概率统计-中文概统课件lecture

1Lecture20PairedttestComparingtheMeansofTwoNormalDistributionsReviewSupposethatX1,…,Xnformarandomsamplefromanormaldistributionforwhichthemeanmisunknown,butthevarianceisknown.Considertestingthehypotheses:

ororLet.Youcansimilarlyderivethe criticalregionsas:ReviewSupposethatX1,…,Xnformarandomsamplefromanormaldistributionforwhichthemeanmisunknown,butthevarianceisunknown.Considertestingthehypotheses:

ororLet.Youcansimilarlyderivethe criticalregionsas:Review:p-值：衡量拒绝原假设的强度通过计算一个概率，即p-值，来判断我们观测到的样本在H0成立的条件下，是否是偏向H1的。

如果p-值很小，则认为我们的样本不太可能在原假设的情况下产生的，应该拒绝原假设。

教学改革以前，MBA教学评估的长期平均水平为4.2。当前收集的教学评估涉及118门课程，其中有52门MBA课程，它们教学评估的平均水平为4.34，标准差为0.54。问题：MBA教学质量比以往提高了吗？H0：MBA教学平均分等于4.2。Ha：MBA教学平均分大于4.2（MBA教学质量比以往提高了）。求p-值。Example用p-值得好处p-值是根据我们观察到的数据，我们将拒绝H0的最小水平。如果p-值比显著性水平小，我们拒绝原假设。统计软件的标准输出。不用预先指定显著性水平。研究者A采用显著性水平0.01，而研究者B采用显著性水平0.05。Matched-sampledesign:e.g.Wewanttocompare2productionmethods.Before/after: e.g.Inaproductionexperiment,eachworkerfirstusesoneproductionmethodandthenusesproductionmethod2. Variationbetweenworkersiseliminatedasasourceofsamplingerror.Paired: e.g.Inaproductionexperiment,eachalloyisdividedinto2parts.Productionmethod1isusedononepart,andproductionmethod2isusedonanotherpart.

Variationbetweenalloysiseliminatedasasourceofsamplingerror.ThePairedtTestConsiderAssuming

then

Assumeyouworkinthefinancedepartment.Isthenewfinancialpackagefaster(0.05level)?Youcollectthefollowingdataentrytimes:PairedtTest:Example

User

CurrentLeader(1)

NewSoftware(2)

Difference

DiC.B. 9.98Seconds 9.88Seconds .10T.F. 9.88 9.86 .02M.H. 9.84 9.75 .09 R.K. 9.99 9.80 .19M.O. 9.94 9.87 .07D.S. 9.84 9.84 .00S.S. 9.86 9.87 -.01C.T. 10.12 9.86 .26K.T. 9.90 9.83 .07S.Z. 9.91 9.86 .05Isthenewfinancialpackagefaster(0.05level)?Alevela0

=.05ttestrejectH0ifTheteststatisticiscalculatedasReject

a0=.051.8331Decision:RejectH0Conclusion:

Thenewsoftwarepackageisfaster.ComparingtheMeansof

TwoNormalDistributionsSupposethatX1,…,Xmformarandomsampleofmobservationsfromanormaldistributionforwhichboththemeanm1andthevarianceareunknown,supposealsothatY1,…,Ynformarandomsampleofnobservationsfromanormaldistributionforwhichboththemeanm2andthevarianceareunknown.Supposethefollowinghypothesesaretobetestedataspecifiedlevelofsignificancea0

:DefineTheteststatisticwewilluseisWewillconsiderthetestthatrejectsH0whenWhenm1=m2,wehaveBecauseareindependent,ZandW

areindependent.Sowhenm1=m2,thestatistic

willhaveatm+n-2distribution.Notethat SothesizeofthetestisGivenasignificancelevela0,wecanchooseaconstantcsuchthat

Arandomsampleof8specimensoforeiscollectedfromacertainlocationinacoppermine,andthattheamountofcopperineachspecimenismeasuresingrams.Wedenotethese8amountsbyX1,…,X8.Supposethatitisfoundthatand .Anotherrandomsampleof10specimensororeiscollectedfromanotherpartofthemine,andtheamountsofcopperinthesespecimensaredenotedbyY1,…,Y10.Supposethatitisfoundthatand

ExampleLetm1denotethemeanamountofcopperinalltheoreatthefirstlocationinthemine,andletm2denotethemeanamountofcopperinalltheoreatthesecondlocation.WeshallcarryoutanttestofthehypothesesExample Solution:Assumethatalltheobservationshaveanormaldistributionandthatthevarianceisthesameatbothlocationsinthemine.Then Itcanbefoundthatthep-valueis Sothenullhypothesiswillberejectedforanyspecifiedlevelofsignificancea0>0.00167.TheOtherOne-SidedHypotheses

andTwo-SidedHypothesesIfwewanttotestthehypotheses Thelevela0

ttestrejectsH0whenIfwewanttotestthehypotheses Thelevela0

ttestrejectsH0when案例：老字号

从20世纪80年代中期以后开始，至今没有停止，老字号在西方先进经营理念和多种业态的冲击下，相继崩溃。有资料显示，国内贸易部曾于1990年认定的1600多家中华老字号企业，现在勉强维持的占70%；长期亏损、面临倒闭或已经倒闭的占20%；生产经营达到一定规模、效益良好的仅有10%。很多老字号企业由于没有及时调整内部机制、进而逐步丧失了竞争优势，市场份额日趋缩减，导致生存困难。

记得北京城的那首民谣：头戴马聚源，脚踩内联升，身穿瑞蚨祥，腰缠四大恒。到如今，这已成为历史写照。老字号的消失，实际上是一种历史文化的消失，它就像文物古迹一样需要后人的精心关心和爱护.扬州的谢馥春鸭蛋香粉

谢馥春背景创建于1830，已有近200年历史是中国第一家化妆品企业1915年与“茅台酒”同获巴拿马国际博览会大奖

如何最大限度地发挥怀旧营销的溢出？广告文本:A广告文本:B广告文本:C广告文本:D非常不可能比较不可能一般比较可能非常可能您购买的可能性12345抽样结果TreatmentGroupSampleSizeSampleMeanSampleSDControl903.200.90A913.881.19B943.221.00C923.271.18D954.210.97讨论各个广告的侧重点是什么?哪个最好?你确信吗?总体和样本?你的决策？Controlvs.D.样本容量:样本均值:样本均值差异:实际工作中常常需要在两个对立的决策中选择一个！！！从样本中我们观察到的样本均值差异:对于总体，我们需要决策：样本均值差异是什么原因产生的？Bonus

Problem：Bamberger’s百货公司Bamberger‘s百货公司成立于1947年，是一家为社区提供大众性商品的零售商店，长期以来，Bamberger’s的口碑一直很好。它的顾客主要是中高收入的工薪家庭。Bamberger's的顾客服务有着极好的声誉，针对每一位顾客的需要