,r_i- " -

09.12.2070
MINITABUYGULAMASI
ISTATISTIK
I
1. ANA KtiTLE ORTALI\MA/VARYANSHiPOTEZ TESTI
Ytirrittilen bir projede sigara igen ve igmeyen hamilelerin plazma askorbik asit seviyeleri
kargrlagtrrrlmrgtrr.
Qahgmaigin 1,5-32yaglanarasrndacinemlibir saflrk problemi olmayanhamileli$inson
3 ayrndaolan 32 kadrnsegilmigtir.Eldeedilenveriler izleyentablodaverilmigtir.
Plazmaaskorbikasit deEerleri
Sisaraicmevenler Sigara icenler
7,L6
0,48
0,97
0,72
0,86
0,7L
0,98
L
0,85
0,58
0,68
0,81
1",18
0,62
0,57
'1,,36
1,32
0,64
1,24
0,78
0,98
L,O9
r,64
0,99
0,9
0,92
0,74
0,78
1,24
0,88
1.18
0,94
:
c
l
i
c
e
j a i g a r a i g r n e y e r r l e*.1-1*1s".:igenlerl
.........ie:ga.r:..
:s_-ll*v*!.fr i s i g a r a .:F:f"*l
i
o , :9 7 :
r. j
.
- o,48:
2
-r
4
"
i
:
-!-
---
s ii o I
,r_iI I
o,72
1,oB'
O,A1
0,71
o.9B
0 , 6 A,
o,oii
1sz
a
n e - r
"-
:
10 ,
ri|
i
f . 1i Qg' i
r,eei
i
8.99i
1,64i
o,74:
:
- , " , __
- _ -_ _" , " ' " J
{ ?
:
n q d i
1r r3 j|
---
il- i--
rr
lr
ii
{l
, r1 tCj i;
:
, o.BE
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i6-l---'
o,es,
uruul
o . E Bj
Soru 1: Sigaraigen ve igmeyenlerinplazmaaskorbik asit seviyeleriarastndafarkliltk oldufu sonucuna
varacakyeterli kantt var mtdtr?(a=0,05)
iki anakiitle var.ttansr hipotez testi
Regression
ANOVA
DOE
ControlCharts
QualityTools
Reliability/5urvival
)l
Mullivariate
ri
Timeseries
,i
Tables
NonparEmetrics
EDA
PowerandSamdesize
ii
Test for EqualVariances
q i dma
T.Ar^rar
vyPvr
0,160997 0,2L4474 0,316900
0 , 2 4 4 9 L 4 O , 3 9 7 4 ' 7 8 0 , 8 9 6 6 15
d
g ir o c + Lr ri lf .! rur ur ff
E_rF6qf
u
TFst
Si-Ati st i c:
P-Vafue
r/nnrmal
\rrvrar.sr
:
N
Factor
Levels
)A
qiaar:
icmorr
cia:r:
icanl
Q
i an\
vrrl
0, 300
0,021
HAZTRLAYAN:ARA$.
C0n. CulqiN OINEYALCrN
L/7
israrisrirt
MINITABUYGULAMASI
09.!2.2070
iki ana kiitle ortalamalanmn hipotez testi
i:i= ii'ffiLs,',lllllsiuii:r.li;LLiwiLl':llilLxi
$#$li
)l
tl^
Regression
ANOVA
DisFldyDescriptivestatistics..'
5tore DesffiDtivestatistics'.
DOE
)
)
controlcharts
Tools
Quality
Reliability/Survival
I
Pairedt,..
) L... -- -
Multivariate
Timeseries
Tables
Nonparametrics
i i3l","naru'o,"rn"
lj c"u:ll"::::::.
""'."""",*"
*;;*;;,;;*
i
Tert.,.
Normalitv
Two-sampleT-Testand Cl: sigara igmeyenler;sigara igenler
TI wr v. r n _ rcq:l m
run
r r lv
a
.l
a
sigara
i
N
24
cinara
u + Y s r s
i
R
!f vo! r
q.i
o f v qo! qa
ra
.i
r Yca m
r r uel v
' ver rnr ! r
lef
Mean
0,91-6
StDev
o , 9 ' 76
n
0,2L4
?q1
rzs
s io:ra
icen
lef
SE Mean
^
olt
0 ,r 4
- mu sigara
iQenfer
: mu sigara
iqmeyenler
Difference
-0' 060
Estimate for difference:
(-0,395; 0,274)
95? CI for difference:
(vs not:):
T-Value: -0,42
d
i
f
f
e
r
e
n
c
e
:
0
o
f
T-Test
P-Va1ue:0,688
DF:8
Soru 2: Sigaraigmeyenhamilelerdekiplazmaaskorbik asit defierlerininL'den ktigiik olduiu soylenebilir
mi?
Tekana ktitle ortalama hipotez testi (standart sapma bilinmUor)
sldtistics.
DisplayDescriptive
r:h|..
Nonpardmetrics
,:
" "" -
-
:
2 Varianaes...
l: .......... ..
t - - ' * * " '
)i
CorrelBtion.,.
EDA
]
FowerEndsampleSize f:
{
*rl|llw
covariance,,,
One-Sample T: sigara igmeYenler
T e s t o f m u : 1 v s m u ( 1
Variable
qi oer: i cmev
Variable
qioar: icmev
N
24
Mean
0,9158
95,0% UPPer Bound
0r9908
StDev
0,2]-44
SE Mean
0,0438
T
-I,92
GoR.GulgittOiNqYAL9IN
HAZTRLAYAN:ARA$.
P
0r033
2/7
MINITABUYGULAMASI
ISTATISTIK
I
09.72.20\0
Soru 3; Sigaraigmeyenhamilelerin plazmaaskorbik asit degerlerininanakritlestandart sapmaslnln0,2
oldu$ubilindifinde bu defierin 1'denkrigtk oldu$usdylenebilirmi?
Tek anaktitle ortalama hipotez testi (standart sapma biliniltor)
Editor rC/krfurv fb$
g"Fh
@
Regreision
l
ANOVA
DOE
ControlCharts
QualityTools
Reliabilityi
5urvival
Multlvariate
Time5eriet
Tables
Nonparametrics
EDA
Powerandsample5ize
t:
li
>)
ll
|:
ri
I Proportion...
ti
a.llolllllonl:::.
)l
)i
"11"i11111"1::
)i
Correlation,,.
rj
.,co1111"1'u-:::
.
Normality
Test,.,
One-Sample Z: sigara igmeyenler
T e s t o f m u : 1 v s m u < 1
The assumed sigrma : 0,2
Variable
q i aa
r:
N
24
i cmarr
Variabfe
sj-gara iqmey
Mean
0,9158
StDev
0,2L44
95,08 Upper Bound
0,9830
Z
-2,06
SE Mean
0,0408
P
0,020
2. ANAKUTLEORANIHiPOTEZTESTI
Soru 1: Otomobilmotoru igin denetleyicii.iretenfirmarunmti$terilerihatahtirtintin en fazla0,05 orantnda
olmaslnlistemektedir.Bununiqin iiretici firma siirecini kontrol etmekamacryla200 adet ornek almtgve 4
tane hatahiiriin bulmugtur.%095giivenseviyesindetireticinin hata orant 0,05altrndamtdtr?
Tekanakiitle orant hipotez testi
,ffiir.mtl,r,r
P|t#rsuffi
re,,$Hiill'1ffi.1.*.lffi
DiiplayDescriptive5tatistics,.,
t
i?@HEtr
DoE
controt ctrarts
QualityTools
)i
):'
)
:
)
|:
Reliabiliiy/survival
r
Multivdriate
Timeseries
Tables
':
Regession
ANOVA
5tore Descrlptivestatistics,,,
l-samplez"'
l-samPlet" '
z-sdmplet" '
ld
I
ra1eo.1"'
'iw
l ;
,i
Nonparametrics
);
EDA
Powerand samplesize )'
2 Prooortions..,
-
2 variances,,,
Conelation,.,
Covariance,,,
Normality
Tert,,,
HAZIRLAYAN:ARA$.
GoR.Gulgir.rOir,rg
YALETN
3/7
MINITABUYGULAMASI
I
ISTATISTIK
09.12.2070
TestandCl for OneProportion
Ta<l-
nf
Qrmnl
a
1
n
:
0,05 vs p < 0,05
X
4
N
200
Sample p
0,020000
95,0?
Exact
Upper Bound P-Vafue
0,045180
0,026
Soru 2: Bir gehir halkrnda kanser oranlnln yakrn klrsal b<ilgelerdekileregore daha ytiksek oldufiu
dtiqilniilmektedir. $ehir halkrnda 200 yetigkinden ZO'sinde,krrsal kesimden 150 yetigkinden 10'unda
kanser oldufiuna gdre 0/oSanlam diizeyinde gehir hakhnda kanserin daha yaygn oldufu sonucuna
varabilir miyiz?
iki anakiitle oram hipotez testi
Regression
ANOVA
DOE
Controlchdrts
Quality Toolt
Rellability,lsurvival
Multivaridte
TimeSeries
Tdbles
Nonparametrics
EDA
Powerand sampleSize
DisdayDescriptive
stitistics,.,
StoreDescriptive
statistici...
NormalltyTest..
Test and Cl for Two Proportions
Sample
7
2
X
20
r0
N
200
1s0
Samplep
0,100000
0,06666"7
0,0333333
Estimate for p(1) - p(2):
(-0,0243048; 0,09097]-4)
95? CI for p (1) - p (2) :
(vs not = 0):
Z:
I,I3
Test for p(1) - p(2) :0
P-Value:0,25'1
HIPOTEZTESTi
3. E$LE$TiRiLMi$GOZLEMLERIN
Soru: Qeliklevhanrngiicti iki farkh metod ile dlgtilebilmektedir.9 rjrneh bu iki ydntem ile tilgtilmiigve
aga$rdakitablo elde edilmigtir. Bu iki ytintem arastndafark var mtdtr?
KarlsruheMetodu
1.,186
1 , 1 5L
L.322
t,339
L,200
L.402
1,365
r.537
1,559
LehishMetodu
r,061.
0,992
1,063
7,062
1,065
1,1.78
t,037
1,086
1.052
iK;;#;h;-h4;iliiliL;hisri"M;i;a;i
3 |
-{-i*-***t..
5 i
1,322,
i,iiei---..-..--...*----.*--i-.*
1,200i
--ri---"--: "--.i.,r!^ri&-i
i
i ii;
1,s59
IN
GoR.GuLEittlit'tE YALC
HAZTRLAYAN:ARA$.
1,063i
1,062i
1
,055
l
..........
......1......
1,178i
110371
11086
i
t ncli
4/7
isrerisrirr
09.72.2010
MINITABUYGULAMASI
Regression
ANOVA
DOE
ControlCharts
QualityTools
Reliabillty/survivEl
muftivdridte
Timeserie5
Tdbles
Nonparametric5
2...
r-suror"
]i
l-samplet...
t,..
2-samole
)i
i
:)i
I Proportion,..
t"fo:t'?n'-'::
]i
)i
2 Vdrinnres,.,
Powerand stsmple
size
Test.
Normality
PairedT-Testand Cl: KarlsruheMetodu;Lehigh Metodu
Paired
T for
Karl-sruhe
Karlsruhe Me
Lehigh Metod
Difference
N
9
9
9
Metodu -
Lehiqh
Mean
1-,3407
1,0662
0,2'139
95? CI for mean difference:
T-Test of mean difference:0
Metodu
StDev
0,1460
0,0494
0, 1351
SE Mean
0,0481
0,0165
0, 0450
(0,1700, 0,311'l)
(vs not:
O): T-Val-ue: 6,08
P-Va1ue:0'000
4. ivi uwru rEsri
Soru: Bir iiriinde grizlenenhatalannsaylslve frekanslanata$daki tablodaverilmigtir. Hatafrekanslarlnrn
mudur?fMinitab 15 )
rmr 0,75 ortalama Ie Poisso
Hata savrsr Frekanst
0
32
1
2
15
9
3
4
'ji
ili lF.
E;4,:;
;' S"&""
T flqy,
l${ill$l
ffi
ffii
'
ili:$il
i=
t t ,
:
' t::t
i
isl
.tl
l.; r$"r, I
ifti.i.
l
;
HAZTRLAYAN:ARA$.
G0R.GULEINliUq YALCIN
s/7
ISTATISTIK
I
09.!2.2070
MINITABUYGULAMASI
'+,ga$*s$ffiilrl
n'u. -.
:t : r
l:
Ghi-SquareGoodness-of-Fit
Test for ObservedGountsin Variable:C2
ITci na
^.1-6n^r\r
v v 4 l r Y v g 9 v Y v ! ] r r g r
Category
0
1
2
3
N
60
DF
3
n.rneS
Observed
32
15
9
4
in
C1
Historical
Counts
0 , 4 72 3 6 1
o , 3 5 4 2 ' 75
0,132853
0,033213
Test
Dr^^^r+
L !vyv!
i ^h
uavrl
0,475836
0,356877
0 , L33829
0,033457
Contribution
F vn6^+
! . l y v v
a.l
u v v
2 8, 5 5 0 2
2r,4126
8, 0 2 9 7
2 , 0 0 14
uv
vrr]
eY
0 , 4 1 6 85
1,92045
0 , L L 12 4
7,97781,
Chi-Sq P-Value
4, 43235
0,278
5. BAGIMSIZLIKTESTi
Soru: Bir firmada her bir vardiyada4 makine kullanrlmaktadrr.Agafrdakitabloda vardiyalarda
makinelerin bozulma say-llangrirtilmektedir.%095gtiven seviyesinegrire makine bozulmalarr
vardiyadanbafrmsrzmldlr?
Vardiyalar Makineler
A
B C
L
4L 20 1 2
2
3\ L\ 9
15 L7 I6
3
D
t6
L4
10
HAZTRLAYAN:
ARA$.Con.Cur,EiwOiwEyALgrN
6/7
ISTATISTIK
I
MINITABUYGULAMASI
09.12.2010
Controlcharts
QualityToolt
Reliabilityi
5urvival
MultivdriEte
Timeseriet
Power and Samde Size
Chi-SquareTest: Cl; C2;G3;C4
Expected counts are printed
below observed
Chi-Square
contributions
are printed
befow
C1
4L
36,52
0,549
C2
20
20,15
0,001
C3
12
15,53
0,804
2
31,
26,67
0,701
11
L4,72
0,939
9 ] _ 4
L1,34 L2,26
0,484 0,246
3
15
2? Rn
3,255
1'l
1? 13
1,,]-39
1,6
10
10,L2 rO,g4
3,4I2 0,081
L
Total
Chi-Sq
87
:
48
11_,649; DF :
counts
C4 Total1-6
89
L6,'79
0,037
6
s
sB
40
2r2
6; P-Value :
0,070
3'7
counts
expected
HAZTRLAYAN:
ARA$.GoR.GuLEir'rOiXqYALETN
7/7