Lecture17

Lecture17 - Lecture17 Stat350 7.5ConfidenceIntervalsfor...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture17 Stat350 7.5ConfidenceIntervalsfor TwoPopula>onMeans Announcement Homework7(DueFridayMar11) Chapter7:25,26,30,31,34,49,50,55,76,78 Exam2 Date:April7(Thursday) Time:6:30PM7:30PM LYNNHall1136(SameRoom) Example1 Inarandomsampleof85automobileengine crankshaZbearings,10haveasurfacefinish thatisrougherthanthespecifica>onsallow. A)Whatisapointes>mateofthepropor>on ofbearingsinthepopula>onthatexceedsthe roughnessspecifica>on? B)Finda95%confidenceintervalforthe propor>onofbearingsinthepopula>onthat exceedstheroughnessspecifica>on. Solu>on Pointes>mateforisp=10/85=0.12 A95%CIforis 0.12(1.96)*0.12*0.88/85 A95%CIforis(0.05,0.19) Note:theCIiswide Example2 ConsiderExample1.Howlargeasampleis requiredifwewanttobe95%confidentthat theerrorinusingptoes>mateislessthan 0.05? A)usep=0.12asanini>ales>mateof B)Findthesamplesizeregardlessofthevalue of Example3 Supposethatamodifica>onismadeinthe surfacefinishingprocessandsubsequently,a secondrandomsampleof85bearingis obtained.Thenumberofdefec>vebearingsin thissecondsampleis8. Finda95%confidenceintervalonthe differenceinthepropor>onofdefec>ve bearingsproducedunderthetwoprocesses TwoSamplePropor>ons Requireslargesamplesizesonboth popula>ons(i.e.n1>30andn2>30) p1 (1- p1 ) p2 (1- p2 ) p1 - p2 Zcrit + n1 n2 TwoSamplePropor>ons Solu>ontoExample3: p1 (1- p1 ) p2 (1- p2 ) p1 - p2 Zcrit + n1 n2 0.12(1- 0.12) 0.09(1- 0.09) = (0.12 - 0.09) (1.96) * + 85 85 = 0.03 0.09 A95%CIfor12is(0.06,0.12) Prac>calInterpreta>on A95%CIfor12is(0.06,0.12) ThisCIincludeszero.Basedonthesample data,itisunlikelythatthechangesmadein thesurfacefinishprocesshavereducedthe propor>onofdefec>vecrankshaZbearings beingproduced SummaryofCIs IntervalEs>ma>onofPopula>onParameters Doesnotmakeadecisiondirectly SampleSizemajers: LargeSamples:Noassump>ononthepopula>on distribu>on SmallSamples:Popula>ondistribu>onsmustbe approximatelynormal(Howtoverify?) Lab3Problem1(c) Supposeyourfriendclaimsthatthemeanweightofthedogsis60 lbs.Doyoubelievehim?Explainhowyouaredeterminingyour beliefreferencingtheconfidenceintervalyoucreated. SASoutput: TheTTESTProcedure Variable:weight N Mean StdDev StdErrMinimumMaximum 12 48.4083 12.8236 3.701928.200067.3000 Mean 99%CLMean StdDev99%CLStdDev 48.4083 36.9111 59.9056 12.82368.222226.3603 ReadingSASoutput TheTTESTProcedure Variable:weight N Mean StdDev StdErr MinimumMaximum 12 48.4083 12.8236 3.701928.200067.3000 Mean 99%CLMean StdDev 99%CLStdDev 48.4083 36.9111 59.9056 12.82368.222226.3603 Sample Size: n=12 Sample mean: 48.41 99% CI for is (36.91, 59.91) Sample Standard DeviaFon: 12.82 Sample Standard Error: 12.82/sqrt(12) =3.7 99% CI for is (8.22, 26.36) Chapter8:HypothesesTes>ng ConfidenceIntervals Es>mateanunknownpopula>onparameter. Givearangeofplausiblevaluesofthetrueparameter. Doesnotmakeadecisionexplicitely HypothesisTests(DecisionMaking) Assesstheevidenceprovidedbythedatainfavorofor againstsomeclaim(calledahypothesis)aboutthe populaFon... 8.1HypothesesandTestProcedures Asta$s$cal hypothesisisaclaimorasser>on aboutapopulaFon parameter(s) Example Parameter: =theaverageweightofall2yearolddogsofa par>cularbreed Hypothesis: =60(lbs) ExampleofSta>s>calHypotheses Parameters: 1=trueaveragelife>meforapar>cularname brand>re(miles) 2=trueaveragelife>meforalessexpansive storebrand>re(miles) Hypothesis: 12>10,000(miles) ExampleofSta>s>calHypotheses Parameter: =propor>onofemailsfromacertainsystemthat areundeliverable Hypothesis: <0.01(or1%) StatementofHypotheses Sta>s>calHypothesis: Ontheparametersina populaFon NOTonthesta>s>csofthesampledata Example(ex1from8.1):Statewhether eachofthefollowingasser>onisa legi>matesta>s>calhypothesisandwhy? A)H:>100 C)H: B)H: D)H:s0.50 E)H:1/2<1 Whatisatest of hypotheses? Amethodforusingsample data todecide betweenthetwocompe>nghypothesesunder considera>on Consider: Whatdoesthehypothesissayabouttheparameter? Whatdoesthesamplesuggestabouttheparameter? Dotheyagreeordisagree? Theresultsofatestmeasureshowwellthedata andthehypothesisagree. NullandAlterna>veHypotheses Twohypothesesinates>ngofhypotheses: H0 :thenullhypothesis Ha :thealterna>vehypothesis [DefiniFons] H0 Thenullhypothesisistheasser>onthatis ini>allyassumedtobetrue. Ha Thealterna>vehypothesisistheclaim thatcontradictorytoH0 NullHypothesis Thenullhypothesiswillberejectedinfavorofthe alterna>vehypothesisonlyifsampleevidence suggeststhatH0isfalse. IfthesampledoesnotstronglycontradictH0,wewill con>nuetobelieveinthetruthofthenull hypothesis. Thetestofsignificanceisdesignedtoassessthe strengthoftheevidenceagainstthenullhypothesis. ...
View Full Document

Ask a homework question - tutors are online