample. Decide whetherasamplesurvey, anobservationalstudy, oranexperimentisthebestmethodforeach Problem Set Designing aStudyandAnalyzingtheResults DIY Name Lesson 4. 3. 2. 1.

every 20thaddress inthetown’ have toconsentsharinginformation.To obtainarandomsample,Icouldsystematicallyselect I choseasamplesurveytogatherdatabecausehealth records are privateandtheindividuals Answers willvary. A companywantstodeterminewhethertheirdrugsare harmfultopeopleina certaintown. and onegirlfrom everyhomeroom ofeverygrade. information abouttheirstudyhabits.To obtainarandomsample,Icouldrandomlyselectoneboy I choseasamplesurveytogatherdatabecausestudentsare thebestsource foraccurate Answers willvary. homework eachweek. howmuchtimestudentsineachgradeof theschoolspendon A highschoolprincipalwantstolearn from eachgendergroup. divide thepopulationofteachersbygender, thenuseacomputertorandomlyselectsample in mycity. To obtainarandomsample,Icouldassignanidentificationnumbertoeachteacher, I choseanobservationalstudybecauseteachersalariesandgendersare publicrecords Answers willvary. You wanttocompare theaverageincomeofmaleandfemalepublicschoolteachersinacertaincity. randomly generateasampleofteachers. random sample,Icouldassignanidentificationnumbertoeachteacheranduseacomputer I choseanobservationalstudybecauseteachersalariesare publicrecords inmycity. To obtaina Answers willvary. You wanttodeterminetheaverageincomeofpublicschoolteachersinacertaincity. 2.5

Skills Practice s directory andsendthesamplesurveysthoseaddresses.

Chapter 2

Date

Skills Practice

03/12/13 12:49PM 291 2 451453_IM3_Skills_CH02_257-304.indd 292 2 292

9. 8. 7. each scenario.Describehowtoobtainasample. Decide whetherrandomsampling,stratifiedorclustersamplingisthebestmethodfor 6. 5. Lesson

Chapter 2 the 11thgradelunch. choose oneboyand girl from eachtableofthe lunchroom. Icouldrepeat thismethodduring I choseastratifiedrandomsamplingtocollectdata. Duringthe9thgradelunch,Icouldrandomly Answers willvary. vegetarians. You conductasamplesurveytodeterminewhether9thgradersor11thare more likelytobe girl from eachtableofthelunchroom. I choseclustersamplingtocollectdata.Duringlunch,couldrandomlychooseoneboyand Answers willvary. You conductasamplesurveytoestimatethenumberofpeopleinyourschoolwhoare vegetarians. select membersfrom eachgroup. groups according totheirgeographiclocation(possiblynorth,south,east,west),andrandomly I choseastratifiedrandomsamplingtocollectdata.coulddividethepopulationoftowninto Answers willvary. number ofsubscriptions. A newspaperconductsanobservationalstudytodeterminewhichareas oftownhavetheleast and usearandomnumbergenerator. study sessions.To obtainarandomsamples,Icouldassignidentificationnumberstostudents using shorter, more frequent studysessionsandtheothertreatment isusinglonger, lessfrequent I choseanexperimenttogatherdatabecausetwotreatments canbeused.Onetreatment is Answers willvary. sessions orlonger, lessfrequent studysessions. betterwithshorter,A teacherwantstodeterminewhetherstudentslearn more frequent study state’ I choseaclustersampletogatherdata.To obtainarandomsample,Icouldarrangeallofthe Answers willvary. enough resources toanalyzethree towns. A universitywantstostudythepopulationtrends ofsmalltownsinthestate,buttheyonlyhave s townsinclustersofthree, thenrandomlyselectoneclusterforanalysis. 2.5 Skills

Practice Skills Practice

page 2 31/03/14 5:26PM

different classroom needs forthecellphonethanothersubject-matterclasses. The samplecouldbebiasedbecauseonlyoneclass issurveyed.Also,mathstudentsmayhave Answers willvary. could usetheircellphonestoimprove instruction. She surveysonemathclasstoseehowmanystudents havecellphonesandasksthemhowthey A principalwantstoknowifstudentsshouldbeallowed tousecellphoneswhileintheclassroom. The samplecouldbebiasedbecausetheyonlyasked adults. Answers willvary. service, “Howmanytextmessagesdidyousendlastmonth?” during onemonth.Thecompanyasksarandomsampleofadultsthatsubscribetotheircellphone A cellphonecompanywantstoknowhowmanytextmessagestheirsubscriberstypicallysend supermarket andaskthemtoparticipateinatastetest. I choserandomsamplingtocollectdata.couldrandomlyselectpeoplethatwalkintothe Answers willvary. vegetables toacompetitors’frozen vegetables. A manufacturer conductsanexperimenttodeterminewhethercustomersprefer theirfrozen randomly surveyasmallsamplefrom eachneighborhood. I chosestratifiedrandomsamplingtocollectdata.coulddividethecityintoneighborhoods,then Answers willvary. currently havehealthinsurance. Health andHumanServicesconductsasurveytodeterminethenumberofcityresidents whodonot then randomlyselectoneofthegroups. I choseclustersamplingtocollectdata.coulddividetheneighborhoodsintogroups ofthree, Answers willvary. the upcomingelection.However, theycanonlyanalyzethree neighborhoods. A politicalcampaignconductsanobservationalstudytodeterminevotingtrends inpreparation for 2.5

Skills Practice

Chapter 2

Date

Skills Practice page 3

03/12/13 12:49PM 293 2 451453_IM3_Skills_CH02_257-304.indd 294 2 294

Lesson 17. 16. 15. 18.

Chapter 2 not havethesameopportunitytorespond. The samplecouldbebiasedbecauseonlystudents passingherroom responded. Allstudentsdid Answers willvary. 10 students whopassherroom, “Howmanyhoursdoyouspendreading eachweek?” The teacherwantstoknowhowmanyhoursstudentsare reading eachweek.Sheasksthefirst representative sampleofallstudents. The samplecouldbebiasedbecauseonly25studentsresponded. Theymaynotbea Answers willvary. 1000 students.Only25respond. A principalwantstoknowwhichtopicsstudentsneeddiscusswithher. Shesendsoutasurveyto The samplecouldbebiasedbecausestudentswhodidnotvolunteermayunderrepresented. Answers willvary. volunteers forsuggestions. A teacherwantstoknowhowstudentsusegraphingcalculatorswhileintheclassroom. Sheasks do notneedagraphingcalculator. The samplecouldbebiasedbecauseonlyoneclassissurveyed.Also,Englishstudentsprobably Answers willvary. improve instruction?” classroom. Shesurveysone Englishclassandasks,“Howdoyouuseagraphingcalculatorto A principalwantstoknowifstudentsshouldbeallowedusegraphingcalculatorsinthe 2.5

Skills Practice

page 4 03/12/13 12:49PM

22, 35,40,42,24,36,30,38, 42, 40,35,24 The followingdatarepresent thenumberofhoursthatrestaurant employeesworkedlastweek. 70, 69,65,60,62,64,73,66,65 The followingdatarepresent theheightsininchesofpeopleanaerobics class. 38, 40,32,41,31,30,39,42,32 The following data represent the salaries in thousands of dollars of employees in a company. 17, 12,16,21,19,15,22,18,17 The followingdatarepresent thenumberofhomerunshitbybaseballplayers. 2.5 22 X X 23

24 Skills Practice X X 25 29 60 X X 11 26 30 61 X X 12 27 X X X 31 62 X X X X X Salary ofEmployees(thousandsdollars) 13 28 32 63 X X 14 29 Employee Work Week (hours)

33 64 Number ofHomeRunsHit 15 30 X X X

34 65 X X X Height (inches) 16 31 X X 35 66 X X 17 32 X X 36 67 18 33 X

68 37 19 34 X X 38 69 X X X 20 35 X X 39 70 X X 21 36 X X X X 40 71 X X 22 37 X 72 41 Chapter 2 X X 23 38 X X 42 73 X X 39

Date

40 X X X X X Skills Practice 41 42 X X page 5

03/12/13 12:49PM 295 2 451453_IM3_Skills_CH02_257-304.indd 296 2 296

Create ahistogramforeachsetofdata. Lesson 25. 24. 23.

Chapter 2 17, 12,16,21,19,15,22,18,17 The followingdatarepresent thenumberofhomerunshitbybaseballplayers. 77, 94,89,86,90,68,95,91,79,82,87,90 The followingdatarepresent students’Englishtestscores. 20, 22,19,14,12,18,21,15,22 The followingdatarepresent thelengthsininchesoffishanaquarium. 2.5

Skills Practice

Skills Practice 68 X X 70 10 72 11 Number of Players 2 4 6 8 74 12 X X 76 13 11 X X 2

78 14 15 X X X Length ofFish(inches) X X Number ofHomeRunsHit English Test Scor 15 80 X 16 82 16

2 17 84 20 86 18 X X X e X 19 88 X X X X 21 X X X 20 90 2 X X X X X X X X X X 25 X X X 21 92 X X X 94 22 X X X 96 23 98 page 6 03/12/13 12:49PM

70, 69,65,60,62,64,73,66,65 The followingdatarepresent theheightsininchesofpeopleanaerobics class. 38, 40,32,41,31,30,39,42,32 The followingdatarepresent thesalariesinthousandsofdollarsemployeesacompany. 2.5

Skills Practice

Number of People Number of Employees 2 4 6 8 2 4 6 8 26 Salary ofEmployees(thousandsdollars) 60 2 30 2

64 31 2 Height (inches) 35 65

2 69 36 2 40 70 41 2 74 2 45 Chapter 2

Date

Skills Practice page 7

03/12/13 12:49PM 297 2 451453_IM3_Skills_CH02_257-304.indd 298 2 298

Lesson

28. 29.

Chapter 2 22, 35, 40, 42, 24, 36, 40, 30, 40, 38, 22, 36, 40, The followingdatarepresent thenumberofhoursthatrestaurant employees worked last week. 20, 22,19,14,12,18,21,15,22 The followingdatarepresent thelengthsininchesoffishanaquarium. 2.5

Skills Practice

Number of Fish 10 2 4 6 8 Number of Employees 2 4 6 8 10 20 2 2 14 24

Employee WorkWeek(hours) 25 2 Length ofFish(inches) 29 40, 42, 40, 35, 24 15 30

2 2 19 34 35 2 39 40 20 2 2 44 24

page 8 03/12/13 12:49PM

1 2 2 1 Number of Home Runs Hit 19, 18,12,15,17 17, 12,16,21,19,15,22, of homerunshitbybaseballplayers. The followingdatarepresent thenumber 77, 94,89,86,90,68,95,91,79,82,87,90 The followingdatarepresent students’Englishtestscores. 2 1 1 2 2 2 = 21 2.5 9 9 8 7 7 6 6 5 5

Skills Practice

Number of Scores 10 2 4 6 8

65 2 69 70

75 2 English TestScore 79 32. 80

84 0 3 4 3 Salary of Employees (thousands of dollars) 42, 31,32 38, 40,32,41,31,30,39, in acompany. in thousandsofdollarsemployees The followingdatarepresent thesalaries 1 0 0 1 0 0 85 = 30 2 89 9 9 8 2 2 1 2 1 1 90 2 94 95 2 Chapter 2 99

Date

Skills Practice page 9

03/12/13 12:49PM 299 2 451453_IM3_Skills_CH02_257-304.indd 300 2 300

Create abox-and-whiskerplotforeachsetofdata. Lesson 35. 33. 38. 37.

Chapter 2 minimum: 32,firstquartile:46,median:76.5,third quartile:100,maximum: 128 43, 32,56,128,85,96,46,122,100,68 U.S.cities. The followingdatashowstheamountsofannualsnowfall ininchesfor10northeastern minimum: 176,firstquartile:199,median:222.5,third quartile:252.5,maximum:282 220, 244,185,261,243,225,273,282,176,190,208,214 The followingdatarepresent theweightsinpoundsof12playersonafootballteam. 2 1 2 2 1 Length of Fish (inches) 15, 19,14,21,12,20,22 20, 22, 20, 19, 14, 12,18,20,21, in inches of fish in an aquarium. The followingdatarepresent thelengths 4 6 0 7 6 Height (inches 66, 65 70, 69,65,60,62,64,73,66, in inchesofpeopleanaerobics class. The followingdatarepresent theheights 170 0 2 0 0 30 = 12 = 64 1 0 0 0 0 4 2 3 32

176 35 2.5 5 4 4 5 4

180 Skills Practice 40 ) 6 5

2 9 1 8 9 5 190 45 2 1 9 9 Skills Practice 6 46 50

200 9

199 55

210 60 65

220

222.5 75 230 36. 34. 76.5 80

240 English Test Score 79, 82,68,90,91,86,87,89,90 77, 94, 89, 86, 90, 68, 95, 91,90,89,77, English test scores. The followingdatarepresent students’ 2 2 4 3 Employee Work Week (hours) 40, 42,35,24 22, 35, 40, 42, 24, 36, 40, 30, 40,38,22,36, worked last week. of hoursthatrestaurant employees The followingdatarepresent thenumber 2 8 2 8 7 2 9 8 6 85 2 2 0 0 0 0 0 0 5 5 0 4 2 2 9 7 7 4 1 1 0 0 0 0 0 = 22 = 82 6 8 90 250 9 9 7 6 8 6 6 4 95 252.5 260 100 9 100

105 5 270 110 280 115 282 120 290 125 128 page 10 300 130 03/12/13 12:49PM

minimum: 22,firstquartile:26,median:33,third quartile:42.5,maximum: 51 26, 35,45,22,23,30,47,33,40,32,51 The followingdatarepresent theagesof13studentsinanadultkarateclass. minimum: 2,firstquartile:5,median:12,third quartile:20,maximum:28 12, 28,11,2,17,5,20,26,7,18 The following data represent the total number of points scored by the 11 players on a basketball team. minimum: 16,firstquartile:22,median:30,third quartile:39,maximum:46 41, 30,22,16,28,32,27,46,39,35,20 The followingdatashowstheheightsinfeetof11trees inaforest. minimum: 44,firstquartile:49,median:53,third quartile:56,maximum:60 60, 44,54,50,59,53,48,46,55,56,52,49,51 The followingdatashowstheaveragedailylowtemperatures indegrees Fahrenheit for15U.S.cities. 14 40 41 16 16 2.5 42 18

0 0 43 Skills Practice 20 2 44 44 22 22 45 10 5 24 46 26 47 10 20 28

22 48 30 12 49 26 30 49 30 50 32 51 34 33 52 36 20 40 20 53 38 2551 42.5 53 54 39 40 50 Chapter 2 55 42 56 28 56

44 Date 57

60 30 Skills Practice 46 46 58 48 59 page 11 60 60 50

03/12/13 12:49PM 301 2 451453_IM3_Skills_CH02_257-304.indd 302 2 302

Determine themean,median,andmodeofeachdataset.Tell ifthedataissymmetric. Lesson 45. 44. 43. 46.

Chapter 2 Symmetry: notsymmetric Mode Median Mean 20, 35,40,15,30,25,35 The followingdatarepresent thepricesindollarsof11shirtsastore. Symmetry: notsymmetric Mode Median Mean 20, 16,32,30,28,25,24,32 The followingdatarepresent thefuelefficiencies inmilespergallonof8carsatadealer. Symmetry: notsymmetric Mode Median Mean 19.9, 22.1,18.5,20.4,20.8,21.3,19.2,20.1,21.0,15.2,20.0,21.6 The followingdatarepresent thelongjumpdistancesinfeetof12participantsatrackmeet. Symmetry: notsymmetric Modes Median Mean 15, 20,30,10,55,45,25,30 to work. The followingdatarepresent theamountsoftimeinminutesthatittakesninedifferent peopletoget 5 5 5 5 5 5 5 5 27.27 25.88 20.00 27.78 5 5 5 5 32 none 20 2.5

20,30 25 26.5 20.25 25 Skills Practice

Skills Practice

page 12 03/12/13 12:49PM

Quartile 3:21.15 Quartile 2:20.25 Quartile 1:19.55 Standard deviation:1.82 19.9, 22.1,18.5,20.4,20.8,21.3,19.2,20.1,21.0,15.2, 20.0,21.6 The followingdatarepresent thelongjumpdistancesinfeetof12participantsatrackmeet. Quartile 3:37.5 Quartile 2:25 Quartile 1:17.5 Standard deviation:14.39 15, 20,30,10,55,45,25,30 to work. The followingdatarepresent theamountoftimeinminutesthatittakesninedifferent peopletoget Symmetry: notsymmetric Mode Median Mean 10, 15,0,5,20,0 The following data represent the number of extra-credit points earned by 14 students in a science class. Symmetry: notsymmetric Modes Median Mean 3, 6,8,11,9,5,7,10 The followingdatarepresent thelengthsininchesof10fishanaquarium. 5 5 5 5 7.5 7.3 5 5 0 2.5 6,8 7.5 7.5

Skills Practice

Chapter 2

Date

Skills Practice page 13

03/12/13 12:49PM 303 2 451453_IM3_Skills_CH02_257-304.indd 304 2 304

Lesson 53. 52. 51. 54.

Chapter 2 Quartile 3:15 Quartile 2:7.5 Quartile 1:0 Standard deviation:7.0 10, 15,0,5,20,0 The following data represent the number of extra-credit points earned by 14 students in a science class. Quartile 3:9 Quartile 2:7.5 Quartile 1:6 Standard deviation:2.41 3, 6,8,11,9,5,7,10 The followingdatarepresent thelengthsininchesof10fishanaquarium. Quartile 3:35 Quartile 2:25 Quartile 1:20 Standard deviation:9.05 20, 35,40,15,30,25,35 The followingdatarepresent thepricesindollarsof11shirtsastore. Quartile 3:31 Quartile 2:26.5 Quartile 1:22 Standard deviation:5.77 20, 16,32,30,28,25,24,32 The followingdatarepresent thefuelefficiencies inmilespergallonof8cars atadealer. 2.5

Skills Practice

page 14 03/12/13 12:49PM