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Lecture

Lecture 4

4 Pages
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Department
Quantitative Methods
Course Code
QMS 202
Professor
Clare Chua

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1/30/2011
1
Lecture4
HypothesisTesting:Onesample
Objectives:
1. Hypothesistestforµ
whenisunknown(trtest)
2. HypothesistestforS
Howtomakestatisticaldecision?
Ifa.05levelofsignificanceisusedina(twor
tailed)hypothesistest,whatwillyoudecideif
thecomputedvalueoftheteststatisticis
+2 21
+2
.
21
0.025 0.025
0-1.96 1.96
+2.21
Z
Hypothesistestforµ
whenisunknown
t
tt
t
r
t
es
t
Onesample
Note:
I sometimes didn’t mention
the assumption, that does
not mean we ignore it. We
have
to consider it at all times.
Hypothesistestforµ
whenisunknown
Trtest
TrtestofHypothesisfortheMean
Ifwedonotknowthepopulationstandarddeviation,
Weusethesamplestddeviation,s.
If we assume thatthe pop. is normally distributed,
If
we
assume
that
the
pop.
is
normally
distributed,
thesamplingdist.ofthemeanwillfollowat
distributionwithnr1degoffreedom.
IfthepopisNOTnormallydist.,youcanusethetr
testifthesamplesizeislarge(n>30)enoughforthe
CLTtotakeeffect.
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Description
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 www.notesolution.com 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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