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Lecture

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

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1/9/2011
1
QMS202
BUSINESSSTATISTICSII
InferentialStatistics
allowsyoutoestimateunknown
populationcharacteristics,i.e.population
meanorpopulationproportion
Dr.Chua
OFFICE:TRS1r030
EMAIL:qms102@ryerson.ca
TheSubjectfieldofeachemailshouldbecarefullycompleted,e.g.QMS202:sick.
Itisrequestedthatemailsbesenttotheprofessoronlyifthequestion(s)being
askedcannotwaittobeansweredinthenextscheduledlecture.Ortheanswers
cannotbe
f
oundinthecourseoutline.
f
OfficeHours:
Byappointmentonly
WhatarerequiredforQMS202?
1. Requiredtextbook
BusinessStatistics,ATworSemesterTextforBusiness
Management,SeventhCustomEditionforRyerson
University,CompiledbyDarrylSmithandClareChua
PrenticeHall,2010
2Rid
Cl lt
2
.
R
equ
i
re
d
C
a
l
cu
l
a
t
or
CASIOFXr9750GII
CasioFXr9750Gplusisacceptable
TIr83calculatormaybeusedinthecourse.Howeverthe
professorwillnotbesupportingitinclass.Youare
responsibleforknowinghowtousetheTIr83functions.
3. StatisticalsoftwarerSPSS
MethodofEvaluation
Component Percent/
Weight
Number of
Crib sheet
allowed
8.5x11inchcrib
sheet(tworsided)
Date
Quiz #1 12%
one
Week 4*
Test 20%
one
Week 8*
Qi #2
13%
one
Wk 11
*
Q
u
i
z
#2
13%
one
W
ee
k 11
*
Group
project
(SPSS)
5% Week 10*
Final Exam 50%
three
TBA
TOTAL 100% *Please refer
to handout for
the testdates
TOPICS–SEQUENCE&SCHEDULE
Week Topic Activities &
Assignments
1 to 2Standardized normal
random variable Z.
Confidence Intervals
Chapter 6
Handouts and
chapter 9 in the
textbook.
Answer questions in
handouts and
questions in ch.9 of
the textbook.
3 to 4Fundamentals of
Hypothesis Testing:
One-Sample Tests
Handouts and
chapter 10 in the
textbook.
Answer questions in
handouts and
questions in ch.10 of
the textbook.
5 to 7Two-Sample Tests
d O
Handouts and
ht
11
i th
Answer questions in
hdt d
an
d O
ne-
a
.c
h
a
pt
er
11
i
n
th
e
textbook.
h
an
d
ou
t
s
an
d
questions in ch.11 of
the textbook.
8 to 9Chi-Square Tests Handouts and
chapter 12 in the
textbook.
Answer questions in
handouts and
questions in ch.12 of
the textbook.
10 to 11 Simple Linear
Regression Handouts and
chapter 13 in the
textbook.
Answer questions in
handouts and
questions in ch.13 of
the textbook.
12 Introduction to
Multiple RegressionChapter 14 Answer questions in
handouts.
13 Review
Statisticscanbe….
Descriptive
_collectinganddescribingthedata
rCollectDatae.g.survey<SourcesofData>
rPresentDatae.g.TablesandGraphs<Chapter2>
rCharacterizeData<NumericalDescriptivemeasures>
QMS102
Inferential
istheprocessofusingsampleresultstodrawconclusion
aboutthecharacteristicsofapopulation.
Estimation isusedtoestimatepopulationparameters
Enablesustoestimateunknownpopulationcharacteristicssuchasa
populationmeanorapopulationproportion
HypothesisTesting
QMS202
www.notesolution.com
1/9/2011
2
WhatIwillbecoveringforthenext
1½weeks?
Chapter9
ConfidenceIntervalEstimation
Topicscovered:
ConfidenceIntervalEstimationfortheMean(known)
ConfidenceIntervalEstimationfortheMean(unknown)
ConfidenceIntervalEstimationfortheProportion
DeterminingSampleSize
Confidence Interval
Estimation
Population Mean PPopulation Proportion E
X Normal and/or nt30?
If no stop.
np t5 and n(1-p) t5?
If no stop.
Quantitative Data Qualitative Data
Vknown? Vunknown?
Limits: Limits:
df=n-1
n
1
zx r
Limits:
p=x/n
n
s
txr
n
)p1(p
zp
r
Two things you need to find: (1) Confidence Interval and (2) Sample size
ESTIMATION
TWOtypesofestimatesusedto
estimatepopulationparameters:
(1) Pointestimate(example:Cx,p)
(2) Intervalestimate
PointestimaterMarginofError
Estimations
x
Whatisapointestimate?
isavalueofasinglesamplestatistics.
Example:samplemean,,isapoint
estimateofthepopulationmean,P
sampleproportion,p,isapoint
estimateofthepopulationproportion,
E.
Whatisintervalestimate?
isarangeofnumbers,calledaninterval,
ttddth it
S
Population
Parameters
Sample
Estimators
sampling Cx
p
cons
t
ruc
t
e
d
aroun
d
th
epo
i
n
t
estimate.
Theconfidenceintervalisconstructed
suchthattheprobabilitythe
populationparameterislocated
somewherewithintheintervalis
known.
S
s
Inference
PointestimaterMarginError
S
Population
Parameters
Sample
Estimators
sampling Cx
s*
x
errordardtans*x
errordardtans*confidencex
z
z2/
V
r
r
r
D
ConfidenceIntervalEstimationfortheMean
S
p
Inference
n
x
z
2/
r
D
PointestimateMarginError
www.notesolution.com
1/9/2011
3
ConfidenceIntervalEstimation
S
Population
Parameters
Sample
Estimators
sampling Cx
p
EXAMPLE
Supposeyouareaskedtoestimate
themeanheightofALLthe
studentswhotaketheQMS202
courseinWinter2011.
Themeanheightofallthe
studentsisanunknown
S
s
Inference
populationmean,denotedbyP.
Yourandomlyselectasampleof10
studentsandfoundthatthe
samplemean,CX,is___,whichis
thepointestimateofthe
populationmean,P.
Howaccurateismyestimateof
_____?
Toanswerthisquestion,youmust
constructaconfidenceinterval
estimate.
ConfidenceIntervalEstimation
S
Population
Parameters
Sample
Estimators
sampling Cx
p
EXAMPLE
Population:ALLthestudentsin
theclass(150students)
POPULATIONDATA:heightmeasurement
are______________________.
Thepopulationmeantestscore,µ,=
S
s
Inference
_
____
Samplesize=10students
Data:<Note:datawillbegiveninclass>
SampleMean=CX=<meanwillbe
calculatedinclass>
Objective
Learnhowtoconstructconstruct andinterpretinterpret
confidenceintervalestimates
n
*x z2/
V
rD
5.621.42 dd
P
Interpretation:Interpretation:
A95%confidenceintervalforthepopulationaverage
(mean) testscoreis(42.1,62.5).
Note:DefineXorNote:DefineXor
ConstructConstruct
95%CI95%CI
Beforelearningtoconstructthe
confidenceinterval,youneedto
know;
know;
1. CentralLimitTheorem
2. Zrvalue
Note:
WeusedCxtoestimate.Therefore,ourobjectiveistousethesampling
distributionofCxtosaysomethingabout.
CentralLimitTheorem
Assumethatthepopulationfromwhichwewillrandomlyselecta
sampleofnmeasurementshasameanPandstandard
deviationV.Thenthepopulationofallpossiblesamplemeans
has:
1. Mean:
2. standarddeviation:
P Px
n
x
V
V
3a.Ifpopulationofindividualmeasurementsis
normal,isnormal
3b.Ifpopulationofindividualmeasurements
isnotnormal,isnormalifsamplesizeis
largeenough(nt30)
x
x
Beforelearningtoconstructthe
confidenceinterval,youneedto
know;
know;
1. CentralLimitTheorem
2. Zrvalue
Note:
Weusedxtoestimate.Therefore,ourobjectiveistousethesampling
distributionofxtosaysomethingabout.
www.notesolution.com

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Description
192011 Dr.Chua OFFICE:TRS1H030 QMS202 EMAIL: qms102 @ryerson.ca TheSubjectfieldofeachemailshouldbecarefullycompleteQMS202. :sick. Itisrequestedthatemailsbesenttotheprofessoronlyifthequestion(s)being BUSINESSSTATISTICSII askedcannotwaittobeansweredinthenextscheduledlecture.Ortheanswers cannotbeffoundinthecourseoutline. OfficeHours: InferentialStatistics Byappointmentonly allowsyoutoestimateunknown populationcharacteristics,i.e.population meanorpopulationproportion MethodofEvaluation WhatarerequiredforQMS202? Component Percent Number of Date Crib sheet Weight 1. Requiredtextbook allowed 8.5x11inchcrib BusinessStatistics,ATwoHSemesterTextforBusiness sheet(twoH sided) Management,SeventhCustomEdition forRyerson Quiz #1 12% one Week 4 * University,CompiledbyDarrylSmithandClareChua Te st 20% one Week 8 * PrenticeHall,2010 onee 2.RequiiredCallcullattor Quiiz ##22 13%% Weekk 11 1 1** CASIOFXH9750GII Gro up 5% Week 1 0* Casio FXH9750Gplus isacceptable project TIH83calculatormaybeusedinthecourse.Howeverthe professorwillnotbesupportingitinclass.Youare (SPSS) Fin al Exam 50% three TBA responsibleforknowinghowtousetheTIH83functions. 3. StatisticalsoftwareH SPSS TO TAL 100% * Ple ase re fe r to ha ndoutfor the test da tes TOPICS SEQUENCE&SCHEDULE Week Topic Acti vi ti es & Assi gnm ents Statisticscanbe. 1 t2 St andard ized n orma lt er 6 Ans w er ques tio ns in ra ndom v ari ableHa nd out s a nd hando uts and Conf idenc e Int et ex t book.he t he t ex t book..9 o Descriptive _collectinganddescribingthedata 3 t4 Fundamentalo f Ha nd out s a nd Ans w er ques tio ns in Hypo thes is Tes t ing:e10 in the hando uts and H CollectDatae.g.sur On e-Samp le T est sex t book. t he t ex t book.h.10 of QMS102 H PresentDatae.g.TablesandGra H CharacterizeDat 5 t7 Tw o-Sam ple Tes tHa nd out s a nd Ans w er ques tio ns in an dd OW ayAANNOOVchhaptt er 1111 iihhanddou tt s andd t ex t book. t he t ex t book.h.11 of Inferential 8 t9 Chi- Squa r e TestHa nd out s a nd Ans w er ques tio ns in istheprocessofusingsampleresultstodrawconclusion t ex t book.the quest ion s in c h.12 of aboutthecharacteristicsofapopulation. t he t ex t book. Estimation isusedtoestimatepopulationparameters 10 t11 Sim ple L inea r Ha nd out s a nd Ans w er ques tio ns in QMS202 Enablesustoestimateunknownpopulationcharacteristicssuchasa Regr essi on t ex t book.the quest ion s in c h.13 of populationmeanorapopulationproportion t he t ex t book. HypothesisTesting 12 Multiple Res sionoCha pt er 14 hando uts .es tio ns in 13 Review 1 www.notesolution.com 192011 WhatIwillbecoveringforthenext Chapter9 1weeks? ConfidenceIntervalEstimation Topicscovered: ConfidenceIntervalEstimationfortheMean(known) ConfidenceIntervalEstimationfortheMean(unknown) ConfidenceIntervalEstimationfortheProportion DeterminingSampleSize Confidence Interval Estimation Quantitative Data Qualitative Data Population Mean 2 Population Proportion - ESTIMATION X Normal andor nJ30? np J 5 and n(1-p) J 5? If no stop. If no stop. TWOtypesofestimatesusedto 8 known? 8 unknown? estimatepopulationparameters: Limits: p H zp(1 p) (1)Pointestimate(example:+x,p) p=xn n (2)Intervalestimate x H z s Limits: n Limits:x H t df=n-1 n PointestimateH MarginofError Two things you need to find: (1) Confidence Interval and (2) Sample size Estimations Whatisapointestimate? PointestimateH MarginError isavalueofasingle samplestatistics. Example:samplemeanx,isapoint ConfidenceIntervalEstimationfortheMean estimateofthepopulationmean,2 Sample sampleproportion,p,isapoint Sample x Hconfidence*standard error Population Estimators estimateofthepopulationproportion, Population Estimators Parameters -. Parameters x H *standard error sampling +x Whatisintervalestimate? sampling +x z,2 5 p isarangeofnumbersalledaninterval, 5 s 8 s consttrudaroudthepoiintt p x H z,2* estimate. n Theconfidence intervalisconstructed suchthattheprobabilitythe populationparameterislocated Pointestimate MarginError Inference known.erewithintheintervalis Inference 2 www.notesolution.com
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