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Lecture 4

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Quantitative Methods
QMS 202
Clare Chua

1/30/2011 Howtomakestatisticaldecision? Lecture4 HypothesisTesting:Onesample Ifa.05levelofsignificanceisusedina(twoH tailed)hypothesistest,whatwillyoudecideif thecomputedvalueoftheteststatisticis +22.21 Objectives: 1. Hypothesistestforµ when isunknown(tHtest) 0.025 0.025 2. Hypothesistestfor5 Z -1.96 0 1.96 +2.21 Note: the assumption, that doesn havemean we ignore it. We to consider it at all times. Hypothesistestforµ when isunknown tHtestt Onesample THtestofHypothesisfortheMean • Ifwedonotknowthepopulationstandarddeviation,  Hypothesistestforµ • Weusethesamplestddeviation,s. when isunknown • IIweeassumeehaatthepoop.snormaalydisributed,, thesamplingdist.ofthemeanwillfollowat distributionwithnH1 degoffreedom. • IfthepopisNOT normallydist.,youcanusethetH testifthemplesizeislarge(n>30)enoughforthe THtest CLTtotakeeffect. 1 1/30/2011 EXAMPLE tTestofHypothesisFortheMean(8 Anewbatteryhasbeendevelopedtopowerlaptop unknown) computers.Itwillsellinacertainpricerange.Itis hopedthatthebatterycanbeusedformorethan x 2 4.00hours beforeitneedstoberecharged.Wewill t assumethatthebatterylivesarenormally s distributed.Arandomsampleof50batteriesis testedd.Theesamp plebaatteriessasteddanaaverrageeoff n 4.12hourswithastandarddeviationof0.25hours beforetheyrequiredrecharging.LetH=0.05 Where the test statistic t follows a t-distribution having n-1 degrees of freedom SAMPLEMEANANDSAMPLE STDDEV(s) Whattestdoyouperform? Ztestorttest? ThesevenHstepMethodofHypothesisTesting Steps (or the thought process) 1. Identifythevariableofinterest,Xor… 1. Clearly identify the variable of Let X=the life (hours) of a battery. 2. StateNullHypothesis,HoandAlternativeHypothesis,Ha interest. 3. Determinetheappropriatetest(refertotheflowchart) 2. Null Hypothesis Ho: µ=4.00 4. Statetheassumptions 5. DeterminethecriticalvaluethatdividetherejectionandnonHrejection more than 4.00 hours? region Alternative hypothesis Ha: µ>4.00 6. Calculatetheteststatisticvalue 3. Determinetheappropriatetest(reT-test 7. MakethestatisticaldecisionandManaalconclusion. totheflowchart)Hgiven 4. What assumption(s) are made to None since n>30 perform this test? 5. DeterminethecriticalvaluethatdGiven 5% significance level. therejectionandnonHrejectionregion A one tailed test 6. Calculatetheteststatisticvalue/pHvalue Use the Casio Calculator 7. Makethestatisticaldecisionand Managerialconclusion. CFXH9850GBCalculator Ho: µ = µ0 Two Tailed Test Ha: µ  µ0 ,/2 ,/2 Lesson9– tHTestofasingleMean STATF3(test) F2(t) F1(1HS)thenenterthefollowingitems: (Noaccidentallyhitthewrongkey,useAC/ON orEXIT togoback.)thecursorz arrow.Ifyou Rejection Region 1HSampletTest Rejection Region Data :F2(Var)z … :F3(>)z …0 :4EXE Ho: µ = µ ONE TAIL TEST x :4.12EXE 0 RIGHT Tailed Test , nnH1 :50EXE Ha: µ > 0 NowkeyEXE orF1(Calc) Rejection Region Thecalculatorwillnowshowtheresults: ONE TAIL TEST 1HSampletTest Ho: µ = 0 t =3.3941 Ha: µ < 0 LEFT Tailed Test , p =6.85
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