1. Pokuste se identifikovat rozdělení na listu Rozdělení. "2. Usoudíte-li, že je to možné, pokuste se transformovat vybraná rozdělení na normální a testovat normalitu jedním z dříve uvedených testů." 3. Vygenerujte libovolným způsobem 100 hodnot s normálním rozdělením o průměru 5 a vložte je na list 100 hodnot. 4. Pracujte s tabulkami kritických hodnot na webu http://cit.vfu.cz\statwelf\WELF\Teorie\tabulky.htm "5. Na listu Dvouvýběový t-test testujte normalitu rozdělení obou souborů za využití Kolmogorovova-Smirnovova, Shapiro-Wilksova nebo χ2 testu." "6. Na listu Dvouvýběový t-test testujte homoskedasticitu za použití Bartlettova, Levenova nebo Brown-Forsytheova testu." 7. Za jakých předpokladů lze použít dvojvýběrový nepárový t-test pro hodnocení pokroku studentů? "8. Pokud jsou podmínky splněny, otestujte, zda se na hlaině významnosti 5 % změnila úspěšnost studentů a pokud ano, určete, zda se zlepšila nebo zhoršila." 9. Na listu Párový t-test rozhodněte na hladině významnosti 5 % o účinnosti fyzických trestů pro žáky 5. třídy na zlepšení jejich průměrného prospěchu 10. Jak velká změna prospěchu ospravedlňuje na této hladině významnosti použití fyzických trestů "11. Kolik žáků by muselo být bito, aby byl test statisticky významný na stejné hladině pravděpodobnosti?" "12. Na listu Wilcoxonův test pomoci Wilcoxonova testu zjistěte, za jsou přístroje Digitel a PS-1 zastupitelné při měřenáí koncentrace fluorenu v atmosféře." ##### Sheet/List 2 ##### Odhadované rozdělení normální normální normální normální normální normální normální normální normální lognormální lognormální lognormální lognormální lognormální lognormální lognormální lognormální lognormální Weibullovo Weibullovo Weibullovo Weibullovo Weibullovo Weibullovo Weibullovo Weibullovo Weibullovo rovnoměrné rovnoměrné rovnoměrné rovnoměrné rovnoměrné rovnoměrné rovnoměrné rovnoměrné rovnoměrné triangulární triangulární triangulární triangulární triangulární triangulární triangulární triangulární triangulární gama (exponenciální) gama (exponenciální) gama (exponenciální) gama (exponenciální) gama (exponenciální) gama (exponenciální) gama (exponenciální) gama (exponenciální) gama (exponenciální) beta beta beta beta beta beta beta beta beta Studentovo Studentovo Studentovo Studentovo Studentovo Studentovo Studentovo Studentovo Studentovo Pearsonovo Pearsonovo Pearsonovo Pearsonovo Pearsonovo Pearsonovo Pearsonovo Pearsonovo Pearsonovo Fisher-Snedecorovo Fisher-Snedecorovo Fisher-Snedecorovo Fisher-Snedecorovo Fisher-Snedecorovo Fisher-Snedecorovo Fisher-Snedecorovo Fisher-Snedecorovo Fisher-Snedecorovo binomciké binomciké binomciké binomciké binomciké binomciké binomciké binomciké binomciké Poissonovo Poissonovo Poissonovo Poissonovo Poissonovo Poissonovo Poissonovo Poissonovo Poissonovo geometrické geometrické geometrické geometrické geometrické geometrické geometrické geometrické geometrické Bernoulliho Bernoulliho Bernoulliho Bernoulliho Bernoulliho Bernoulliho Bernoulliho Bernoulliho Bernoulliho 0.83724792 4.61609373 3.26290358 0.943696128 3.64258028 4.45608219 3 2 5 0.071849582 0.608915088 9.70192921 0.430030242 2.27420464 5.7382018 0 1 6 1.31989358 1.75820056 7.07101415 0.452449665 3.65780734 1.48498348 0 1 2 0.91985278 3.12215934 4.28991919 1.08700354 2.42844959 1.75744318 1 0 7 1.05892946 0.834213822 2.24728478 0.637960326 3.98020874 5.47427702 0 0 6 0.00178966 0.837800434 9.58439219 0.385202714 4.74212918 2.05390924 1 1 5 4.15915917 2.60094408 7.92119846 0.888666509 5.39536208 4.09100813 0 0 4 0.783542872 5.18533923 0.863716153 0.508818312 4.1553429 3.83404057 0 0 7 6.3284335 1.83451629 5.96511877 0.958985606 3.24255846 1.89414694 1 0 4 2.8073022 0.577465846 5.37570545 1.11013093 4.89032651 2.91389649 1 1 8 0.55203912 0.131489531 4.86624839 0.831230295 2.87728907 6.61097553 0 2 5 0.170394839 1.57231182 7.9652391 1.47842809 4.73857063 3.35037361 1 1 4 0.466027577 3.59915828 7.18263541 0.51763942 1.73431205 8.48091098 0 1 6 0.114185821 0.737232488 1.94543702 0.778830538 3.18089944 9.08705423 1 2 6 1.82758919 3.23633773 2.19359963 1.12606135 3.14744279 5.31762353 0 2 7 0.06192141 1.10017851 3.62330893 0.73229543 2.45595489 4.15662717 0 0 4 0.212036995 2.54890037 5.44930288 0.196746924 3.65791974 5.2310288 2 1 1 0.027526495 6.71745082 4.78998244 0.422268736 11.242188 4.58892052 1 2 5 1.92801684 1.38264531 8.65718203 0.37690687 1.46913987 2.44022348 1 1 3 0.197521788 1.86910377 0.446404205 0.749986089 6.59317111 1.41464975 0 2 3 3.17377047 2.11712896 1.74982443 1.39092854 3.94508208 4.11731541 0 3 7 0.148811037 0.852968511 8.20333403 0.516043929 4.31991121 5.63501984 0 0 6 0.509351005 1.31825622 4.04724664 0.698933438 3.92696248 5.01687963 6 1 5 2.54132275 1.32066283 4.16136402 0.958285142 7.70828813 3.54237354 2 1 3 0.702876862 0.686375942 9.40333299 0.609235015 2.43438265 5.44411379 1 2 4 1.35738303 2.49307546 5.63651057 0.405727458 3.49995637 4.33317227 1 4 5 0.151739659 1.20225567 3.9427647 0.602162755 8.1244091 3.38044449 0 0 3 1.4738019 1.47478962 5.46180571 0.799992903 2.8720639 3.75150181 0 0 5 0.736150556 3.06457554 2.98255071 1.75867078 3.64566971 6.28405233 0 3 7 0.23096583 1.46358479 0.809379239 0.847613917 3.91096717 6.71780021 0 1 3 2.62476041 1.92808163 6.75934661 1.78470666 5.39051044 1.70609794 0 3 6 1.27594857 1.68589717 0.125460352 0.602874171 3.4555584 6.17447267 4 0 8 0.801732927 1.11047925 6.4736633 1.01375942 6.82342869 1.53119298 0 1 5 0.041726587 0.377271797 2.82735015 0.973589558 3.8761521 4.03022949 4 1 6 0.007679839 2.91477322 4.69542382 0.695888515 8.11860285 4.69174737 0 0 5 0.276265948 3.14393822 5.488029 1.15859087 3.91584124 2.47314385 1 0 5 0.670956762 0.124067061 9.80000649 1.28487194 3.68093389 4.56814133 2 2 7 2.58507514 6.60228369 2.52981674 0.811424673 1.95160718 5.13330569 0 3 7 0.27611967 0.874037606 7.12683624 0.30176571 3.31608657 3.92517482 1 1 8 0.225459692 2.67779369 1.83423823 0.832734715 3.49648668 3.62199729 1 1 5 1.19013975 1.66673258 7.93019075 0.433209241 3.35563429 3.93240781 1 4 5 1.41750937 3.63083559 2.08007314 0.924535488 2.81465134 4.61246642 2 1 7 0.415386056 1.48066605 9.92599539 0.848284264 2.98220365 4.95739961 0 0 4 0.432010834 1.78854863 6.70108591 1.26098292 9.05577139 2.84829568 1 0 6 0.238463996 3.32665568 4.70749084 1.217107 5.49529653 4.88614503 0 0 6 1.33154287 3.82992767 7.27728685 0.748016717 3.11386497 3.050163 0 1 6 0.450007934 4.31767945 6.72914126 1.73823615 4.40751783 1.87858063 0 1 3 4.56566964 1.20549968 2.40223971 1.30641105 8.36708102 3.46789411 1 0 4 0.217266093 0.78527914 2.3670483 0.43749231 3.53702901 3.68206138 1 1 5 0.109468804 1.287577 1.2381821 1.26300237 4.65498669 0.889635497 0 1 6 2.50419308 2.14273821 7.84160511 0.535398288 5.5525804 0.995908441 0 1 7 2.10892388 1.07438398 5.17471471 0.300064326 7.17921745 3.35410491 0 0 3 0.146475326 2.80908187 0.117250641 0.711834236 2.38528129 3.9802728 0 1 5 2.09145502 2.19044442 1.18802244 1.04811929 3.44519113 2.24900425 2 0 7 1.0323149 0.770268925 9.32234298 0.905217468 3.6756243 5.60156967 0 1 5 1.20839546 1.02139249 2.88576387 0.928882341 2.13438479 4.88548778 0 0 6 0.640756396 0.297616571 9.40664098 0.489609753 3.63778477 5.76389176 2 2 3 2.99182239 2.50024209 2.23420467 0.901182898 2.34732834 4.8365108 1 0 6 0.342962777 2.08730876 9.59688556 0.85923329 5.54529954 6.31341028 3 0 5 0.348470398 6.04415206 8.55456247 1.71826586 4.44208832 3.03699163 0 0 3 0.717577255 1.81276428 5.68246523 0.189329697 6.63473311 5.57978692 1 0 7 4.12650122 0.275175607 3.38114065 0.473666435 5.36108282 3.45555332 0 2 3 0.286196837 1.51638096 4.15980907 0.337055819 2.81499049 5.42687997 0 0 6 0.578617728 0.84460481 8.93378986 0.274977168 3.6758382 4.74796921 0 1 3 0.239297224 0.319951028 2.2308222 1.52090035 2.62617724 3.21235179 0 0 4 0.282632072 1.26838315 8.19469695 0.479263382 3.11744143 4.5084163 3 1 7 0.336426601 2.01030092 7.88809959 0.917116676 4.79370716 5.08413653 1 1 5 0.047664427 0.609423593 6.08197488 0.646731118 3.07617685 2.82284327 0 2 4 0.306363653 0.480824807 0.485396609 0.467104965 4.56464458 5.5110548 0 1 5 3.36644643 7.53220842 4.31906746 2.30790301 5.24608146 4.71251113 3 1 3 1.12452852 1.04666112 0.822722241 0.66028428 4.56962693 3.36710802 0 0 9 1.89948372 0.840595134 7.68842133 0.339281322 2.78195084 2.12137971 0 1 4 0.807869479 1.18509793 8.58136965 1.03682942 7.07053321 5.8423055 0 2 7 0.579195923 3.74700644 5.77471828 1.03788534 5.50474685 4.87629835 0 0 7 1.94706915 0.04379697 7.15872766 0.364250084 8.14049645 5.89211735 2 1 6 0.318372743 0.575456954 8.89257425 0.456584505 6.46335318 4.7964227 0 0 6 0.14565372 0.881446614 5.10879893 0.665985268 5.10687745 2.20935075 0 2 7 0.073001802 3.51613664 9.95424798 1.22459269 3.19687647 5.26830281 0 2 4 3.642943 0.225511139 1.23085368 0.58837527 2.57816325 4.77306746 0 1 2 0.955024108 3.54284737 6.37067682 1.29847537 2.49566119 3.74548744 0 0 6 1.17439596 5.11648831 4.39208425 0.47166812 2.90357186 6.63560448 0 0 5 0.35404116 4.77127546 3.59796184 0.385652252 9.21144283 3.89085995 1 0 6 0.127717127 0.542940024 4.85046573 0.717846347 5.25432553 2.91386657 2 0 6 0.559676019 0.841594524 0.147984561 1.78545494 5.24961241 1.05198782 0 1 5 0.013213168 2.13143463 2.83696791 1.83464432 4.51906927 3.26185436 2 0 3 0.845784354 3.04816108 0.358787184 0.927375513 6.15349922 5.22454327 1 2 5 1.58616483 2.21548555 8.96248137 0.897847465 5.11239232 3.53347272 0 2 7 2.92493756 0.629703484 6.91195694 1.25541672 3.90808275 4.8373349 0 0 2 0.8879428 0.807477963 9.94677059 1.89777199 6.60505704 2.92526934 0 1 3 0.676715844 1.08919394 2.38304025 0.868626346 5.0580403 3.68076298 4 1 7 0.457851317 2.09421839 3.91330234 0.609757408 2.86760685 6.32544967 1 1 9 0.17733821 3.42135302 3.75862162 0.682942547 2.41347406 3.19725535 0 0 4 0.083952699 0.780820453 3.16243757 0.143767027 1.86023221 5.38095709 0 1 4 0.599107278 1.82457624 0.443153 0.888342678 10.3867769 0.281903208 0 1 5 0.120531698 3.41610141 2.48894887 1.23441214 4.19860861 3.83903734 0 0 5 1.19676861 2.29244799 2.30249165 1.07224566 5.60452417 4.34454117 2 1 6 0.211791829 0.480155166 4.75924115 0.618430211 3.86354048 1.77642847 0 0 2 0.781846907 3.46911179 7.03886696 1.23451929 1.59179378 5.27424246 0 2 5 0.698858526 1.90171556 3.41347401 0.832096284 8.54168176 3.68517517 0 0 6 0.582511968 0.854716378 7.76185633 0.264851726 3.41338698 2.81501822 2 1 9 2.10778968 0.510274004 8.57174605 1.15561954 3.84413902 1.80679292 0 0 1 0.562664932 0.916306151 5.78767429 0.43106686 4.4904394 5.92414514 0 0 8 1.09936564 5.3219318 4.70571977 1.04404331 13.9662853 4.46623178 0 0 3 1.11520793 1.27234088 5.37493672 1.31649142 3.02763993 2.64099995 1 1 9 3.03945892 1.73072669 3.84093399 0.590133727 6.06831942 4.9135266 2 1 3 0.08684067 1.81653558 5.18499843 0.705796681 5.21494599 2.47513561 1 1 5 1.02121237 1.81428574 8.0717028 1.82638737 4.63566885 1.77112182 2 0 6 2.77746448 1.07878033 8.10219464 1.42621738 9.59324849 6.08913908 1 2 7 0.632487322 2.75477741 7.6336743 1.46931204 3.36665039 4.61699724 3 2 6 1.55247216 1.05716119 7.50802205 0.799734401 2.76841507 2.83716045 5 1 2 2.04898924 2.15940081 0.343087723 0.636491514 6.10398453 2.04294708 0 1 7 0.293944535 0.899142593 3.82128033 1.36238289 4.5567332 3.98173797 0 0 6 0.093653326 1.02888509 9.44860579 0.79813452 2.42237175 1.97060943 6 2 7 0.650956845 2.2555387 9.2030612 1.12713536 1.82205193 2.18940978 1 3 3 0.170131238 0.697397768 7.84729125 1.56586872 11.7381841 5.24888862 1 3 5 0.213744027 0.737077266 2.56385624 0.711362595 5.12898424 4.06702564 0 0 5 0.609283112 1.82877206 3.21349402 1.24373304 3.57023764 2.41931867 0 1 5 2.95394702 4.93463168 0.062893326 0.674180827 4.8426281 6.94635519 0 1 5 1.11271409 1.4241893 1.25139523 0.313809272 3.88379612 5.15682522 2 0 2 0.097610514 1.62858508 0.934685143 0.087888065 4.13567917 3.47102305 0 0 5 1.77790948 2.31114064 2.39465273 1.29075349 1.5681156 5.19881714 0 1 6 2.18945501 1.68989423 7.58704994 0.982784813 3.85412206 0.089630905 0 1 5 1.45191538 1.57714892 1.7419679 1.16559564 4.3447838 6.73728999 6 2 5 3.02504863 0.580265563 3.79437587 0.497938034 8.18298275 4.03682226 1 1 7 0.456428607 1.18611034 7.79922123 0.371010399 2.69735477 6.80357358 0 2 5 0.030115943 1.94990828 3.23048891 0.260513008 3.39725848 2.94831539 0 1 7 1.60698929 1.32987656 9.64490192 1.03492747 3.55540795 5.59217506 1 2 4 0.741315391 0.729600934 6.1249164 0.900155005 2.81650256 3.04979461 0 0 6 1.7750115 1.47247923 4.8136523 1.1406648 2.82984975 3.58324928 1 1 5 0.565989237 2.68195831 1.20306368 1.80986399 5.50812256 4.86202933 0 1 7 0.009658118 1.579176 7.97521417 0.733488908 5.30464056 4.74582711 0 0 3 0.858337562 1.27635909 8.79579717 0.320184089 3.15528244 3.50410233 1 3 3 3.41357508 3.67613896 5.512226 1.78961749 3.99767309 3.21063219 9 1 3 0.266017496 1.93869757 0.397965952 0.304849406 3.29479019 3.34099728 0 0 6 0.445298201 0.460368279 9.38664563 0.522207969 5.23971423 4.2448349 0 0 10 1.27101806 5.15349806 2.37793817 0.137245506 5.11431821 5.64397049 0 1 7 0.449136228 3.81757384 5.10134953 0.644014729 3.63401554 8.17664387 1 1 5 2.44974553 0.528987738 7.75081676 0.346265232 3.40555852 3.25524538 0 0 2 0.332138975 3.86367505 8.57625868 1.79549926 2.76962873 2.37003907 0 0 4 1.7677909 0.706844576 5.78417652 0.994613001 2.33241162 2.93483088 0 1 5 0.633840103 2.73653881 7.27119649 1.68442753 4.08432367 5.58447681 0 3 6 0.61513267 1.05011975 9.59600096 1.13470183 4.22036014 8.02214655 0 0 5 0.364933827 0.838756134 1.20876992 0.137810652 3.61158715 4.70652608 0 0 5 0.311998794 0.800066359 1.26127897 0.566226436 3.04067677 6.0789061 1 1 7 1.33364097 1.6310202 2.30300493 0.696055683 6.36145824 3.53500266 0 1 2 0.146285194 0.698319612 8.06050293 0.77313056 4.82485184 5.88649262 3 0 6 0.559904481 0.161527938 3.33852184 0.467908965 2.47015946 2.26670618 0 1 7 0.734658215 3.21770993 0.8046489 0.689392831 1.42861737 2.66244057 1 1 4 0.053866186 0.6397556 9.53609159 1.36413551 6.0641076 5.19315087 0 1 3 1.66389728 2.14519842 8.06439391 1.07460841 4.00949282 2.56650703 0 1 9 2.72111221 1.08918206 0.614138113 0.941620464 1.74347465 2.73137086 0 0 4 1.92483172 1.33302262 6.15975316 1.14648381 7.10863011 2.59533872 1 2 4 0.023677949 0.685832303 1.74530328 0.595883696 3.6392017 3.90581542 0 0 7 1.40512725 1.07883025 7.22121317 0.883192178 3.92841511 4.6838245 2 2 4 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0 0 4 1.65874722 0.522013107 2.82551392 0.400469357 3.4979316 6.17599845 0 1 4 0.817188581 2.73186533 8.88361465 0.79626558 6.50882472 1.9336714 1 1 2 0.323532092 1.04215656 9.91578265 0.066181832 3.68709143 8.23965259 2 3 7 1.93321805 0.982278969 8.13908146 0.8234485 3.1640297 0.648633492 1 0 2 0.13156068 1.90980317 8.16796429 0.987871229 1.79006936 6.7201488 0 0 4 0.478158405 0.863719956 0.002618933 0.414943308 3.66539965 4.50673259 0 5 7 0.126997356 2.83277033 5.05157848 0.781681618 3.93275324 6.40308312 2 1 5 1.60359178 2.93439867 1.83903363 0.846619567 3.86508945 1.80180524 0 0 6 2.4583323 0.748879851 4.3837252 0.569063381 5.67985714 6.48507384 2 2 5 0.195518219 3.54911373 3.17377213 1.51246091 3.76747665 2.98293629 0 0 5 1.01952607 3.04049428 5.31936974 0.720634941 4.8091639 5.42039821 0 1 6 0.031587493 1.00369703 2.38715196 0.595234164 5.40726415 4.8284898 1 1 7 1.14651368 1.46137224 7.97209236 0.386139673 3.35823836 3.48089395 0 1 3 2.10151468 1.695374 7.90915709 1.19536679 3.78856653 2.43712715 0 1 6 0.230395732 0.651309636 4.58608762 1.00089011 8.85790007 2.86090875 3 0 4 2.20416748 3.31125817 4.53617607 0.693790403 1.15850936 6.32001938 0 0 4 0.777798687 3.32208976 6.42307065 1.42587567 5.36242772 4.50457733 0 0 4 0.558474425 3.47570696 6.61340303 1.49314236 2.59577847 4.03473678 0 1 3 1.45511993 3.86062266 9.13690033 1.29480937 2.984014 6.80004598 0 1 7 1.09910839 1.43400732 3.68070744 1.13088326 2.61812906 4.56088972 0 1 6 0.289433633 3.57982011 9.0115866 0.714139679 6.07295345 7.28765214 1 1 2 1.38791401 1.60933092 8.47211867 1.19973802 2.16526927 5.50669539 1 1 6 2.03059285 1.44653446 2.57053551 0.431351446 4.39390851 2.31206653 0 0 6 0.299909897 1.63219273 9.35105439 1.42496736 3.29557648 7.60845185 1 3 5 0.076720114 1.72390983 6.90101812 0.448144133 3.6462213 4.610217 0 1 2 0.352273496 0.960201188 3.19138795 0.441544596 3.48203301 4.04296222 3 2 5 0.488890145 4.48783209 1.66079674 0.931736632 5.6857871 3.37617232 0 0 7 0.139170235 3.72316907 3.31154268 1.04524094 5.63182232 1.91770727 2 4 3 0.398129412 1.71726525 9.88710911 0.587534838 8.46911876 1.8550207 1 1 4 1.19910005 1.51613109 1.98348437 1.60657542 3.01077752 3.90077475 1 3 6 1.24663878 1.47276636 3.07100239 0.531332518 4.88657505 4.85391663 1 2 4 1.8286937 0.728007496 1.8609596 1.78448341 1.96006925 3.26715474 1 1 4 1.70239633 1.3693002 2.06664103 1.45030793 1.47304978 1.08136184 0 0 4 0.094800038 1.77279014 0.189961384 0.372365784 1.181142 3.04936149 0 3 5 1.01733685 1.98661264 9.80490961 0.661622179 3.2619037 3.56996226 0 0 3 0.904056588 1.14788066 5.78504057 0.837129234 4.31352152 5.29057272 0 2 2 0.006647983 1.57221605 5.54293124 1.12685243 1.94319442 4.18343286 0 3 4 2.17107547 2.59153795 9.58746792 0.594061931 3.61145871 3.58059616 1 1 4 0.206631104 1.62883287 8.61414337 0.66247612 3.21671752 4.83615292 2 2 4 0.457848358 0.24081517 6.98004845 0.257131219 3.27144117 3.25258417 0 0 4 1.88862893 3.28486186 6.53072301 1.23934723 3.44747654 4.60737375 2 1 7 1.68861885 2.79761405 0.436104829 0.193723035 3.17316615 2.97093169 0 0 2 0.38266099 2.72421538 1.56774901 0.282072624 6.02659205 3.71326094 3 0 7 0.436888235 1.71739539 2.05181584 0.541822483 4.55263634 5.93942313 4 3 4 1.07962992 2.92879154 0.670757857 0.898324385 5.56897963 2.35006075 0 2 5 2.15301518 0.912011631 7.72857735 1.54035012 1.9584851 4.37606006 2 1 6 0.015894167 3.18452271 1.74052229 0.231366145 3.15695628 1.90392496 2 1 8 1.73413458 6.2451032 5.92399747 0.591743159 3.07732893 4.63969585 1 1 5 0.744064257 2.53301864 9.88188313 0.851258891 2.74111818 5.42907862 0 1 4 1.2849908 0.664648515 4.32196528 1.05958278 5.58710701 1.15635293 0 3 7 1.80082623 0.754649791 7.27664291 0.822166052 6.29217245 3.97658544 2 2 9 1.47522243 1.92958253 9.96986639 0.862447307 4.87473424 3.38334352 3 1 5 0.159605346 1.03276467 8.70907241 0.540822724 4.51549225 3.55636154 0 1 5 0.865840887 2.9255537 5.30214742 0.085058681 5.06380901 2.73528847 0 1 4 ##### Sheet/List 3 ##### Vygenerujte 100 normálně rozdělených hodnot o průměru 5: ##### Sheet/List 4 ##### Následující tabulka uává počty bodů z písemky předmětu Analýza dat na PC v letech 2010 a 2011. "Testujte normalitu rozdělení obou souborů za využití Kolmogorovova-Smirnovova, Shapiro-Wilksova nebo χ2 testu." "Testujte homoskedasticitu za použití Bartlettova, Levenova nebo Brown-Forsytheova testu." Za jakých předpokladů lze použít dvojvýběrový nepárový t-test pro hodnocení pokroku studentů? "Pokud jsou podmínky splněny, otestujte, zda se na hlaině významnosti 5 % změnila úspěšnost studentů a pokud ano, určete, zda se zlepšila nebo zhoršila." podzim 2010 jaro 2011 Výpočet p v Excelu: 75 63 44 78 Výsledek pro p ze Statistiky: 62 83 57 66 Průměrný zisk podzim 2010: 54 60 59 63 Půměrný zisk jaro 2011: 65 98 62 82 68 79 70 78 68 79 59 71 48 93 42 52 28 38 90 85 53 41 76 26 74 89 68 95 83 88 68 62 59 ##### Sheet/List 5 ##### Na hladině významnosti 5 % rozhodněte o účinnosti fyzických trestů pro žáky 5. třídy na zlepšení jejich průměrného prospěchu. Ověřte normalitu rozdílů. Jak velká změna prospěchu ospravedlňuje na této hladině významnosti použití fyzických trestů? "Kolik žáků by muselo být bito, aby byl test statisticky významný na stejné hladině pravděpodobnosti?" Prospěch bez rákosky Prospěch s rákoskou Průměrný prospěch před bitím 2.51 2.46 Průměrný prospěch po bití 2.52 2.32 Směrodatná odchylka před bitím 1.93 1.78 Směrodatná odchylka po bití 1.42 1.44 Rozdíl prospěchů 2.03 2.32 s 3.10 3.12 stupně volnosti 1.01 1.19 1-α/2 1.09 1.27 t 5 % hv 2.35 2.29 t výpočet 2.31 2.14 n z tabulky 2.06 2.15 1.92 2.18 Výpočet p v Excelu: 1.75 1.54 2.19 2.38 Výsledek pro p ze Statistiky: 2.35 1.94 2.50 2.67 2.37 2.00 2.49 2.55 2.03 2.03 1.75 1.65 1.03 1.35 1.70 1.63 2.82 2.73 2.94 2.89 1.18 1.07 2.84 2.63 1.60 1.62 ##### Sheet/List 6 ##### Následující tabulka obsahuje výsledky měření koncentrace fluorenu (ng/m3) na observatoři v Košeticích dvěma vzorkovači značek Digitel a PS-1. "Na hladině významnosti 5 % rozhodněte, zda lze považovat výsledky z obou měřících přístrojů za ekvivalntní." "Jak velká je pracděpodobnost, že se dopustíme chyby 1. druhu?" 1/5/2011 3.289 0.636 p-hodnota Wilcoxonova testu 1/12/2011 2.412 0.2733 1/19/2011 2.099 2.021 1/26/2011 3.048 2.905 2/2/2011 7.0699 4.408 2/9/2011 1.881 3.786 2/16/2011 2/23/2011 8.616 7.888 3/2/2011 2.385 3.935 3/9/2011 2.426 1.539 3/16/2011 0.7609 1.0873 3/23/2011 3/30/2011 2.225 0.874 4/6/2011 0.998 0.5423 4/13/2011 0.88 0.77 4/20/2011 0.957 0.734 4/27/2011 0.95 0.627 5/4/2011 0.86 0.771 5/11/2011 0.586 0.299 5/18/2011 0.432 0.267 5/25/2011 0.392 0.3903 6/1/2011 0.38 0.344 6/8/2011 0.368 0.3 6/15/2011 0.338 0.148 6/22/2011 0.247 0.1633 6/29/2011 0.39 0.351