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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$inson 3 ayrndaolan 32 kadrnsegilmigtir.Eldeedilenveriler izleyentablodaverilmigtir. Plazmaaskorbikasit deEerleri Sisaraicmevenler Sigara icenler 7,L6 0,48 0,97 0,72 0,86 0,7L 0,98 L 0,85 0,58 0,68 0,81 1",18 0,62 0,57 '1,,36 1,32 0,64 1,24 0,78 0,98 L,O9 r,64 0,99 0,9 0,92 0,74 0,78 1,24 0,88 1.18 0,94 : c l i c e j a i g a r a i g r n e y e r r l e*.1-1*1s".:igenlerl .........ie:ga.r:.. :s_-ll*v*!.fr i s i g a r a .:F:f"*l i o , :9 7 : r. j . - o,48: 2 -r 4 " i : -!- --- s ii o I ,r_iI I o,72 1,oB' O,A1 0,71 o.9B 0 , 6 A, o,oii 1sz a n e - r "- : 10 , ri| i f . 1i Qg' i r,eei i 8.99i 1,64i o,74: : - , " , __ - _ -_ _" , " ' " J { ? : n q d i 1r r3 j| --- il- i-- rr lr ii {l , r1 tCj i; : , o.BE i - -- i6-l---' o,es, uruul o . E Bj Soru 1: Sigaraigen ve igmeyenlerinplazmaaskorbik asit seviyeleriarastndafarkliltk oldufu sonucuna varacakyeterli kantt var mtdtr?(a=0,05) iki anakiitle var.ttansr hipotez testi Regression ANOVA DOE ControlCharts QualityTools Reliability/5urvival )l Mullivariate ri Timeseries ,i Tables NonparEmetrics EDA PowerandSamdesize ii Test for EqualVariances q i dma T.Ar^rar vyPvr 0,160997 0,2L4474 0,316900 0 , 2 4 4 9 L 4 O , 3 9 7 4 ' 7 8 0 , 8 9 6 6 15 d g ir o c + Lr ri lf .! rur ur ff E_rF6qf u TFst Si-Ati st i c: P-Vafue r/nnrmal \rrvrar.sr : N Factor Levels )A qiaar: icmorr cia:r: icanl Q i an\ vrrl 0, 300 0,021 HAZTRLAYAN:ARA$. 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