Sigma綠帶培訓(xùn)教材2

Revision :1.00Date :June20016西格瑪綠帶培訓(xùn)MaterialsTWO-6-4-20246標(biāo)準(zhǔn)偏差第二天:TestsofHypothesesWeek1recapofStatisticsTerminologyIntroductiontoStudentTdistributionExampleinusingStudentTdistributionSummaryofformulaforConfidenceLimitsIntroductiontoHypothesisTestingTheelementsofHypothesisTesting-----------------------------------------------------Break--------------------------------------------------------------------LargesampleTestofHypothesisaboutapopulationmeanp-Values,theobservedsignificancelevelsSmallsampleTestofHypothesisaboutapopulationmeanMeasuringthepowerofhypothesistestingCalculatingTypeIIErrorprobabilitiesHypothesisExerciseI-----------------------------------------------------Lunch--------------------------------------------------------------------HypothesisExerciseIPresentationComparing2populationMeans:IndependentSamplingComparing2populationMeans:PairedDifferenceExperimentsComparing2populationProportions:F-Test-----------------------------------------------------Break--------------------------------------------------------------------HypothesisTestingExerciseII(paperclip)HypothesisTestingPresentation

第一天wrapup第二天:Analysisofvariance和simplelinearregressionChi-square:AtestofindependenceChi-square:InferencesaboutapopulationvarianceChi-squareexerciseANOVA-AnalysisofvarianceANOVA–Analysisofvariancecasestudy-----------------------------------------------------Break--------------------------------------------------------------------TestingthefittnessofaprobabilitydistributionChi-square:agoodnessoffittestTheKolmogorov-SmirnovTestGoodnessoffitexerciseusingdiceResult和discussiononexercise------------------------------------------------------Lunch-------------------------------------------------------------------Probabilistic關(guān)系hipofaregressionmodelFittingmodelwithleastsquareapproachAssumptions和varianceestimatorMakinginferenceabouttheslopeCoefficientofCorrelation和DeterminationExampleofsimplelinearregressionSimplelinearregressionexercise(usingstatapult)------------------------------------------------------Break-------------------------------------------------------------------Simplelinearregressionexercise(con’t)Presentationofresults

第二天wrapupDay3:Multipleregression和modelbuildingIntroductiontomultipleregressionmodelBuildingamodelFittingthemodelwithleastsquaresapproachAssumptionsformodelUsefulnessofamodelAnalysisofvarianceUsingthemodelforestimation和predictionPitfallsinpredictionmodel--------------------------------------------------------Break-----------------------------------------------------------------Multipleregressionexercise(statapult)Presentationformultipleregressionexercise--------------------------------------------------------Lunch------------------------------------------------------------------Qualitativedata和dummyvariablesModelswith2ormorequantitativeindependentvariablesTestingthemodelModelswithonequalitativeindependentvariableComparingslopes和responsecurve--------------------------------------------------------Break-----------------------------------------------------------------ModelbuildingexampleStepwiseregression–anapproachtoscreenoutfactorsDay3wrapupDay4:設(shè)計ofExperimentOverviewofExperimentalDesignWhatisadesignedexperimentObjectiveofexperimental設(shè)計和itscapabilityinidentifyingtheeffectoffactorsOnefactoratatime(OFAT)versus設(shè)計ofexperiment(DOE)formodellingOrthogonality和itsimportancetoDOEH和calculationforbuildingsimplelinearmodelType和usesofDOE,(i.e.linearscreening,linearmodelling,和non-linearmodelling)OFATversusDOE和itsimpactinascreeningexperimentTypesofscreeningDOEs---------------------------------------------------Break----------------------------------------------------------------------PointstonotewhenconductingDOEScreeningDOEexerciseusingstatapultInterpretatingthescreeningDOE’sresult---------------------------------------------------Lunch----------------------------------------------------------------------ModellingDOE(Fullfactoriawithinteractions)InterpretinginteractionoffactorsParetooffactorssignificanceGraphicalinterpretationofDOEresults

某些rulesofthumbinDOE

實例ofModellingDOE和itsanalysis--------------------------------------------------Break-----------------------------------------------------------------------ModellingDOEexercisewithstatapultTargetpractice和confirmationrunDay4wrapupDay5:Statistical流程ControlWhatisStatistical流程ControlControlchart–thevoiceofthe流程

流程controlversus流程capabilityTypesofcontrolchartavailable和itsapplicationObservingtrendsforcontrolchartOutofControlreactionIntroductiontoXbarRChartXbarRChartexampleAssignable和ChancecausesinSPCRuleofthumbforSPCruntest-------------------------------------------------------------Break------------------------------------------------------------XbarRChartexercise(usingDice)IntroductiontoXbarSChartImplementingXbarSChart

為什么XbarSChart?IntroductiontoIndividualMovingRangeChartImplementingIndividualMovingRangeChart

為什么XbarSChart?-------------------------------------------------------------Lunch------------------------------------------------------------Choosingthesub-groupChoosingthecorrectsamplesizeSamplingfrequencyIntroductiontocontrolchartsforattributedatanpCharts,pCharts,cCharts,uCharts-------------------------------------------------------------Break------------------------------------------------------------Attributecontrolchartexercise(paperclip)OutofcontrolnotnecessarilyisbadDay5wrapupRecapofStatisticalTerminologyDistributionsdiffersinlocationDistributionsdiffersinspreadDistributionsdiffersinshapeNormalDistribution-6-5-4-3-2-10123456------------------------------99.9999998%-------------------------------------------99.73%--------------------95.45%---------68.27%--±3

variationiscallednaturaltoleranceAreaunderaNormalDistribution流程capabilitypotential,CpBasedontheassumptionsthat:流程isnormalNormalDistribution-6-5-4-3-2-10123456LowerSpecLimitLSLUpperSpecLimitUSLSpecificationCenterItisa2-sidedspecification流程meaniscenteredtothedevicespecificationSpreadinspecificationNaturaltoleranceCP=USL-LSL686=1.33流程CapabilityIndex,CpkBasedontheassumptionthatthe流程isnormal和incontrol2.Anindexthatcomparethe流程centerwithspecificationcenterNormalDistribution-6-5-4-3-2-10123456LowerSpecLimitLSLUpperSpecLimitUSLSpecificationCenterThereforewhen,Cpk<Cp;then流程isnotcenteredCpk=Cp;then流程iscenteredUSL-Y3Y-LSL3Cpk=min,The流程ofcollecting,presenting和describingsampledata,usinggraphical工具和numbers.ParetoChartPopulationmeanHistogramPopulation標(biāo)準(zhǔn)偏差DescriptiveStatisticsEstimatesforDescriptiveStatisticsThe流程ofestimatingthepopulationparametersfromsample(s)thatwastakenfromthepopulation.Samplemean,XPopulationmean,mSample標(biāo)準(zhǔn)偏差,SPopulation標(biāo)準(zhǔn)偏差,(whensamplesize,n>20)Estimated標(biāo)準(zhǔn)偏差,R/d2

Population標(biāo)準(zhǔn)偏差,(whensamplesize,n20)ProbabilityTheoryProbabilityisthechanceforaneventtooccur.Statisticaldependence/independencePosteriorprobabilityRelativefrequencyMakedecisionthroughprobabilitydistributions(i.e.Binomial,Poisson,Normal)CentralLimitTheoremRegardlesstheactualdistributionofthepopulation,thedistributionofthemeanforsub-groupsofsamplefromthatdistribution,willbenormallydistributedwithsamplemeanapproximatelyequaltothepopulationmean.Setconfidenceintervalforsamplebasedonnormaldistribution.Abasistocomparesamplesusingnormaldistribution,hencemakingstatisticalcomparisonoftheactualpopulations.Itdoesnotimpliesthatthepopulationisalwaysnormallydistributed.(Cp,Cpkmustalwaysbasedontheassumptionthat流程isnormal)InferentialStatisticsThe流程ofinterpretingthesampledatatodrawconclusionsaboutthepopulationfromwhichthesamplewastaken.ConfidenceInterval(Determineconfidencelevelforasamplingmeantofluctuate)T-Test和F-Test(Determineiftheunderlyingpopulationsissignificantlydifferentintermsofthemeans和variations)Chi-SquareTestofIndependence(Testifthesampleproportionsaresignificantlydifferent)Correlation和Regression(Determineif關(guān)系hipbetweenvariablesexists,和generatemodelequationtopredicttheoutcomeofasingleoutputvariable)CentralLimitTheoremThemeanxofthesamplingdistributionwillapproximatelyequaltothepopulationmeanregardlessofthesamplesize.Thelargerthesamplesize,thecloserthesamplemeanistowardsthepopulationmean.2. Thesamplingdistributionofthemeanwillapproachnormalityregardlessoftheactualpopulationdistribution.3. Itassuresusthatthesamplingdistributionofthemeanapproachesnormalasthesamplesizeincreases.m=150Populationdistributionx=150Samplingdistribution(n=5)x=150Samplingdistribution(n=20)x=150Samplingdistribution(n=30)m=150Populationdistributionx=150Samplingdistribution(n=5)某些takeawaysforsamplesize和samplingdistribution

Forlargesamplesize(i.e.n30),thesamplingdistributionofxwillapproachnormalityregardlesstheactualdistributionofthesampledpopulation.Forsmallsamplesize(i.e.n<30),thesamplingdistributionofxisexactlynormalifthesampledpopulationisnormal,和willbeapproximatelynormalifthesampledpopulationisalsoapproximatelynormallydistributed.Thepointestimateofpopulation標(biāo)準(zhǔn)偏差usingSequationmay提供apoorestimationifthesamplesizeissmall.IntroductiontoStudenttDistrbutionDiscoveredin1908byW.S.GossetfromGuinnessBreweryinIreland.Tocompensatefor標(biāo)準(zhǔn)偏差dependenceonsmallsamplesize.Containtworandomquantities(x和S),whereasnormaldistributioncontainsonlyonerandomquantity(xonly)Assamplesizeincreases,thetdistributionwillbecomeclosertothatofstandardnormaldistribution(orzdistribution).PercentilesofthetDistributionWhereby,df=Degreeoffreedom=n(samplesize)–1Shadedarea=one-tailedprobabilityofoccurencea=1–ShadedareaApplicablewhen:Samplesize<30

標(biāo)準(zhǔn)偏差isunknownPopulationdistributionisatleastapproximatelynormallydistributedt(a,u)aAreaunderthecurvePercentilesoftheNormalDistribution/ZDistributionZaAreaunderthecurveWhereby,Shadedarea=one-tailedprobabilityofoccurencea=1–ShadedareaStudenttDistrbutionexampleFDArequirespharmaceuticalcompaniestoperformextensivetestsonallnewdrugsbeforetheycanbemarketedtothepublic.Thefirstphaseoftestingwillbeonanimals,whilethesecondphasewillbeonhumanonalimitedbasis.PWDisapharmaceuticalcompanycurrentlyinthesecondphaseoftestingonanewantibioticproject.Thechemistsareinterestedtoknowtheeffectofthenewantibioticonthehumanbloodpressure,和theyareonlyallowedtoteston6patients.Theresultoftheincreaseinbloodpressureofthe6testedpatientsareasbelow: (1.7,3.0,0.8,3.4,2.7,2.1)Constructa95%confidenceintervalfortheaverageincreaseinbloodpressureforpatientstakingthenewantibiotic,usingbothnormal和tdistributions.StudenttDistrbutionexample(con’t)UsingnormalorzdistributionUsingstudenttdistributionAlthoughtheconfidencelevelisthesame,usingtdistributionwillresultinalargerintervalvalue,because:

標(biāo)準(zhǔn)偏差,Sforsmallsamplesizeisprobablynotaccurate

標(biāo)準(zhǔn)偏差,SforsmallsamplesizeisprobablytoooptimisticWiderintervalisthereforenecessarytoachievetherequiredconfidencelevelSummaryofformulaforconfidencelimit6Sigma流程和1.5SigmaShiftinMeanStatistically,a流程thatis6Sigmawithrespecttoitsspecificationsis:NormalDistribution-6-5-4-3-2-10123456------------------------------99.9999999998%----------------------------LSLUSLDPM=0.002Cp=2Cpk=2ButMotoroladefines6Sigmawithascenarioof1.5SigmashiftinmeanDPM=3.4Cp=2Cpk=1.51.5某些Expl鵝anat損ions仙on扯1.5鍋Sigm濤aMe衡anS跳hiftMot姿orl蝕ah識as寧con騾duc射ted物a談lot廚of查ex竭per冷ime波nts鳥,和fou夾nd禁tha姿ti慢nl誼ong圍te谷rm,努th蒜e流程mea濤nw翠ill釘sh珠ift燃wi蜻thi膀n1障.5盼sig惱m(xù)a非if貍the流程is粗und跨er耀con僅tro帽l.1.5曲si柄gma廢me也an互shi乖ft浴in斤a3腎Si鏡gma流程cont戴rol密plan擠wil許lbe澆tra氏nsla廁ted圖toa估ppro宴xima琴tely指14%舌of釋the慕time刪ad鉆ata康poin吵twi殿llb藍(lán)eou麻tof狠con賠trol鹿,和this橋is壺deem夢acc潛epta謀ble辨ins冠tati鳴stic撐al流程con腎tro李l(部SPC運)p靈rac裝tic熊es.NormalDistribution-3-2-10123------------------99.74%-----------------LCLUCLDistributionwith1.5SigmaShift-3-2-10123-----------------86.64%----------------LCLUCLOutofcontroldatapointsOur衣Expl黨anat惰ionMost則fre煩quen珠tly宗used漿sam犬ple創(chuàng)size突for股SPC擔(dān)in騎indu搞stry誘is垃3to俯5u鞭nits叨per短sam權(quán)plin季g.Take聾the傍mid謹(jǐn)dle垂valu嘩eof濱4a暮san侍ave垃rage聽sam刑ple靠size凡use交din魄the靜sam附plin許g.Assu極ming先the流程iso豈f6安sigm域aca變pabi林lity手,is免in長cont停rol,和isn怒orma沒lly頸dist妄ribu怖ted.Unde換rth吳eco譜nfid轎ence可int需erva顏lfo火rsa慰mpli族ngd羅istr金ibut品ion,烤we撐expe裁ctt葛hea慚vera獅gev蒜alue紗of持the決samp遣les混tof銳luct即uate介wit捐hin3st龍anda谷rde掃rror黎s(i脾.e.再natu乓ral冠tole頂ranc掩e),森givi錫ngc肚onfi蒸denc冶ein慈terv恥alo陰f:Int族rod撞uct伙ion棒to鄰Hy黨pot似hes勿is自Tes執(zhí)tin絞g?What惡is幻玉hypo冠thes家ist要esti電ngi扁nst咳atis喝tic槍?Ahy制poth鑼esis造is付“at它enta忌tive她ass巡壽umpt憶ion律made配in由orde壺rto目dra雷wou娘tor簽tes背tit柱slo賊gica祖lor權(quán)emp況iric翠alc障onse炊quen兩ces.鋼”Ast嶄atis勉tica飽lhy胡poth孝esis禮is杯ast量atem刪ent飼abou屋tth葛eva孝lue貼ofo防neo賤fth測ech根arac線teri悲stic博sfo輸ron沖eor笨mor畫epo否pula羊tion陪s.The圍pu卻rpo江se待of祥the驅(qū)hy叫pot聾hes益is圣is妄to蔥est猛abl鬧ish裂a蕩bas飽is,筒so惹th運at倆one節(jié)ca升ng普ath消er如evi篩den理ce汁to無eit棗her宣di幸spr米o(hù)ve隔th邁es忽tat雞eme冷nt喜or誰acc悠ept葵it譯as汽tr策ue.Exam貞ple踏ofs訪tati陳stic致alh牧ypot叛hesi監(jiān)sThe開av幼era綱ge撲com更mut炮et兔ime杏us瞧ing唱Hi擺ghw震ay衛(wèi)92槽is向sho供rte逃rt巾han暈us厚ing漆Fr德anc伐eA服ven蜂ue.Thi尖s流程chan尚g(shù)ew氣ill蛙not燥caus萌ean近yef沫fect鏡on幫the咽down紗stre林am流程es.The遇vari芬atio韻nof鉤Ven難dor漸B’s使part重sar平e40茄%wi飾der疫than諒tho盛seo委fVe純ndor飛A.Elem絮ents士of什Hypo長thes態(tài)isT咽esti礎(chǔ)ngPos跡sib呼le決out習(xí)com鞏es哲for杏hy悲pot璃hes敏is畢tes胡tin樹go已nt珠wo觀tes腦ted友po嶄pul蔥ati領(lǐng)ons奶:NoSignificantDifferenceSignificantDifferenceinVariationSignificantDifferenceinMeanSignificantDifferenceinbothMean和Variationm1<>m21=2m1<>m21<>2m1=m21<>2m1=m21=2為什么Hypo罩thes卷isT鼠esti殖ng?Man大yp掘rob都lem惡sr愛equ堡ire對a玩dec牢isi述on壤to籮acc善ept瓣or煮re捧jec岸tastat司emen晝tabo艘ut詞ap拾ara宜met憶er.That遷sta葛teme關(guān)nti懸saHyp肢oth逃esi全s.I論tre磚pres呆ents按the斗tra億nsla追tion瞞of揪apr氧acti鈴cal筑ques顯tion晃int咸oa拜stat散isti紡cal蹄ques乒tion冤.Sta熄tis頁tic孔al撓tes權(quán)tin酸g提供sa謠nobj蘆ect續(xù)ivesolu然tion狂,wi榴thk課nownris刺ks,t術(shù)oq園ues菌tio忠ns畜whi披ch夜are蓋tr射adi理tio些nal活ly偶ans恒wer虧ed給sub厚jec毛tiv盈ely護(hù).Iti群sa殘step兵ping際sto苦net磨o設(shè)計of斯Exp己eri龍men廟t,誼DOE激.Hyp照oth耳esi詳sT典est供ing叫De削scr森ipt飾ion燒sHypo涉thes劫isT灶esti與nga勤nswe家rst刪hep昌ract罩ical覆que息stio孟n:“員Ist聞here牧ar窮eal講diff硬eren險ceb使etwe禍enA和B?疊”In寄hyp蜂oth哀esi嗽st高est香ing醫(yī),r餓ela繩tiv兼ely訊sm符all斗sa斧mpl吐es費are蘿us榮ed跌to蔑ans照wer榴qu險est泛ion陽sa窮bou炸tp泥opu掙lat里ion患pa牛ram賄ete固rs.The芳re信is律alw娃ays爹a歉cha粘nce哭th均at身as絞amp恨le頂tha罵ti叉sn供ot艇rep梁res變ent閱ati劉ve溪of朽the丙po敞pul丈ati價on攀bei紹ng軋sel粥ect研ed和res撓ult書si琴nd扶raw吉ing綠a瞧wro較ng喂con裕clu籮sio駁n.Ele嫁men林ts耳of再Hyp腔oth熄esi襯sT諒est脈ing婆(c屠on’肯t)The痰Null粒Hyp搬othe涉sisStat洞emen流tgene啄rall碧yas布sume幫dto閉be糧trueunl蘿ess謊su沒ffi博cie茫nt月evi息den淺ce磚is蹄fou衰nd晶to搜be月con粱tra惕ryOft駝en陸ass甚ume冬dt跑ob膚et地he薄sta筆tus潑qu護(hù)o,季or畢the饑pr闊efe鮮rre胃do籍utc映ome壞.H喪owe修ver叛,i粥ts截ome彈tim鑰esrepr虛esen巧tsa懂sta易tey尸ous訊tron儉gly想want編to戰(zhàn)disp賢rove.Desi塊gnat窄eda寺sH0Inh鎮(zhèn)ypot麗hesi婆ste閱stin救g,w桃eal位ways鎮(zhèn)bia堪sto蜂ward隊nul爹lhy鋪poth李esisThe搞Alte統(tǒng)rnat栽ive壟Hypo蠟thes穩(wěn)is(哲orR搞esea湊rch攀Hypo狐thes滔is)Sta閃tem脫ent的th忍at過wil虛lb償ea幸cce洽pte訓(xùn)do導(dǎo)nly型if侍da劃ta提供conv往inci食nge摔vide層nce葛ofi興tst落ruth沫(i.徑e.b差yre改ject拌ing刪the掘null天hyp理othe青sis)取.Inst盼ead譽ofc句ompa勺ring籌two涌pop蛇ulat段ions斬,it哄can傅als畜obe勢bas貼edo跪na牌spec溝ific爛eng麥inee敘ring釋dif償fere假nce服ina歲cha框ract曠eris良tic硬valu餡eth崗ato塘ned烈esir撇est監(jiān)ode枝tect(i.錦e.覺ins首tea從do偏fa售ski飲ng劍ism1=m2,爆we艇ask建ism1>炕450).Des著ign攀ate鮮da愁sH1Ele慮men醒ts愧of途Hyp御oth純esi紡sT拜est椅ing科(c帆on’估t)Exam濤ple灶ifw安ewa使ntt賓ote兇stw棗heth灰era姓pop很ulat因ion狗mean返is蘭equa址lto滿500租,we閣wou慢ldt鼠rans練late捧it講to:Nul蜻lH濃ypo晚the韻sis媽,H0:mp=50腦0和con退sid艇er腦alt豬ern及ate場hy敘pot禁hes吉is尾as:Alt爬ern削ate踢Hy糕pot圓hes送is,凈H1:mp<>亡500航;壓(2償tai哄ls安tes癢t)Reme損mber些con末fide亂nce腹inte宇rval槳,at星95%便con抄fide演nce享leve像lst娃ates縮慧tha群t:95%吹of畫th極et討ime本th新em鞠ean誼va稼lue激wi闊ll講flu版ctu極ate邊wi煌thi袖nt臟he屆con陷fid繳enc纏ei年nte賢rva它l(鈔lim未it)5%落cha找nce墾th旁at研the存me足an名is扣nat孫ura拌lf注luc別tua灣tio當(dāng)n,洗but班we柱th啄ink休it溪is士no境t–姨al突pha敵(a)p熔rob申abi啄lit衣y---Confidencelimit---mH0=5000.025ofarea0.025ofarea(a/2)rejectarea(a/2)rejectarea1.96stderror1.96stderrorType洽II寬Erro訴rAcc躁ept垮ing削a貧nul抄lh闊ypo雨the全sis演(H0),女whe支ni乒ti慢sf涼als辰e.晴Pro行bab畢ili趣ty齡of捉thi童se脹rro也re殲qua枯lsbTyp渣eI款Er想rorReje姻ctin干gth洪enu潮llh板ypot績hesi拳s(H0),牢whe員ni北ti森st噸rue戲.P詞rob淋abi狀lit倡yo疫ft儉his侍er棉r(nóng)or體eq符ual茅saIfmpiswithinconfidencelimit,acceptthenullhypothesisH0.Ifmpisinrejectarea,rejectthenullhypothesisH0.Use商th引es慚td蒸err斃or講obs稈erv徑ed找fro撈mt貞he魚sam迷ple械to咽se美tc似onf林ide注nce剩li毒mit臉on擋50做0(mH0).研The柴as擦sum床pti懷on躍ismH0has蕩the款same旬var肺ianc惠easmp.Ele繡men戲ts峰of軌Hyp棚oth辱esi花sT鍬est印ing占(c懸on’畏t)Othe乒rpo活ssib失lea劈燕l(xiāng)ter蔥nate煩hyp挽othe茂sis提are:Alt賴ern洗ate睡Hy梳pot撤hes轎is,若H1:mp>5糧00舊;(西1t安ail替te等st)Alte螞rnat木eHy野poth覽esis緊,H1:mp<50索0;覺(1t蟲ail另test兇)1.645stderrorAcceptanceareamH0=5000.05ofarea(a)rejectareaTak置ing歲ex炮amp豎le致for崇al土ter圍nat雜eh愧ypo短the趕sis被,H1:mp>5慎00For缸95謹(jǐn)%c奇onf街ide菠nce嘆le連vel促,a=0.委05.Sinc仙eH1iso祖net辟ail撲test披,re說ject智are疾ado今esn求otn杠eed監(jiān)tob雞edi嘴vide牽dby冶2.Fromstandardnormaldistributiontable:Z-valueof1.645willgive0.95area,leavingatobe0.05.Thereforeifmpismorethan500by

1.645stderror,itwillbeintherejectarea,和wewillrejectthenullhypothesisH0,concludingonalternatehypothesisH1thatmpis>500.某些hyp陶oth歲esi紫st臺est燃ing范st滋hat凈ar賤ea傅ppl拆ica損ble貓to尚en就gin女eer育s:The怨impa顛cto巾nre簡spon苦sem禁easu導(dǎo)reme晝ntw絨ith圣new和old流程para鈔mete盡rs.Com丘par貓iso吼no研f告an鑼ew喘ven參dor料s’質(zhì)par攔ts僻(wh罩ich粗ar衫es禾lig向htl值ym轉(zhuǎn)ore梯ex創(chuàng)pen衰siv郊e)腹to法the唇pr適ese塞nt驢ven答dor讓,w枯hen脆va何ria穿tio旅ni織sa小ma銅jor所is警sue隱.Is霞the虛yi釣eld縱on率Te帖ste歇rE衡CTZ晃21昏the田sa辨me萌as鵲the腦yi立eld國on板Te喉ste綢rE嫂CTZ搭33舊?流程Sit押uat賢ion勺sComp強(qiáng)aris哈ono對fon絨epo咸pula翁tion得fro窯ma異sing幼le流程toa湖des爽irab閣les識tand柱ardComp縣aris索ono曾ftw美opo文pula貫tion假sfr荒omt盟wod科iffe沿rent流程esorSing鞠les粘ided戲:co談mpar解ison貿(mào)con去side平rsa冒dif央fere俊nce內(nèi)only此if肢iti飲sgr存eate叮ror劍onl販yif科it鴉isl衣ess,運but忘not浸bot屋h.Two封si埋ded歉:c妖omp旁ari帶son邊co共nsi丘der有sa岔ny惑dif軍fer刃enc掌eo疼fi腸ne質(zhì)量imp仰ort鑰antInf襪ere脾nce界sb遷ase凳do賊na噸si全ngl雀es道amp賀le“Lar粒ge蝦sam雖ple戶te姻st濁of晴hyp蜓oth胃esi嚴(yán)sa嚇bou填tapop藏ula碑tio黎nm果ean”Exa夠mpl鞋e:An疊aut淺omo朗tiv耀em祝anu管fac慨tur老er則wan關(guān)ts攪to甜eva錘lua拼te嘆if零the尼ir生new溉th刪rot嬌tle設(shè)計ona米llt畝hel錢ates俊tca泄rmo且del濱isa香ble罰tog恥ive難ana螞dequ簡ate菜resp疑onse詞tim齡e,r倦esul童ting捉in買anp貧redi描ctab融lep針ick-沃upo財fth若eve緒hicl鳳esp并eed零when舟the浮fue蜜lpe余dal孝isb次eing憂dep主ress爆ed.廈Base給don濤fin論ite音elem啟ent唱mode睡llin巨g,t坐he設(shè)計team物com笨mitt康edt裝hat啞the授thro劣ttle健res僻pons唇eti虹mei六s1.鏡2ms怪ec,和this草is仙the彈reco須mmen航ded滾valu掉eth牙atw你ill竄give河the炸dri與ver壯the足best撫con連trol腳ove寺rth答eve叢hicl滔eac診cele盛rati掘on.The騎test衣eng斗inee狗rof結(jié)thi障spr嫌ojec桑tha捐ste球sted顛on艇100蜻vehi捕cles隙wit壓hth根ene種wth六rott溪le設(shè)計和obta爺ina廊nav勉erag珠eth城rott這ler紅espo屆nse說time恥of柴1.05丙mse四cwi打tha標(biāo)準(zhǔn)偏盼差Sof栽0.5壺mse愛c.B留ased政on券99%直conf捕iden呈cel寺evel軟,ca肅nhe虧con哈clud石edt體hat安the潑new種thro勇ttle設(shè)計wil惰lg跌ive陣an欲av戶era厘ge欲res醋pon搞se堵tim將eo煎f1磚.2節(jié)mse路c?“Lar很ge桶sam虧ple散te鴨st說of韻hyp寶oth瓜esi堂sa宇bou債tapopu栗lati貢onm餡ean”(帝con慈’t)Solution:Sincethesamplesizeisrelativelylarge(i.e.>30),weshouldusezstatistic.m

X=1.05msec; s

S=0.5msec; n=100;NullhypothesisH0:m

=

mH0(1.2msec)AlternatehypothesisH1:m<>mH0(1.2msec)-----AcceptanceArea-----mH0=1.20.005ofarea0.005ofarea(a/2)RejectArea(a/2)RejectArea2.58stderror2.58stderrorFro宇ms裕tan芳dar坦dn朵orm彈al朋dis賣tri咬but靠ion贊ta囑ble堵,The會Z娘val配ue妖cor衫res柏pon奮din情gt鳥o0句.00夕5t體ail另ar清ea晉is2.5見8.a=0果.01再(2t錄ails稍),s于ince西2t鍛ails萄tes齊t,t俯here都fore牢tai鴿lar事ea=a/2隙=0介.00做5;HowmanystderrorisXawayfrom1.2msec?X=1.02ThereforeXis–3stderrorsawayfrom1.2msec.-----AcceptanceArea-----mH0=1.20.005ofarea0.005ofarea(a/2)RejectArea(a/2)RejectArea2.58stderror2.58stderrorX=1.02“Larg插esa住mple經(jīng)tes艙tof敬hyp未othe妹sis辛abou擁tapopu棒lati亞onm隸ean”(桑con檔’t)Baedon99%confidencelevel,sinceXisatthenegativerejectarea,wewillrejectthenullhypothesis和concludeonthealternatehypothesisthattheaverageresponsetimeissignificantlydifferentthan1.2msecTheaverageresponsetimeappearstobelowerthan1.2msec.Wha噸td魯oes描99叢%c碎onf剛ide鄉(xiāng)豐nce拿le君vel篩me奸ans須in畜th慨ea丸bov襖ee次xam臺ple個?Itd勞efin含est堂hel在imit爐swh途ereb幅y99引%of玩the盛ave隆rage惰sam待plin丟gva費lue驚shou巧ldf樓all游with卻in,瞇give置nth待ede唇sira調(diào)ble(hy驕pot闊hes貼ise乖d)mean弟asmH0.A扯ny搬val仿ue尋fal宵lo夕uts畝ide夠th狹is竹con殿fid抗enc辭el援imi厲ti吳ndi智cat泳es教the莫sa工mpl題emeanis咸sig著nif第ica極ntl膀yd泡iff乏ere兆nt撥fro衡mmH0.In愉oth目erw熟ords問,we賺wil右lon種lyc糖oncl次ude每the儀alte顯rnat凈ehy口poth塌esis燙H1(th傭at吩the另me舒ans翼ar臨ed遺iff兔ere節(jié)nt)松if濟(jì)we版ar御em預(yù)ore旗th檢an桑99%煤su帳re.The勻Ob辟ser捷ved伏Si貼gni滿fic騰anc長el計eve示l,惠p-v授alu核ep-v趕alu缸ei路st園he擋pro斯bab呢ili忍ty轟for額co谷ncl符udi酒ng毛the秒nu亞ll起hyp猛oth躺esi鴨sH0that桐bot茂hpo擠pula塞tion觀mea盡nsa意ree徑qual真wit牽hth灶eob條serv滋eds敬ampl椒eda鴿ta.映Henc竄e1炊–pv隊alue六wil桂lbe株the閑con主fide兆nce帶leve資lwe其hav細(xì)eon時the摔alt范erna洪teh樣ypot愁hesi飯s.--AcceptanceArea--mH0=1.22.58stderror2.58stderrorX=1.023stderrorP/2AcceptanceAreamH0=1.22.58stderrorX=1.023stderrorPFor2tailstestFor1tailtest