APPENDIX
651
14.7SymbolsandtheirMeanings
14
SymbolsandtheirMeanings
Chapter(1stused)
Symbol
Spoken
Meaning
SamplingandData
p
Thesquarerootof
same
SamplingandData
p
Pi
3.14159... (a specific
number)
DescriptiveStatistics
Q1
Quartileone
thefirstquartile
DescriptiveStatistics
Q2
Quartiletwo
thesecondquartile
DescriptiveStatistics
Q3
Quartilethree
thethirdquartile
DescriptiveStatistics
IQR
inter-quartilerange
Q3-Q1=IQR
DescriptiveStatistics
x
x-bar
samplemean
DescriptiveStatistics
m
mu
populationmean
DescriptiveStatistics
ss
x
sx
s
samplestandarddevia-
tion
DescriptiveStatistics
s
2
s
2
x
s-squared
samplevariance
DescriptiveStatistics
ss
x
sx
sigma
population
standard
deviation
DescriptiveStatistics
s2s2
x
sigma-squared
populationvariance
DescriptiveStatistics
S
capitalsigma
sum
ProbabilityTopics
fg
brackets
setnotation
ProbabilityTopics
S
S
samplespace
ProbabilityTopics
A
EventA
eventA
ProbabilityTopics
P(A)
probabilityofA
probabilityofA occur-
ring
ProbabilityTopics
P(AjB)
probabilityofAgivenB
prob. of f A A occurring
givenBhasoccurred
ProbabilityTopics
P(AorB)
prob.ofAorB
prob. ofAorBorboth
occurring
continuedonnextpage
14
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652
APPENDIX
ProbabilityTopics
P(AandB)
prob.ofAandB
prob. ofbothAandB
occurring(sametime)
ProbabilityTopics
A
A-prime, complement
ofA
complementofA,notA
ProbabilityTopics
P(A)
prob.ofcomplementof
A
same
ProbabilityTopics
G
1
greenonfirstpick
same
ProbabilityTopics
P(G
1
)
prob. ofgreenonfirst
pick
same
Discrete Random Vari-
ables
PDF
prob.distributionfunc-
tion
same
Discrete Random Vari-
ables
X
X
therandomvariableX
Discrete Random Vari-
ables
X
thedistributionofX
same
Discrete Random Vari-
ables
B
binomialdistribution
same
Discrete Random Vari-
ables
G
geometricdistribution
same
Discrete Random Vari-
ables
H
hypergeometricdist.
same
Discrete Random Vari-
ables
P
Poissondist.
same
Discrete Random Vari-
ables
l
Lambda
averageofPoissondis-
tribution
Discrete Random Vari-
ables
greaterthanorequalto
same
Discrete Random Vari-
ables
lessthanorequalto
same
Discrete Random Vari-
ables
=
equalto
same
Discrete Random Vari-
ables
6=
notequalto
same
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APPENDIX
653
Continuous
Random
Variables
f(x)
fofx
functionofx
Continuous
Random
Variables
pdf
prob.densityfunction
same
Continuous
Random
Variables
U
uniformdistribution
same
Continuous
Random
Variables
Exp
exponential
distribu-
tion
same
Continuous
Random
Variables
k
k
criticalvalue
Continuous
Random
Variables
f(x)=
fofxequals
same
Continuous
Random
Variables
m
m
decay rate e (for exp.
dist.)
The Normal l Distribu-
tion
N
normaldistribution
same
The Normal l Distribu-
tion
z
z-score
same
The Normal l Distribu-
tion
Z
standardnormaldist.
same
The CentralLimitThe-
orem
CLT
CentralLimitTheorem
same
The CentralLimitThe-
orem
X
X-bar
therandomvariableX-
bar
The CentralLimitThe-
orem
m
x
meanofX
theaverageofX
The CentralLimitThe-
orem
m
x
meanofX-bar
theaverageofX-bar
The CentralLimitThe-
orem
s
x
standarddeviationofX
same
The CentralLimitThe-
orem
s
x
standard deviation of
X-bar
same
The CentralLimitThe-
orem
SX
sumofX
same
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654
APPENDIX
The CentralLimitThe-
orem
Sx
sumofx
same
ConfidenceIntervals
CL
confidencelevel
same
ConfidenceIntervals
CI
confidenceinterval
same
ConfidenceIntervals
EBM
errorboundforamean
same
ConfidenceIntervals
EBP
error bound for a a pro-
portion
same
ConfidenceIntervals
t
student-tdistribution
same
ConfidenceIntervals
df
degreesoffreedom
same
ConfidenceIntervals
t
a
2
student-twitha/2area
inrighttail
same
ConfidenceIntervals
p
^
p
p-prime;p-hat
sample proportion n of
success
ConfidenceIntervals
q
^
q
q-prime;q-hat
sample proportion n of
failure
HypothesisTesting
H
0
H-naught,H-sub0
nullhypothesis
HypothesisTesting
H
a
H-a,H-suba
alternatehypothesis
HypothesisTesting
H
1
H-1,H-sub1
alternatehypothesis
HypothesisTesting
a
alpha
probabilityofTypeIer-
ror
HypothesisTesting
b
beta
probability of Type e II
error
HypothesisTesting
X1
X2
X1-barminusX2-bar
difference in sample
means
m
1
m
2
mu-1minusmu-2
difference in popula-
tionmeans
P
1
P
2
P1-prime minus s P2-
prime
difference in sample
proportions
p
1
p
2
p1minusp2
difference in popula-
tionproportions
Chi-Square
Distribu-
tion
X
2
Ky-square
Chi-square
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APPENDIX
655
O
Observed
Observedfrequency
E
Expected
Expectedfrequency
Linear Regression and
Correlation
y=a+bx
yequalsaplusb-x
equationofaline
^
y
y-hat
estimatedvalueofy
r
correlationcoefficient
same
e
error
same
SSE
SumofSquaredErrors
same
1.9s
1.9timess
cut-off value e for out-
liers
F-Distribution
and
ANOVA
F
F-ratio
Fratio
Table14.17
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656
APPENDIX
14.8Formulas
15
Formula14.1:Factorial
n!=n(1)(2)...(1)
0!=1
Formula14.2:Combinations
n
r
=
n!
(n r)!r!
Formula14.3:BinomialDistribution
XB(n,p)
P(X=x)=
n
x
p
x
q
n x
,forx=0,1,2,...,n
Formula14.4:GeometricDistribution
XG(p)
P(X=x)=q
1
p,forx=1,2,3,...
Formula14.5:HypergeometricDistribution
XH(r,b,n)
P(X=x)=
(
r
x
)
b
n x
r+b
n
!
Formula14.6:PoissonDistribution
XP(m)
P(X=x)=
m
x
e
m
x!
Formula14.7:UniformDistribution
XU(a,b)
f(X)=
1
b a
,a<x<b
Formula14.8:ExponentialDistribution
XExp(m)
f(x)=me
mx
,m>0,x0
Formula14.9:NormalDistribution
XN
m,s
2
f(x)=
1
s
p
2p
e
(x
m
)
2
2s
2
,
¥<x<¥
Formula14.10:GammaFunction
G(z)=
R
¥
0
xz
1
e
x
dxz>0
G
1
2
=
p
p
G(m+1)=m!form,anonnegativeinteger
otherwise:G(a+1)=aG(a)
Formula14.11:Student-tDistribution
Xt
df
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APPENDIX
657
f(x)=
1+
x
2
n
(n+1)
2
G
(
n+1
2
)
p
npG
(
n
2
)
X=
Z
q
Y
n
ZN(0,1),YX2
df
,n=degreesoffreedom
Formula14.12:Chi-SquareDistribution
XX
2
df
f(x)=
x
2
2
e
x
2
2
n
2
G
(
n
2
)
,x>0,n=positiveintegeranddegreesoffreedom
Formula14.13:FDistribution
XF
df(n),df(d)
df(n)=degreesoffreedomforthenumerator
df(d)=degreesoffreedomforthedenominator
f(x)=
G
(
u+v
2
)
G
(
u
2
)
G
(
v
2
)
u
v
u
2
x
(
u
2
1
)
h
1+
u
v
x
.5(u+v)
i
X=
Y
u
W
v
,Y,Warechi-square
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658
APPENDIX
14.9NotesfortheTI-83,83+,84Calculator
16
14.9.1QuickTips
Legend
representsabuttonpress
representsyellowcommandorgreenletterbehindakey
 < < >representsitemsonthescreen
Toadjustthecontrast
Press
,thenhold
toincreasethecontrastor
todecreasethecontrast.
Tocapitalizelettersandwords
Press
togetonecapitalletter,orpress
, then
tosetallbuttonpressestocapital
letters.Youcanreturntothetop-levelbuttonvaluesbypressing
again.
Tocorrectamistake
Ifyouhitawrongbutton,justhit
andstartagain.
Towriteinscientificnotation
NumbersinscientificnotationareexpressedontheTI-83,83+,and84usingEnotation,suchthat...
 4.321E4=4.32110
4
 4.321E-4=4.32110
4
Totransferprogramsorequationsfromonecalculatortoanother:
Bothcalculators:Insertyourrespectiveendofthelinkcablecableandpress
,then
.
Calculatorreceivinginformation:
Step1. Usethearrowstonavigatetoandselect<
>
Step2. Press
Calculatorsendinginformation:
Step1. Pressappropriatenumberorletter.
Step2. Useupanddownarrowstoaccesstheappropriateitem.
Step3. Press
toselectitemtotransfer.
Step4. Pressrightarrowtonavigatetoandselect<
>.
Step5. Press
NOTE
:ERROR35LINKgenerallymeansthatthecableshavenotbeeninsertedfarenough.
Bothcalculators: InsertyourrespectiveendofthelinkcablecableBothcalculators: press
,then
Toexitwhendone.
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APPENDIX
659
14.9.2ManipulatingOne-VariableStatistics
NOTE
:Thesedirectionsareforenteringdatawiththebuilt-instatisticalprogram.
SampleData
Data
Frequency
-2
10
-1
3
0
4
1
5
3
8
Table14.18
:Wearemanipulating1-variablestatistics.
Tobegin:
Step1. Turnonthecalculator.
Step2. Accessstatisticsmode.
Step3. Select<
>tocleardatafromlists,ifdesired.
,
Step4. Enterlist
tobecleared.
,
,
Step5. Displaylastinstruction.
,
Step6. Continueclearingremaininglistsinthesamefashion,ifdesired.
,
,
,
Step7. Accessstatisticsmode.
Step8. Select<
>
Step9. Enterdata.Datavaluesgointo
.(Youmayneedtoarrowoverto
)
 Typeinadatavalueandenterit.(Fornegativenumbers,usethenegate(-)keyatthebottomof
thekeypad)
,
,
 Continueinthesamemanneruntilalldatavaluesareentered.
Step10. In
,enterthefrequenciesforeachdatavaluein
.
 Typeinafrequencyandenterit.(Ifadatavalueappearsonlyonce,thefrequencyis"1")
,
 Continueinthesamemanneruntilalldatavaluesareentered.
Step11. Accessstatisticsmode.
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660
APPENDIX
Step12. Navigateto<
>
Step13. Access<
>
Step14. Indicatethatthedataisin
...
,
,
Step15. ...andindicatethatthefrequenciesarein
.
,
,
Step16. Thestatisticsshouldbedisplayed.Youmayarrowdowntogetremainingstatistics.Repeatasneces-
sary.
14.9.3DrawingHistograms
NOTE
:Wewillassumethatthedataisalreadyentered
Wewillconstruct2histogramswiththebuilt-inSTATPLOTapplication.Thefirstwaywillusethedefault
ZOOM.Thesecondwaywillinvolvecustomizinganewgraph.
Step1. Accessgraphingmode.
,
Step2. Select<
>Toaccessplotting-firstgraph.
Step3. Usethearrowsnavigategoto<
>toturnonPlot1.
<
>,
Step4. Usethearrowstogotothehistogrampictureandselectthehistogram.
Step5. Usethearrowstonavigateto<
>
Step6. If"L1"isnotselected,selectit.
,
,
Step7. Usethearrowstonavigateto<
>.
Step8. Assignthefrequenciesto
.
,
,
Step9. Gobacktoaccessothergraphs.
,
Step10. Usethearrowstoturnofftheremainingplots.
Step11. Besuretodeselectorclearallequationsbeforegraphing.
Todeselectequations:
Step1. Accessthelistofequations.
Step2. Selecteachequalsign(=).
Step3. Continue,untilallequationsaredeselected.
Toclearequations:
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