Tsu-2011 - ieeetsu

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doniT aris Tu ara eqimebSi mwevelTa proporcia ufro maRali vidre iuristebSi? 3. SemTxveviT SerCeuli 100 momxmareblidan 43 angariSsworebisaTvis iyenebs “masterqards”, xolo SemTxveviT SerCeuli sxva 100 momxmareblidan 58 angariSsworebisaTvis iyenebs “vizaqards”. 0.05 mniSvnelovnebis doniT aris Tu ara gnsxvaveba im momxmarebelTa proporciebs Soris, romlebic angariSsworebisaTvis iyeneben sxvadasxva tipis sakredito baraTebs? 4. TbilisSi SemTxveviT SerCeuli 73 fostalionidan erTi kviris ganmavlobaSi 10 dakbenil iqna mawanwala ZaRlis mier, xolo quTaisSi ki SemTxveviT SerCeuli 80 fostalionidan 16 dakbenil iqna ZaRlis mier. 0.05 mniSvnelovnebis doniT aris Tu ara mniSvnelovani gansxvaveba proporciebs Soris? aageT 95%-iani ndobis intervali proporciaTa sxvaobisaTvis. 5. gamokiTxvam aCvena, rom gamokiTxuli mamakacebis 83% leqciasTan SedarebiT upiratesobas aniWebs kompiuterul swavlebas, xolo igive maCvenebeli qalebisaTvis Seadgens 75%-s. TiToeuli populaciisaTvis aRebuli iyo 100 – 100 adamianisagan Semdgari SerCeva. 0.05 mniSvnelovnebis doniT SeamowmeT hipoTeza imis Sesaxeb, rom mamakacebsa da qalebSi ar arsebobs gansxvaveba im adamianebis proporciebs Soris, romlebic leqciasTan SedarebiT upiratesobas aniWeben kompiuterul swavlebas. aageT 95%-iani ndobis intervali proporciaTa sxvaobisaTvis. 6. SemTxveviT SerCeuli 200 qirurgidan 15%-s miaCnia, rom janmrTelobis dacvaze kontrols unda axorcielebdes saxelmwifo, xolo SemTxveviT SerCeuli 200 Terapevtidan ase fiqrobs 21%. 0.1 mniSvnelovnebis doniT aris Tu ara gansxvaveba proporciebs Soris? aageT 90%-iani ndobis intervali proporciaTa sxvaobisaTvis. 7. 80 gamokiTxuli amerikelidan 55% Tvlis, rom is mdidaria, xolo 90 gamokiTxuli evropelidan 45% Tvlis, rom is mdidaria. 0.01 mni- Svnelovnebis doniT aris Tu ara gansxvaveba proporciebs Soris? aageT 99%-iani ndobis intervali proporciaTa sxvaobisaTvis. 8. 200 gamokiTxuli mamakacidan 130 xmarobs usafrTxoebis Rveds, xolo 300 gamokiTxuli qalidan 63 xmarobs usafrTxoebis Rveds. 0.01 mniSvnelovnebis doniT SeamowmeT hipoTeza imis Sesaxeb, rom mamakacebi ufro seriozulad ekidebian usafrTxoebas, vidre qalebi. isargebleT P - mniSvnelobis meTodiT. 9. 80 gamokiTxuli Tbiliselidan 45-s aqvs kondicioneri, xolo 120 gamokiTxuli quTaiselidan 63-s aqvs kondicioneri. 0.05 mniSvnelovnebis doniT aris Tu ara gansxvaveba proporciebs Soris? aageT 95%-iani ndobis intervali proporciaTa sxvaobisaTvis. 10. 100 bavSvisgan Semdgar SerCevaSi 30% namyofia cirkSi. sxva 100 bavSvisagan Semdgar SerCevaSi 24% namyofia cirkSi. 0.02 mniSvnelovnebis doniT aris Tu ara gansxvaveba proporciebs Soris? isargebleT P - mniSvnelobis meTodiT. 181
11. 200 gamokiTxuli mozardidan 50-s sjera, rom omi Seuqcevadia, ma- Sin roca 300 asakovani adamianidan 93-s sjera, rom omi Seuqcevadia. 0.01 mniSvnelovnebis doniT aris Tu ara gansxvaveba proporciebs Soris? aageT 99%-iani ndobis intervali proporciaTa sxvaobisaTvis. 12. 50 pirvelkurseli studentidan 8-s aqvs sakuTari avtomanqana, xolo 75 meoTxekurselidan ki 20-s. 0.05 mniSvnelovnebis doniT Segvi- Zlia Tu ara, rom sakuTari avtomobilis mqone studentebis proporcia meoTxekurselebSi ufro maRalia? isargebleT P -mniSvnelobis meTodiT. amocanebi gamocdisaTvis igulisxmeT, rom sidideebi ganawilebulia normalurad an daaxloebiT normalurad 13. SemTxveviT SerCeuli 100 – 100 qirurgisa da stomatologis saSualo wliuri Semosavali Seadgens Sesabamisad 54107-sa da 58417 lars. orive SerCevis Sesworebuli standartuli gadaxraa 81 lari. 0.1 mniSvnelovnebis doniT SeamowmeT hipoTeza imis Sesaxeb, rom am populaciaTa saSualoebi ar gansxvavdeba. aageT 90%-iani ndobis intervali saSualoTa sxvaobisaTvis. 14. gamokiTxuli martoxela da daqorwinebuli mZRolebis ori jgufis mier kviris ganmavlobaSi ganvlili manZilebis qvemoT moyvanili monacemebis mixedviT 0.01 mniSvnelovnebis doniT SeiZleba Tu ara davaskvnaT, rom martoxela mZRolebi saSualod ufro mets gadian kviraSi daqorwinebulebTan SedarebiT? martoxela mZRolebi daqorwinebuli mZRolebi ------------------------------------------------- --------------------------------------------------- 106 119 110 115 108 97 133 139 140 101 110 97 117 114 117 115 113 104 120 108 115 118 116 103 152 136 114 109 119 138 121 122 138 98 147 119 117 113 116 147 132 135 142 99 117 99 102 136 145 113 154 107 86 133 115 113 106 108 115 96 138 116 142 104 140 114 150 135 88 105 15. ganaTlebis inspeqtors ainteresebs Seadaros moswavleebze daxarjuli Tanxebis dispersiebi qalaqad da soflad. Sesabamisi SemTxveviTi '2 SerCevebidan miRebuli Sesworebuli SerCeviTi dispersiebia: s1 585, '2 s2 261 (SerCevaTa moculobebia: n 18, m 16 ). 0.05 mniSvnelovnebis doniT aris Tu ara mniSvnelovani gansxvaveba populaciaTa dispersiebs Soris? 16. mkvlevars surs Seadaros I da II ligis fexburTelebis simaRleebis dispersiebi. TiToeuli ligidan SemTxveviT SearCies 25 – 25 moTama- 182
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omar furTuxia albaToba da statistik
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statistikuri hipoTezis Semowmeba no
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. Tu P( ) aTobebi. P( A): P( ) A
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I. kursze, romelzec sami jgufia, jg
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magaliTi 4. vipovoT albaToba imisa,
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3 10! 8910 С 10 120. 3!7! 6 mag
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C 2 4 6 2 496 C32 0,012 . davaleb
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sa, rom: a). orive nomeri iqneba er
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Tu A ,..., 1 , A2 An xdomilebaTa sr
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1 1 1 1 1 . * * m m1 m 1 m1 sauke
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kamaTelze movida kenti qula, C -- o
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amocanis pirobebSi cxadia agreTve,
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is SemTxvevaSi ukanaskneli Sedegi S
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Sesabamisad, saZiebeli albaToba alb
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oba aris wina cdaze CaWris albaTobi
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22. ( A B) , P( A| B) 1/3, PA ( )
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42. albaToba imisa, rom oTx damouki
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5). P{ xk} F( xk 0) F( xk ) (Se
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E( | B) xiP( xi | B) . 1 cxadia,
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{ ggg,ggs,gsg,sgg,gss,sgs,ssg, sss}
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magaliTi 6. mocemulia SemTxveviTi s
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P{ 2} P{ 0} P{ 2} 0.1 0.4
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aqedan gamomdinare, korelaciis koef
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17. kompiuteri daprogramebulia 0-da
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37. samSeneblo kompanias sTavazoben
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Tavi IV diskretul ganawilebaTa gamo
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ualod drois mocemul intervalSi xidz
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9. universitetis studentTa 30%-is a
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27. martis TveSi Semosuli satelefon
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43. umaRlesi ligis fexburTis matCeb
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va arcerT kamaTelze, maSin is arafe
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2 2 2 () D x f x dx . asimet
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gavixsenoT, rom ( MA) . meore mxri
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x amoxsna. visargebloT formuliT: F(
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a). ipoveT c ; b). gamoTvaleT moda;
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Tavi VI normaluri ganawileba SemTxv
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magaliTi 4. vipovoT albaToba imisa,
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X -s Soris mdebare aris farTobi 0.5
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amitom 12 a 16a 0.407 da 0.900 .
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cali SuSis sawmendidan ramdenis sig
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obili 56 mili/sT siCqariT moZraobis
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52. uwyveti SemTxveviTi sididis ga
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Tavi VII albaTobis Teoriis zRvariTi
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Tu axla gavixsenebT, rom ( x) ( x)
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amoxsna. SemoviRoT xdomilebebi: A {
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n n 2(0.005 ) 1 0.95, anu ( 0.005 )
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18. detalebis 80% I xarisxisaa. ram
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s t a t i s t i k a Tavi I wertilov
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ucnobi parametris maqsimaluri dasaj
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magaliTi 2. cnobilia, rom garkveuli
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ndobis intervali mexuTe klaselebis
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tervalisaTvis, roca n 10 ; e). 95%
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Tavi II ndobis intervali bernulis s
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4. gamokiTxuli 1015 axalgazrdidan 1
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Tavi III ndobis intervali dispersii
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18.6 19.5 20.2 20.4 19.3 21 20.3 19
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26. 22 balaxis sakreWi manqanis mie
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Tavi IV 2 hipoTezaTa Semowmeba saSu
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xE 43260 42000 z 1.32 . / n 523
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2. CamoayalibeT ZiriTadi da alterna
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15. miuTiTeT unda ukuvagdoT Tu ara
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pasuxebi: 1. 2.58 ; 1.65; -2.58; -
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X E gamoiyene T , T.x. n 1 * ' S
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Seesabameba 0.025 -sa da 0.01 -
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mniSvnelovnebis doniT gvaqvs Tu ara
Page 131 and 132: gadawyvetileba: Tu T.V.C.R., maSin
Page 133 and 134: magaliTi 5. vipovoT P -mniSvneloba,
Page 135 and 136: 8. plastikatis boTlSi moTavsebuli 1
Page 137 and 138: hipoTezis Semowmeba puasonis popula
Page 139 and 140: 3. samSobiaro saxlis warsuli Canawe
Page 141 and 142: Tavi VIII ndobis intervali da hipoT
Page 143 and 144: 3. uZravi qonebis agentis mtkicebiT
Page 145 and 146: finansur daxmarebas. imis gasarkvev
Page 147 and 148: pasuxebi: 1. H0 : E 1800 , H1 : E
Page 149 and 150: ( xn y ) z / n / m a a ( x y )
Page 151 and 152: P{ T t | H0}, Tu H1 : a1 a2 0; P
Page 153 and 154: (sadac z aris N(0,1) -is zeda -kr
Page 155 and 156: amerika evropa 729 329 450 330 481
Page 157 and 158: TiToeuli jgufidan SemTxveviT SerCeu
Page 159 and 160: SeniSvna: saSualoTa Sesaxeb tolobis
Page 161 and 162: gadavideT saSualoebis Sesaxeb hipoT
Page 163 and 164: 4. mkvlevaris SefasebiT studenti go
Page 165 and 166: Tavi XI oramokrefiani amocanebi pop
Page 167 and 168: '2 '2 '2 '2 TV . . s1 / s2 246.38
Page 169 and 170: 5. sagadasaxado inspeqtoris mtkiceb
Page 171 and 172: 15. qvemoT moyvanilia A da B tipis
Page 173 and 174: s n s n ' ' D D d n tn 1, /2 aD d
Page 175 and 176: s 1 1 1 1 [ d ( d ) ] [4890 (
Page 177 and 178: 4. mkvlevars ainteresebs axali diet
Page 179 and 180: Tavi XIII oramokrefiani amocanebi b
Page 181: ( 0.36 0.242, 0.36 0.242) , ( 0.60
Page 185 and 186: 23. dedaqalaqis SemTxveviT SerCeuli
Page 187 and 188: Tavi XIV Tanxmobis kriteriumebi xi-
Page 189 and 190: nabiji 4. gadawyvetilebis miReba: r
Page 191 and 192: e 26.7 55.1 66.64 38.96 12.6 i (aq
Page 193 and 194: programebs. SemTxveviT SerCeul myid
Page 195 and 196: nabiji 2. SevadginoT niSanTa SeuRle
Page 197 and 198: 32 29 3235 32 24 e2,1 10.55 , e 8
Page 199 and 200: nebis doniT, aris Tu ara avtomobili
Page 201 and 202: hipoTeza imis Sesaxeb, rom arCeuli
Page 203 and 204: proporcia, romlebic institutSi dadi
Page 205 and 206: is Sesaxeb, rom im momxmareblebis p
Page 207 and 208: fatalur avariaTa ricxvi Tavi XVII d
Page 209 and 210: uaryofi Ti wrfi vi kavSi ri 400 300
Page 211 and 212: ' ' ' 2 x i y i y i yi yi ( yi yi)
Page 213 and 214: B trestis monacemebi 5. rac ufro ko
Page 215 and 216: anu y 2.29 x 49.9 . es gantoleba ko
Page 217 and 218: daskvna. korelaciis koeficientis mi
Page 219 and 220: 218 amocanebi 1. gamoTvaleT korelac
Page 221 and 222: gacdena, x 10 12 2 0 8 5 Sefaseba,
Page 223 and 224: Tavi XVIII regresia da korelacia 1.
Page 225 and 226: wrfiT (regression sum of squares).
Page 227 and 228: saxlis gayidvis fasi a). ormxrivi a
Page 229 and 230: 2 SSE 21995.88 S 168.91 . n2 13
Page 231 and 232: determinaciis koeficienti. davweroT
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2 va damakmayofilebel Sedegs (deter
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x1 (b 1 ) 4.146 0.751 5.520 0.000 2
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spirmenis rangobrivi korelaciis koe
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Tavi XIX dispersiuli analizi (ANOVA
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Cven gvaqvs sakmarisi safuZveli dav
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fexburTi kalaTburTi xelburTi ------
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gazze benzinze eleqtronuli meqaniku
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sakredito baraTiT sargeblobisas pro
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pasuxebi: 1. H 0 : a 1 a 2 a 3 , H
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varianti # 2007.1.1 1. Ada B damouk
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( XY , ) (0.5q.); cov(5 X, 4Y 7) (0
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danarTi (statistikuri cxrilebi) k
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1 x N(0.1) -is ganawilebis funqcii
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t (stiudentis) ganawilebis zeda -k
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2 (xi kvadrat) ganawilebis zeda -
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F( n, m ) (fiSeris) ganawilebis zed
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14. studentma unda Caabaros 4 gamoc
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44. saTamaSo kamaTels agoreben samj
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). A -- pirveli agdebisas movida 1
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81. msrolelis mier samiznis daziane
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literatura 1. g. mania. albaTobis T
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