{"text_format":"3","workbook":"xls","n_sheets":44,"sheets":["1a","L1a","1","L1","2","L2","3","3a","L3a","4","L4","5","L5","6","L6","7","L7","8a","L8a","8","L8","9","L9","10","L10","11","L11","12","L12","13","L13","14","L14","15","29","L29","30","L30","31","L31","32","L32","40","L40"],"not_rendered":{"charts":10,"images":9,"external_links":2},"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"1a","index":0,"n_rows":61,"n_cols":7,"rows_kept":61,"flags":["formulas_cached_only"]}
["Übung 1a",{"$nulls":3},"Del Buono","Salzgeber","SS 03"]
[]
[]
[]
[]
["In einem Kurort beträgt die durchschnittliche Anzahl Gäste pro Hotel im Monat April 420 (Standardabweichung 30). Durch eine Werbekampagne"]
["für Frühlingsskifahren sollen die Frequenzen erhöht werden. Die 50 Hotels konnten im nächsten April unten aufgelistete Zahlen verbuchen."]
["(rechtsseitiger Test, Signifikanzniveau = 0,01)"]
[]
[]
["Gästezahlen"]
[350]
[420]
[486]
[425]
[493]
[395]
[422]
[380]
[510]
[600]
[290]
[402]
[395]
[455]
[425]
[315]
[423]
[433]
[386]
[336]
[566]
[425]
[430]
[460]
[470]
[370]
[366]
[399]
[385]
[422]
[455]
[496]
[510]
[601]
[290]
[510]
[366]
[425]
[425]
[502]
[377]
[364]
[389]
[486]
[401]
[700]
[425]
[245]
[425]
[405]

{"sheet":"L1a","index":1,"n_rows":60,"n_cols":7,"rows_kept":60,"flags":["formulas_cached_only"]}
["Lösung Übung 1a"]
[]
[]
["alter Durchschnitt",null,420,null,"z-Wert",2.031753484609348]
["Standardabweichung",null,30]
["Anzahl Daten",null,50,null,"p-Wert",0.02108924043911542,">0.01"]
["neuer Durchschnitt",null,428.62]
[{"$nulls":4},"Das Resultat ist also nicht signifikant. Die Werbekampagne hat nicht zu mehr"]
[{"$nulls":4},"Buchungen verholfen."]
[]
[350]
[420,null,null,"(Die Autoren hatten eine Standardabweichung von 1 vorgegeben. Damit wäre der Test signifikant. "]
[486,null,null,"Allerdings beträgt die Standardabweichung der Stichprobe ca 81.7. Der Unterschied der beiden "]
[425,null,null,"Standardabweichungen ist nicht realistisch."]
[493,null,null,"Deshalb wurde die Standardabweichung angepasst. "]
[395,null,null,"Man beachte, dass die Unterschied der Durchschnitte nur "]
[422]
[380]
[510]
[600]
[290]
[402]
[395]
[455]
[425]
[315]
[423]
[433]
[386]
[336]
[566]
[425]
[430]
[460]
[470]
[370]
[366]
[399]
[385]
[422]
[455]
[496]
[510]
[601]
[290]
[510]
[366]
[425]
[425]
[502]
[377]
[364]
[389]
[486]
[401]
[700]
[425]
[245]
[425]
[405]

{"sheet":"1","index":2,"n_rows":36,"n_cols":7,"rows_kept":36,"flags":["formulas_cached_only"]}
["Neue Diätmethode","Rohrer/Robert",{"$nulls":4},"WS 03"]
["Es wird eine neue Diätmethode getestet. Die alte Diätmethode weist folgende Kennzahlen auf:"]
["Durchschnittlicher Gewichtverlust alte Methode",15.49,"Neue Methode",null,null,"Methode 1"]
[null,9.266936033461963,"Gewichtverlust",null,null,"Gewichtverlust"]
[]
["Die neue Diätmethode wird an 30 Personen getestet, mit folgenden Resultaten: "]
["Ist die neue Methode besser (alpha = 0.01)?",1,15,null,1,5]
["Liegt ein links oder ein rechtsseitiger Test vor?",2,30,null,2,20]
["Formulieren Sie die Hypothesen",3,20,null,3,15]
[null,4,15,null,4,13]
[null,5,22,null,5,18]
[null,6,32,null,6,30]
[null,7,13,null,7,12]
[null,8,12,null,8,10.5]
[null,9,4.5,null,9,3.5]
[null,10,6,null,10,6.3]
[null,11,10,null,11,9.8]
[null,12,18,null,12,17]
[null,13,30,null,13,33]
[null,14,41,null,14,40]
[null,15,7,null,15,7.9]
[null,16,6.5,null,16,6.2]
[null,17,9,null,17,8]
[null,18,5,null,18,4.5]
[null,19,8,null,19,8.5]
[null,20,17,null,20,16]
[null,21,18,null,21,17.5]
[null,22,2,null,22,2.5]
[null,23,28,null,23,26]
[null,24,20,null,24,22]
[null,25,10,null,25,17]
[null,26,15,null,26,16.5]
[null,27,14,null,27,13.2]
[null,28,15,null,28,14.8]
[null,29,25,null,29,22]
[null,30,27,null,30,29]

{"sheet":"L1","index":3,"n_rows":41,"n_cols":11,"rows_kept":41,"flags":["formulas_cached_only"]}
["Es kann ein z-Test angewendet werden (n >=30; Mittelwert und Standardabweichung der Grundgesamtheit sind bekannt)"]
[]
[null,null,"Neue Methode",null,null,"Methode 1",null,"Z",0.5969608305082387]
[null,null,"Gewichtverlust",null,null,"Gewichtverlust",null,"Normalverteilung",0.724733285557446]
[null,1,15,null,1,5,null,"p-Wert:",0.275266714442554,"> 0.01","Nich signifikante Abweichung"]
[null,2,30,null,2,20,{"$nulls":4},"Die neue Methode ist nicht besser"]
[null,3,20,null,3,15]
[null,4,15,null,4,13]
[null,5,22,null,5,18]
[null,6,32,null,6,30]
[null,7,13,null,7,12]
[null,8,12,null,8,10.5]
[null,9,4.5,null,9,3.5]
[null,10,6,null,10,6.3]
[null,11,10,null,11,9.8]
[null,12,18,null,12,17]
[null,13,30,null,13,33]
[null,14,41,null,14,40]
[null,15,7,null,15,7.9]
[null,16,6.5,null,16,6.2]
[null,17,9,null,17,8]
[null,18,5,null,18,4.5]
[null,19,8,null,19,8.5]
[null,20,17,null,20,16]
[null,21,18,null,21,17.5]
[null,22,2,null,22,2.5]
[null,23,28,null,23,26]
[null,24,20,null,24,22]
[null,25,10,null,25,17]
[null,26,15,null,26,16.5]
[null,27,14,null,27,13.2]
[null,28,15,null,28,14.8]
[null,29,25,null,29,22]
[null,30,27,null,30,29]
[]
["Durchschnittlicher Gewichtverlust ",15.49,16.5]
["Standardabweichung",9.266936033461963]
["n",30]
["Ho:","Die neue Diätmethode ist nicht besser."]
["Ha:","Die neue Diätmethode ist besser.",{"$nulls":4},"Rechtsseitiger Test"]
["Signifikanzniveau:",0.01]

{"sheet":"2","index":4,"n_rows":56,"n_cols":8,"rows_kept":56,"flags":["formulas_cached_only"]}
["Neues Düngemittel",null,"Anja Kimmig","Sonja Borter",{"$nulls":3},"WS03"]
[]
[]
[]
["Wir wollen testen, ob die Benutzung des neuen Düngemittels XS305 zu einem erhöhten Gewicht der Tomate führt."]
[]
["Mittelwert / Gewicht vor Einführung",null,null,"100g"]
["Standardabweichung",null,null,"8.5g"]
[]
["Wir testen den neuen Dünger an 40 Tomaten:",null,null,"Signifikanzniveau:",null,0.05]
["Formulieren Sie die Hypothesen."]
["Ist der Test rechts-, links- oder zweiseitig?"]
["Führt das neue Düngemittel zu erhöhtem Gewicht der Tomate"]
[]
["Gewicht der getesteten Tomaten:"]
[]
[110]
[105]
[108]
[95]
[100]
[97]
[105]
[115]
[85]
[127]
[103]
[121]
[102]
[99]
[107]
[117]
[130]
[109]
[104]
[115]
[96]
[115]
[102]
[96]
[104]
[115]
[86]
[106]
[106]
[113]
[108]
[95]
[106]
[80]
[104]
[94]
[119]
[112]
[100]
[113]

{"sheet":"L2","index":5,"n_rows":55,"n_cols":6,"rows_kept":55,"flags":["formulas_cached_only"]}
["Es kann ein z-Test angewendet werden."]
["(n > 30), Mittelwert und Standardabweichung der Grundgesamtheit sind bekannt"]
[]
[]
[]
[]
["Ho = Die Ergebnisse unterscheiden sich nicht"]
["Ha = Der Mittelwert mit dem neuen Düngermittels XS305 ist grösser als der Mittelwert der alten Anwendung"]
[]
["Rechtsseitiger Test",null,"Mittelwert der Grundgesamtheit",100,"neuer Mittelwert",105.6]
["p-Wert:",null,"Standardabweichung der Grundgesamtheit",8.5]
[null,null,"n = ",40]
["Testwert Z",4.166765858104214,"p-Wert",1.5456801137014864e-05,"<0.05"]
["Die Nullhypothese kann verworfen werden. "]
[]
[110]
[105]
[108]
[95]
[100]
[97]
[105]
[115]
[85]
[127]
[103]
[121]
[102]
[99]
[107]
[117]
[130]
[109]
[104]
[115]
[96]
[115]
[102]
[96]
[104]
[115]
[86]
[106]
[106]
[113]
[108]
[95]
[106]
[80]
[104]
[94]
[119]
[112]
[100]
[113]

{"sheet":"3","index":6,"n_rows":27,"n_cols":7,"rows_kept":27,"flags":["formulas_cached_only"]}
["Übung 3",null,"Anja Kimmig","Sonja Borter",null,null,"WS03"]
["Eine Person behauptet, sie könne für jeden Tag das Wetter richtig voraussagen!"]
[]
["Ho: Sie kann die Prognosen nicht richtig voraussagen"]
["Ha: Sie sagt die Prognosen richtig voraus."]
[]
[]
["Signifikantsniveau",0.05]
[]
["Es wird ein Test durchgeführt. "]
["Die Person macht eine Vorhersage für 3 Wochen"]
[]
["Anzahl Versuche",21]
[]
["Anzahl richtiger Voraussagen xi","P(X=xi)","umgekehrt kumulativ"]
[21,4.7683715820312495e-07,4.7683715820312495e-07]
[20,1.0013580322265625e-05,1.049041748046875e-05]
[19,0.00010013580322265625,0.000110626220703125]
[18,0.0006341934204101565,0.0007448196411132815]
[17,0.0028538703918457036,0.0035986900329589852]
[16,0.009703159332275394,0.013301849365234378]
[15,0.025875091552734396,0.03917694091796878]
[14,0.05544662475585942,0.0946235656738282]
[13,0.097031593322754,0.1916551589965822]
[12,0.14015674591064464,0.33181190490722684]
[]
[null,null,"Die Nullhypothese wird verworfen, wenn die Person mindestens 15 richtige Voraussagen macht."]

{"sheet":"3a","index":7,"n_rows":120,"n_cols":10,"rows_kept":120,"flags":["formulas_cached_only"]}
[null,"Übung 50",{"$nulls":5},"Claudia Sofia Paiva Lima",null,"SS 03"]
[]
[null,"Zwei Kühe geben folgende Litereinheiten an Milch pro Tag: "]
[]
[null,"HO:",null,"Die zwei Kühen unterscheiden sich nicht"]
[null,"HA:",null,"Die zweite Kuh gibt mehr Milch (einseitiger Test, a = 0.05)"]
[]
[]
[null,"Kuh 1","Kuh 2"]
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[2,{"v":25.699091423883065,"d":"25.70"},{"v":22.908723000000002,"d":"22.9087"}]
[3,{"v":25.818352222596843,"d":"25.82"},{"v":23.1088155,"d":"23.1088"}]
[4,{"v":26.110805105444637,"d":"26.11"},{"v":23.346327,"d":"23.3463"}]
[5,{"v":26.29046700821274,"d":"26.29"},{"v":23.9885625,"d":"23.9886"}]
[6,{"v":26.296330253717585,"d":"26.30"},{"v":24.378909,"d":"24.3789"}]
[7,{"v":26.46811964122573,"d":"26.47"},{"v":24.694315500000002,"d":"24.6943"}]
[8,{"v":26.47299907243596,"d":"26.47"},{"v":25.395429,"d":"25.3954"}]
[9,{"v":26.78893284463213,"d":"26.79"},{"v":25.512057,"d":"25.5121"}]
[10,{"v":26.86882210485406,"d":"26.87"},{"v":25.592848500000002,"d":"25.5928"}]
[11,{"v":26.88082297112587,"d":"26.88"},{"v":25.6330545,"d":"25.6331"}]
[12,{"v":26.902330074414245,"d":"26.90"},{"v":25.687884,"d":"25.6879"}]
[13,{"v":26.970113781858142,"d":"26.97"},{"v":26.286039,"d":"26.2860"}]
[14,{"v":27.022160799283217,"d":"27.02"},{"v":26.544366,"d":"26.5444"}]
[15,{"v":27.22526633511601,"d":"27.23"},{"v":26.5989465,"d":"26.5989"}]
[16,{"v":27.274249536331357,"d":"27.27"},{"v":26.730306,"d":"26.7303"}]
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[21,{"v":27.835265151306984,"d":"27.84"},{"v":27.0775185,"d":"27.0775"}]
[22,{"v":28.094713013403315,"d":"28.09"},{"v":27.1051485,"d":"27.1051"}]
[23,{"v":28.149607611392472,"d":"28.15"},{"v":27.1221375,"d":"27.1221"}]
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[35,{"v":29.354090461165523,"d":"29.35"},{"v":28.18188,"d":"28.1819"}]
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[92,{"v":33.23792761842847,"d":"33.24"},{"v":33.7738965,"d":"33.7739"}]
[93,{"v":33.27862778826403,"d":"33.28"},{"v":33.990069,"d":"33.9901"}]
[94,{"v":33.668029278000645,"d":"33.67"},{"v":34.9314675,"d":"34.9315"}]
[95,{"v":34.06030515132736,"d":"34.06"},{"v":35.2648785,"d":"35.2649"}]
[96,{"v":34.3222803230716,"d":"34.32"},{"v":35.331873,"d":"35.3319"}]
[97,{"v":34.402264940817474,"d":"34.40"},{"v":35.688171,"d":"35.6882"}]
[98,{"v":34.62775708353834,"d":"34.63"},{"v":35.7328395,"d":"35.7328"}]
[99,{"v":34.793780214313166,"d":"34.79"},{"v":35.772174,"d":"35.7722"}]
[100,{"v":34.81006224113603,"d":"34.81"},{"v":36.072213,"d":"36.0722"}]
[101,{"v":35.09269398209159,"d":"35.09"},{"v":36.497979,"d":"36.4980"}]
[102,{"v":35.11658832886335,"d":"35.12"},{"v":36.4991295,"d":"36.4991"}]
[103,{"v":35.23188994051191,"d":"35.23"},{"v":37.500723,"d":"37.5007"}]
[104,{"v":36.03597643273169,"d":"36.04"},{"v":37.6026855,"d":"37.6027"}]
[105,null,{"v":37.735158,"d":"37.7352"}]
[106,null,{"v":38.346057,"d":"38.3461"}]
[107,null,{"v":39.065740500000004,"d":"39.0657"}]
[]
["Mittelwert:"]
["Varianz:"]
["Standartabw.:"]

{"sheet":"L3a","index":8,"n_rows":120,"n_cols":12,"rows_kept":120,"flags":["formulas_cached_only"]}
["Es handelt sich um einen Zweistichprobentest:"]
[]
[null,"Zwei Kühe geben folgende Litereinheiten an Milch pro Tag: "]
[]
[null,"HO:",null,"Die zwei Kühen unterscheiden sich nicht"]
[null,"HA:",null,"Die zweite Kuh gibt mehr Milch (einseitiger Test, a = 0.05)"]
[]
[{"$nulls":7},"Überprüfung Normalverteilung:"]
[null,"Kuh 1",{"$nulls":3},"Kuh 2"]
[1,{"v":25.373969297798613,"d":"25.37"},0.022122544152475276,{"v":0.009615384615384616,"d":"0.01"},{"v":0.009345794392523364,"d":"0.01"},{"v":22.836609,"d":"22.8366"},0.02097188769289904]
[2,{"v":25.699091423883065,"d":"25.70"},0.030107271483520992,{"v":0.019230769230769232,"d":"0.02"},{"v":0.018691588785046728,"d":"0.02"},{"v":22.908723000000002,"d":"22.9087"},0.021996847191453006]
[3,{"v":25.818352222596843,"d":"25.82"},0.03358009834231346,{"v":0.028846153846153848,"d":"0.03"},{"v":0.028037383177570093,"d":"0.03"},{"v":23.1088155,"d":"23.1088"},0.025064539122040985]
[4,{"v":26.110805105444637,"d":"26.11"},0.04350581198447312,{"v":0.038461538461538464,"d":"0.04"},{"v":0.037383177570093455,"d":"0.04"},{"v":23.346327,"d":"23.3463"},0.029163565461466257]
[5,{"v":26.29046700821274,"d":"26.29"},0.050696871680999456,{"v":0.04807692307692308,"d":"0.05"},{"v":0.04672897196261682,"d":"0.05"},{"v":23.9885625,"d":"23.9886"},0.04310233540607811]
[6,{"v":26.296330253717585,"d":"26.30"},0.050946615451742616,{"v":0.057692307692307696,"d":"0.06"},{"v":0.056074766355140186,"d":"0.06"},{"v":24.378909,"d":"24.3789"},0.05392791750828252]
[7,{"v":26.46811964122573,"d":"26.47"},0.058708190775051294,{"v":0.0673076923076923,"d":"0.07"},{"v":0.06542056074766354,"d":"0.07"},{"v":24.694315500000002,"d":"24.6943"},0.0641610545566682]
[8,{"v":26.47299907243596,"d":"26.47"},0.058941502738669826,{"v":0.07692307692307693,"d":"0.08"},{"v":0.07476635514018691,"d":"0.07"},{"v":25.395429,"d":"25.3954"},0.09225119878338739]
[9,{"v":26.78893284463213,"d":"26.79"},0.07565419681923391,{"v":0.08653846153846154,"d":"0.09"},{"v":0.08411214953271028,"d":"0.08"},{"v":25.512057,"d":"25.5121"},0.09769596415729476]
[10,{"v":26.86882210485406,"d":"26.87"},0.08040433537743819,{"v":0.09615384615384616,"d":"0.10"},{"v":0.09345794392523364,"d":"0.09"},{"v":25.592848500000002,"d":"25.5928"},0.10160348425345811]
[11,{"v":26.88082297112587,"d":"26.88"},0.08113694917635228,{"v":0.10576923076923077,"d":"0.11"},{"v":0.102803738317757,"d":"0.10"},{"v":25.6330545,"d":"25.6331"},0.10358994740834371]
[12,{"v":26.902330074414245,"d":"26.90"},0.08246247333085677,{"v":0.11538461538461539,"d":"0.12"},{"v":0.11214953271028037,"d":"0.11"},{"v":25.687884,"d":"25.6879"},0.10634412449919428]
[13,{"v":26.970113781858142,"d":"26.97"},0.08674678888916365,{"v":0.125,"d":"0.13"},{"v":0.12149532710280374,"d":"0.12"},{"v":26.286039,"d":"26.2860"},0.13986533032810655]
[14,{"v":27.022160799283217,"d":"27.02"},0.09014774710637796,{"v":0.1346153846153846,"d":"0.13"},{"v":0.1308411214953271,"d":"0.13"},{"v":26.544366,"d":"26.5444"},0.1563570456101412]
[15,{"v":27.22526633511601,"d":"27.23"},0.10436844139603729,{"v":0.14423076923076922,"d":"0.14"},{"v":0.14018691588785046,"d":"0.14"},{"v":26.5989465,"d":"26.5989"},0.15999907676160552]
[16,{"v":27.274249536331357,"d":"27.27"},0.10802917025576053,{"v":0.15384615384615385,"d":"0.15"},{"v":0.14953271028037382,"d":"0.15"},{"v":26.730306,"d":"26.7303"},0.1689899606605092]
[17,{"v":27.412258504151776,"d":"27.41"},0.11883796991790985,{"v":0.16346153846153846,"d":"0.16"},{"v":0.1588785046728972,"d":"0.16"},{"v":26.7750795,"d":"26.7751"},0.1721272336003974]
[18,{"v":27.58403459602045,"d":"27.58"},0.13332974409169862,{"v":0.17307692307692307,"d":"0.17"},{"v":0.16822429906542055,"d":"0.17"},{"v":26.940312,"d":"26.9403"},0.18402414945179546]
[19,{"v":27.694188013219303,"d":"27.69"},0.14323840320608816,{"v":0.18269230769230768,"d":"0.18"},{"v":0.17757009345794392,"d":"0.18"},{"v":26.9613555,"d":"26.9614"},0.18557523072681703]
[20,{"v":27.759704262842007,"d":"27.76"},0.14936200276994993,{"v":0.19230769230769232,"d":"0.19"},{"v":0.18691588785046728,"d":"0.19"},{"v":26.97117,"d":"26.9712"},0.1863014072104212]
[21,{"v":27.835265151306984,"d":"27.84"},0.1566384494533154,{"v":0.20192307692307693,"d":"0.20"},{"v":0.19626168224299065,"d":"0.20"},{"v":27.0775185,"d":"27.0775"},0.19428263873333607]
[22,{"v":28.094713013403315,"d":"28.09"},0.18336867387919087,{"v":0.21153846153846154,"d":"0.21"},{"v":0.205607476635514,"d":"0.21"},{"v":27.1051485,"d":"27.1051"},0.19638980087040603]
[23,{"v":28.149607611392472,"d":"28.15"},0.18936927338968546,{"v":0.22115384615384615,"d":"0.22"},{"v":0.21495327102803738,"d":"0.21"},{"v":27.1221375,"d":"27.1221"},0.1976922926213589]
[24,{"v":28.203655149429125,"d":"28.20"},0.19539390360794295,{"v":0.23076923076923078,"d":"0.23"},{"v":0.22429906542056074,"d":"0.22"},{"v":27.2136195,"d":"27.2136"},0.20479522315612098]
[25,{"v":28.394955509891247,"d":"28.39"},0.2176357933815244,{"v":0.2403846153846154,"d":"0.24"},{"v":0.2336448598130841,"d":"0.23"},{"v":27.3462375,"d":"27.3462"},0.2153573031658036]
[26,{"v":28.680946495282065,"d":"28.68"},0.2534688730549751,0.25,{"v":0.24299065420560748,"d":"0.24"},{"v":27.366801,"d":"27.3668"},0.21702288489961663,"Normalverteilung ist i.O."]
[27,{"v":28.762751960240582,"d":"28.76"},0.26426093626735614,{"v":0.25961538461538464,"d":"0.26"},{"v":0.2523364485981308,"d":"0.25"},{"v":27.549165,"d":"27.5492"},0.23211596550637192]
[28,{"v":29.03710216118583,"d":"29.04"},0.3020825577044084,{"v":0.2692307692307692,"d":"0.27"},{"v":0.2616822429906542,"d":"0.26"},{"v":27.638277,"d":"27.6383"},0.23969853499308547,"Test der Varianzen:",null,{"v":0.4594276459148661,"d":"0.4594"}]
[29,{"v":29.054789147859662,"d":"29.05"},0.30460208112700304,{"v":0.27884615384615385,"d":"0.28"},{"v":0.27102803738317754,"d":"0.27"},{"v":27.6546405,"d":"27.6546"},0.24110545549045959,"Fvert:",null,0.99995372121068,{"v":4.627878931995344e-05,"d":"0.00004627878932"},"Die Varianzen untescheiden sich"]
[30,{"v":29.12309524872021,"d":"29.12"},0.3144188025617549,{"v":0.28846153846153844,"d":"0.29"},{"v":0.2803738317757009,"d":"0.28"},{"v":27.7077465,"d":"27.7077"},0.24570223725622298,{"$nulls":4},"nicht signifikant. "]
[31,{"v":29.12844980919265,"d":"29.13"},0.315194040492381,{"v":0.2980769230769231,"d":"0.30"},{"v":0.2897196261682243,"d":"0.29"},{"v":27.9797205,"d":"27.9797"},0.2699631621043649,{"$nulls":4},"Somit können wir den t-Test verwenden"]
[32,{"v":29.16434617983196,"d":"29.16"},0.3204120460849461,{"v":0.3076923076923077,"d":"0.31"},{"v":0.29906542056074764,"d":"0.30"},{"v":28.0632255,"d":"28.0632"},0.27764555589126116]
[33,{"v":29.222505141573695,"d":"29.22"},0.32894169593068856,{"v":0.3173076923076923,"d":"0.32"},{"v":0.308411214953271,"d":"0.31"},{"v":28.148712,"d":"28.1487"},0.2856192716855568,null,null,"Testwert:",0.25859125769307967]
[34,{"v":29.32696937121117,"d":"29.33"},0.34448596604142856,{"v":0.3269230769230769,"d":"0.33"},{"v":0.3177570093457944,"d":"0.32"},{"v":28.1680875,"d":"28.1681"},0.2874415469152569,null,null,"p-Wert",0.39810255757970864,"> 0.05"]
[35,{"v":29.354090461165523,"d":"29.35"},0.348566237063169,{"v":0.33653846153846156,"d":"0.34"},{"v":0.32710280373831774,"d":"0.33"},{"v":28.18188,"d":"28.1819"},0.28874207946978825,null,null,"nicht signifikantes Ergebnis"]
[36,{"v":29.415860657851674,"d":"29.42"},0.3579243347653116,{"v":0.34615384615384615,"d":"0.35"},{"v":0.3364485981308411,"d":"0.34"},{"v":28.202463,"d":"28.2025"},0.2906880431657939]
[37,{"v":29.456030900576394,"d":"29.46"},0.36405663372538677,{"v":0.3557692307692308,"d":"0.36"},{"v":0.34579439252336447,"d":"0.35"},{"v":28.4190135,"d":"28.4190"},0.3115229331910365]
[38,{"v":29.55099974802601,"d":"29.55"},0.3786909308757126,{"v":0.36538461538461536,"d":"0.37"},{"v":0.35514018691588783,"d":"0.36"},{"v":28.4578815,"d":"28.4579"},0.3153300053898136,null,null,"Mit SPSS"]
[39,{"v":29.584446442689355,"d":"29.58"},0.3838878733035066,{"v":0.375,"d":"0.38"},{"v":0.3644859813084112,"d":"0.36"},{"v":28.6521975,"d":"28.6522"},0.33465166899964327]
[40,{"v":29.624806507711128,"d":"29.62"},0.39018684559651184,{"v":0.38461538461538464,"d":"0.38"},{"v":0.37383177570093457,"d":"0.37"},{"v":28.7223045,"d":"28.7223"},0.3417351324046358]
[41,{"v":29.68170078514891,"d":"29.68"},0.39911512514310576,{"v":0.3942307692307692,"d":"0.39"},{"v":0.38317757009345793,"d":"0.38"},{"v":28.725864,"d":"28.7259"},0.34209629385992535]
[42,{"v":29.725488821184044,"d":"29.73"},0.40602306393973586,{"v":0.40384615384615385,"d":"0.40"},{"v":0.3925233644859813,"d":"0.39"},{"v":28.7487285,"d":"28.7487"},0.3444196526921126]
[43,{"v":29.912626395493405,"d":"29.91"},0.43585080116047636,{"v":0.41346153846153844,"d":"0.41"},{"v":0.40186915887850466,"d":"0.40"},{"v":28.81104,"d":"28.8110"},0.35078103336420363]
[44,{"v":30.025221205883387,"d":"30.03"},0.45398623519906867,{"v":0.4230769230769231,"d":"0.42"},{"v":0.411214953271028,"d":"0.41"},{"v":28.929903,"d":"28.9299"},0.36303116612790887]
[45,{"v":30.132698594496418,"d":"30.13"},0.4713879554927922,{"v":0.4326923076923077,"d":"0.43"},{"v":0.4205607476635514,"d":"0.42"},{"v":29.286096,"d":"29.2861"},0.40054196625777316]
[46,{"v":30.1694691052853,"d":"30.17"},0.4773557561199936,{"v":0.4423076923076923,"d":"0.44"},{"v":0.42990654205607476,"d":"0.43"},{"v":29.425959,"d":"29.4260"},0.4155474816190108]
[47,{"v":30.177234267695674,"d":"30.18"},0.47861672641327113,{"v":0.4519230769230769,"d":"0.45"},{"v":0.4392523364485981,"d":"0.44"},{"v":29.5556745,"d":"29.5557"},0.42957576171808465]
[48,{"v":30.1903456511956,"d":"30.19"},0.4807463395958279,{"v":0.46153846153846156,"d":"0.46"},{"v":0.4485981308411215,"d":"0.45"},{"v":29.576703,"d":"29.5767"},0.4318588122100946]
[49,{"v":30.197606381667793,"d":"30.20"},0.48192590264967106,{"v":0.47115384615384615,"d":"0.47"},{"v":0.45794392523364486,"d":"0.46"},{"v":29.6087355,"d":"29.6087"},0.43534091278177667]
[50,{"v":30.23984180960066,"d":"30.24"},0.48879019673970103,{"v":0.4807692307692308,"d":"0.48"},{"v":0.4672897196261682,"d":"0.47"},{"v":29.6129265,"d":"29.6129"},0.43579687356585184]
[51,{"v":30.285766343436684,"d":"30.29"},0.4962577779516053,{"v":0.49038461538461536,"d":"0.49"},{"v":0.4766355140186916,"d":"0.48"},{"v":29.7969585,"d":"29.7970"},0.45589439429419965]
[52,{"v":30.31840099580738,"d":"30.32"},0.5015653117697241,{"v":0.5,"d":"0.50"},{"v":0.48598130841121495,"d":"0.49"},{"v":29.98383405,"d":"29.9838"},0.4764183605388961]
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[54,{"v":30.40463305302365,"d":"30.40"},0.5155858184364581,{"v":0.5192307692307693,"d":"0.52"},{"v":0.5046728971962616,"d":"0.50"},{"v":30.0165696,"d":"30.0166"},0.4800216174082801]
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[56,{"v":30.42157252427891,"d":"30.42"},0.5183382908288516,{"v":0.5384615384615384,"d":"0.54"},{"v":0.5233644859813084,"d":"0.52"},{"v":30.2405295,"d":"30.2405"},0.5047017563309415]
[57,{"v":30.45261026301295,"d":"30.45"},0.5233792065656695,{"v":0.5480769230769231,"d":"0.55"},{"v":0.5327102803738317,"d":"0.53"},{"v":30.276807,"d":"30.2768"},0.5087002897077643]
[58,{"v":30.633633852501877,"d":"30.63"},0.5526794477872043,{"v":0.5576923076923077,"d":"0.56"},{"v":0.5420560747663551,"d":"0.54"},{"v":30.4061775,"d":"30.4062"},0.5229496598372394]
[59,{"v":30.707435960133093,"d":"30.71"},0.5645520257083264,{"v":0.5673076923076923,"d":"0.57"},{"v":0.5514018691588785,"d":"0.55"},{"v":30.5294625,"d":"30.5295"},0.536501729381144]
[60,{"v":30.72425732361491,"d":"30.72"},0.5672503581206669,{"v":0.5769230769230769,"d":"0.58"},{"v":0.5607476635514018,"d":"0.56"},{"v":30.53655,"d":"30.5366"},0.5372796852669867]
[61,{"v":30.74609256810281,"d":"30.75"},0.5707482823962038,{"v":0.5865384615384616,"d":"0.59"},{"v":0.5700934579439252,"d":"0.57"},{"v":30.687507,"d":"30.6875"},0.5538108032303413]
[62,{"v":30.828173333937663,"d":"30.83"},0.5838455061576873,{"v":0.5961538461538461,"d":"0.60"},{"v":0.5794392523364486,"d":"0.58"},{"v":30.721422,"d":"30.7214"},0.5575129961056122]
[63,{"v":30.969643483557135,"d":"30.97"},0.6061943822274188,{"v":0.6057692307692307,"d":"0.61"},{"v":0.5887850467289719,"d":"0.59"},{"v":30.783321,"d":"30.7833"},0.5642567919150265]
[64,{"v":31.117272295808306,"d":"31.12"},0.6291478623081633,{"v":0.6153846153846154,"d":"0.62"},{"v":0.5981308411214953,"d":"0.60"},{"v":30.8052435,"d":"30.8052"},0.5666408435284129]
[65,{"v":31.121515053154702,"d":"31.12"},0.6298012195658356,{"v":0.625,"d":"0.63"},{"v":0.6074766355140186,"d":"0.61"},{"v":30.834006,"d":"30.8340"},0.569765051364512]
[66,{"v":31.146070144759044,"d":"31.15"},0.6335751390855506,{"v":0.6346153846153846,"d":"0.63"},{"v":0.616822429906542,"d":"0.62"},{"v":30.9099195,"d":"30.9099"},0.5779893959824582]
[67,{"v":31.18708276199991,"d":"31.19"},0.6398495773438463,{"v":0.6442307692307693,"d":"0.64"},{"v":0.6261682242990654,"d":"0.63"},{"v":31.0713225,"d":"31.0713"},0.5953586723755104]
[68,{"v":31.20769150547135,"d":"31.21"},0.6429884264555772,{"v":0.6538461538461539,"d":"0.65"},{"v":0.6355140186915887,"d":"0.64"},{"v":31.165749,"d":"31.1657"},0.6054361813068695]
[69,{"v":31.338006184978852,"d":"31.34"},0.6626050815838214,{"v":0.6634615384615384,"d":"0.66"},{"v":0.6448598130841121,"d":"0.64"},{"v":31.2884865,"d":"31.2885"},0.618429462033453]
[70,{"v":31.359498555699975,"d":"31.36"},0.6658000645595858,{"v":0.6730769230769231,"d":"0.67"},{"v":0.6542056074766355,"d":"0.65"},{"v":31.3177605,"d":"31.3178"},0.6215094712233771]
[71,{"v":31.362186356045623,"d":"31.36"},0.6661987859967369,{"v":0.6826923076923077,"d":"0.68"},{"v":0.6635514018691588,"d":"0.66"},{"v":31.4139495,"d":"31.4139"},0.631574632791246]
[72,{"v":31.369194017314275,"d":"31.37"},0.6672374536955261,{"v":0.6923076923076923,"d":"0.69"},{"v":0.6728971962616822,"d":"0.67"},{"v":31.7176425,"d":"31.7176"},0.6627366918593134]
[73,{"v":31.391678358068695,"d":"31.39"},0.6705613682416531,{"v":0.7019230769230769,"d":"0.70"},{"v":0.6822429906542056,"d":"0.68"},{"v":31.744368,"d":"31.7444"},0.6654299585362964]
[74,{"v":31.670140708198282,"d":"31.67"},0.7105471980772678,{"v":0.7115384615384616,"d":"0.71"},{"v":0.6915887850467289,"d":"0.69"},{"v":31.8810225,"d":"31.8810"},0.6790661791940952]
[75,{"v":31.74739748533115,"d":"31.75"},0.7212232039163525,{"v":0.7211538461538461,"d":"0.72"},{"v":0.7009345794392523,"d":"0.70"},{"v":32.1555555,"d":"32.1556"},0.7057284883776875]
[76,{"v":31.772436662537757,"d":"31.77"},0.7246417413678481,{"v":0.7307692307692307,"d":"0.73"},{"v":0.7102803738317757,"d":"0.71"},{"v":32.202894,"d":"32.2029"},0.7102205840255921]
[77,{"v":31.81108817144448,"d":"31.81"},0.729877903026116,{"v":0.7403846153846154,"d":"0.74"},{"v":0.719626168224299,"d":"0.72"},{"v":32.3305605,"d":"32.3306"},0.7221720843544002]
[78,{"v":31.839399727889088,"d":"31.84"},0.7336814382183083,0.75,{"v":0.7289719626168224,"d":"0.73"},{"v":32.358615,"d":"32.3586"},0.7247657884846972]
[79,{"v":31.879619151704194,"d":"31.88"},0.7390377420799255,{"v":0.7596153846153846,"d":"0.76"},{"v":0.7383177570093458,"d":"0.74"},{"v":32.373597000000004,"d":"32.3736"},0.7261460098061345]
[80,{"v":31.885925377998916,"d":"31.89"},0.7398725344434638,{"v":0.7692307692307693,"d":"0.77"},{"v":0.7476635514018691,"d":"0.75"},{"v":32.4363885,"d":"32.4364"},0.7318932000758673]
[81,{"v":32.02858159621506,"d":"32.03"},0.7583824451041099,{"v":0.7788461538461539,"d":"0.78"},{"v":0.7570093457943925,"d":"0.76"},{"v":32.621496,"d":"32.6215"},0.7484748603079983]
[82,{"v":32.030767653764954,"d":"32.03"},0.7586604180868842,{"v":0.7884615384615384,"d":"0.79"},{"v":0.7663551401869159,"d":"0.77"},{"v":32.685241500000004,"d":"32.6852"},0.7540570354349434]
[83,{"v":32.080746335491156,"d":"32.08"},0.7649679266531089,{"v":0.7980769230769231,"d":"0.80"},{"v":0.7757009345794392,"d":"0.78"},{"v":32.7995085,"d":"32.7995"},0.7638946537648219]
[84,{"v":32.09921221440603,"d":"32.10"},0.7672751455660505,{"v":0.8076923076923077,"d":"0.81"},{"v":0.7850467289719626,"d":"0.79"},{"v":32.860515,"d":"32.8605"},0.7690567979637343]
[85,{"v":32.14601043374163,"d":"32.15"},0.7730655906831742,{"v":0.8173076923076923,"d":"0.82"},{"v":0.794392523364486,"d":"0.79"},{"v":32.88246,"d":"32.8825"},0.7708981765862047]
[86,{"v":32.17077259499933,"d":"32.17"},0.7760962902179568,{"v":0.8269230769230769,"d":"0.83"},{"v":0.8037383177570093,"d":"0.80"},{"v":32.9198055,"d":"32.9198"},0.7740127773451814]
[87,{"v":32.2271753021812,"d":"32.23"},0.7829129870807366,{"v":0.8365384615384616,"d":"0.84"},{"v":0.8130841121495327,"d":"0.81"},{"v":32.9858925,"d":"32.9859"},0.7794653093702495]
[88,{"v":32.51237276960053,"d":"32.51"},0.8154964076259715,{"v":0.8461538461538461,"d":"0.85"},{"v":0.822429906542056,"d":"0.82"},{"v":33.19521,"d":"33.1952"},0.796229173424024]
[89,{"v":32.971207614206556,"d":"32.97"},0.8611247110600643,{"v":0.8557692307692307,"d":"0.86"},{"v":0.8317757009345794,"d":"0.83"},{"v":33.307014,"d":"33.3070"},0.8048632146496245]
[90,{"v":33.04098948602768,"d":"33.04"},0.8673248169888361,{"v":0.8653846153846154,"d":"0.87"},{"v":0.8411214953271028,"d":"0.84"},{"v":33.455325,"d":"33.4553"},0.8159672291786522]
[91,{"v":33.11434556964923,"d":"33.11"},0.873634040726089,{"v":0.875,"d":"0.88"},{"v":0.8504672897196262,"d":"0.85"},{"v":33.637221,"d":"33.6372"},0.8290364625577477]
[92,{"v":33.23792761842847,"d":"33.24"},0.8837843392943128,{"v":0.8846153846153846,"d":"0.88"},{"v":0.8598130841121495,"d":"0.86"},{"v":33.7738965,"d":"33.7739"},0.8384557065132535]
[93,{"v":33.27862778826403,"d":"33.28"},0.8869969792053967,{"v":0.8942307692307693,"d":"0.89"},{"v":0.8691588785046729,"d":"0.87"},{"v":33.990069,"d":"33.9901"},0.8526493211297236]
[94,{"v":33.668029278000645,"d":"33.67"},0.914571866293981,{"v":0.9038461538461539,"d":"0.90"},{"v":0.8785046728971962,"d":"0.88"},{"v":34.9314675,"d":"34.9315"},0.9045620093721152]
[95,{"v":34.06030515132736,"d":"34.06"},0.9369143648080998,{"v":0.9134615384615384,"d":"0.91"},{"v":0.8878504672897196,"d":"0.89"},{"v":35.2648785,"d":"35.2649"},0.9192614206671237]
[96,{"v":34.3222803230716,"d":"34.32"},0.9490985140639456,{"v":0.9230769230769231,"d":"0.92"},{"v":0.897196261682243,"d":"0.90"},{"v":35.331873,"d":"35.3319"},0.921996950373075]
[97,{"v":34.402264940817474,"d":"34.40"},0.9524197244636632,{"v":0.9326923076923077,"d":"0.93"},{"v":0.9065420560747663,"d":"0.91"},{"v":35.688171,"d":"35.6882"},0.9353774788348083]
[98,{"v":34.62775708353834,"d":"34.63"},0.9608561079867379,{"v":0.9423076923076923,"d":"0.94"},{"v":0.9158878504672897,"d":"0.92"},{"v":35.7328395,"d":"35.7328"},0.9369208881871441]
[99,{"v":34.793780214313166,"d":"34.79"},0.9662545380859414,{"v":0.9519230769230769,"d":"0.95"},{"v":0.9252336448598131,"d":"0.93"},{"v":35.772174,"d":"35.7722"},0.9382560860572509]
[100,{"v":34.81006224113603,"d":"34.81"},0.9667492634551623,{"v":0.9615384615384616,"d":"0.96"},{"v":0.9345794392523364,"d":"0.93"},{"v":36.072213,"d":"36.0722"},0.9477272081882027]
[101,{"v":35.09269398209159,"d":"35.09"},0.9744267510770946,{"v":0.9711538461538461,"d":"0.97"},{"v":0.9439252336448598,"d":"0.94"},{"v":36.497979,"d":"36.4980"},0.9591453854955633]
[102,{"v":35.11658832886335,"d":"35.12"},0.9750014944787957,{"v":0.9807692307692307,"d":"0.98"},{"v":0.9532710280373832,"d":"0.95"},{"v":36.4991295,"d":"36.4991"},0.9591732475002557]
[103,{"v":35.23188994051191,"d":"35.23"},0.9776248693393627,{"v":0.9903846153846154,"d":"0.99"},{"v":0.9626168224299065,"d":"0.96"},{"v":37.500723,"d":"37.5007"},0.9782009432886071]
[104,{"v":36.03597643273169,"d":"36.04"},0.9902229015577301,{"v":1,"d":"1.00"},{"v":0.9719626168224299,"d":"0.97"},{"v":37.6026855,"d":"37.6027"},0.9796271606564747]
[105,{"$nulls":3},{"v":0.9813084112149533,"d":"0.98"},{"v":37.735158,"d":"37.7352"},0.9813613369631481]
[106,{"$nulls":3},{"v":0.9906542056074766,"d":"0.99"},{"v":38.346057,"d":"38.3461"},0.9878236265106336]
[107,{"$nulls":3},{"v":1,"d":"1.00"},{"v":39.065740500000004,"d":"39.0657"},0.9928647351624921]
[]
["Mittelwert:",{"v":30.308776382846933,"d":"30.31"},{"$nulls":3},{"v":30.197877135140192,"d":"30.1979"}]
["Varianz:",{"v":6.017110134605618,"d":"6.02"},{"$nulls":3},{"v":13.096970084644436,"d":"13.0970"}]
["Standartabw.:",{"v":2.452979847981964,"d":"2.45"},{"$nulls":3},{"v":3.6189736230932157,"d":"3.6190"}]

{"sheet":"4","index":9,"n_rows":6,"n_cols":10,"rows_kept":6,"merged":[[2,0,2,12],[3,0,3,12],[4,0,4,12],[8,0,8,4],[9,0,9,4],[21,0,21,5]],"flags":["formulas_cached_only"]}
["Übung 4",{"$nulls":4},"Renato Del Buono",null,"Ivan Salzgeber",null,"WS03"]
[]
["Die Firma Filtrus ist in der Produktion von Filtern tätig. Im Jahre 2002 wurden ihr insgesamt 40 Filter aufgrund Mängel zurückgesandt,"]
["während bei anderen Firmen mit gleicher Tätigkeit und gleichem Absatz gerade mal 25 Filter den Weg zurück fanden."]
["Hat die Firma Filtrus ein Qualitätsproblem in der Herstellung oder kann der hohe Rücklauf nur eine Folge von unglücklichen Zufällen sein?"]
["(Signifikanzniveau 0,05)"]

{"sheet":"L4","index":10,"n_rows":9,"n_cols":2,"rows_kept":9,"merged":[[0,0,0,4],[1,0,1,4],[8,0,8,5]],"flags":["formulas_cached_only"]}
["H0:  Der Rücklauf weicht vom Durchschnitt nicht ab"]
["HA: Der Rücklauf ist grösser als der Durchschnitt"]
[]
["(rechtsseitiger Test)"]
["Wir verwenden die Poissonverteilung"]
["P(X>=40)","für X ist Poissonverteilt mit Lamda = 25"]
[0.003443568729431856,"<0.05"]
[]
["Somit ist der höhere Rücklauf als signifikant zu bezeichnen!"]

{"sheet":"5","index":11,"n_rows":16,"n_cols":10,"rows_kept":16,"flags":["formulas_cached_only"]}
["Übung 5",{"$nulls":3},"von","claudia paiva",{"$nulls":3},"WS 03"]
[{"$nulls":5},"christian escher"]
[{"$nulls":5},"marco volken"]
{"$rows_empty":10}
["Signifikanzniveau",null,null,0.05]
[]
["Sind die genmanipulierten Zuckerrüben (Sorte B) weniger anfällig für Pilze?"]

{"sheet":"L5","index":12,"n_rows":11,"n_cols":3,"rows_kept":11,"flags":["formulas_cached_only"]}
["H0","Die genmanipulierten Zuckerrüben (Sorte B) sind nicht resistenter!"]
["HA","Die genmanipulierten Zuckerrüben (Sorte B) sind resistenter!"]
["Linksseitiger Test"]
["Die Zufallsvariable ist stetig. "]
[]
["Da wir die Standardabweichung der Grundgesamtheit nicht kennen, verwenden wir den t-Test."]
[]
["T-Wert",-7.888106377466155]
["p-Wert",1.7367239730619704e-09,"<0.05"]
[]
[null,"hochsignifikante Abweichung"]

{"sheet":"6","index":13,"n_rows":59,"n_cols":8,"rows_kept":59,"flags":["formulas_cached_only"]}
["Übung 6",{"$nulls":4},"Escher","Volken","WS 2003"]
[]
["Es wird der Einfluss des Chiptunings auf den Benzinverbrauch eines Wagens überprüft."]
["ohne Chiptuning gilt:"]
["Durchschnittlicher Benzinverbrauch",null,null,{"v":8.4,"d":"8.40"},"Liter / 100 km"]
["Standardabweichung",null,null,{"v":0.6,"d":"0.60"},"Liter / 100 km"]
[]
["mit Chiptuning erhalten wir die Stichprobe:"]
[]
[1,6.800240249131261,null,"Testen Sie, ob der Bezinverbrauch reduziert wird."]
[2,6.800260125704949,null,"(Signifikanzniveau 0.01)"]
[3,6.842889445665934]
[4,6.914940592856701]
[5,6.91980773548085]
[6,6.930526790916694]
[7,6.942279842555603]
[8,6.946396431729367]
[9,6.950675993597974]
[10,6.964135527549006]
[11,6.972852597677427]
[12,6.977609082348008]
[13,6.986343058789665]
[14,7.01858718262711]
[15,7.025631906408976]
[16,7.049216170077232]
[17,7.068510120066192]
[18,7.086507373307111]
[19,7.089208617956905]
[20,7.094313144952682]
[21,7.108952963299231]
[22,7.138189677505312]
[23,7.219642872718403]
[24,7.228572885134549]
[25,7.23837956175363]
[26,7.29193372591357]
[27,7.292449197176282]
[28,7.31012473978533]
[29,7.323979967435355]
[30,7.329163954769465]
[31,7.3370029824037]
[32,7.341660738582492]
[33,7.354618519573921]
[34,7.354892468266555]
[35,7.370813718114008]
[36,7.372149779670599]
[37,7.421029107288209]
[38,7.435572020010951]
[39,7.460723580295524]
[40,7.521151027901436]
[41,7.553630964474828]
[42,7.563333328497237]
[43,7.566021548311099]
[44,7.596688790013839]
[45,7.610257845836928]
[46,7.643097157430003]
[47,7.6614406186613095]
[48,7.707946171366826]
[49,7.756047580849157]
[50,7.770683014114444]

{"sheet":"L6","index":14,"n_rows":56,"n_cols":8,"rows_kept":56,"flags":["formulas_cached_only"]}
["H0","Der Benzinverbrauch wird dadurch nicht beeinflusst.",{"$nulls":3},"Mittelwert alt",{"v":8.4,"d":"8.40"},"Liter / 100 km"]
["HA","Der durchschnittliche Benzinverbrauch verringert sich.",{"$nulls":3},"Standardabweichung alt",{"v":0.6,"d":"0.60"},"Liter / 100 km"]
[null,"Linksseitiger Test !!",{"$nulls":3},"Mittelwert (neu)",{"v":7.2452216499310795,"d":"7.25"},"Liter / 100 km"]
[]
[]
[]
[1,6.800240249131261,null,"z-Wert:",null,-13.609193368352448]
[2,6.800260125704949,null,"p-Wert",null,0,"<0.01"]
[3,6.842889445665934]
[4,6.914940592856701,null,"Die Nullhypothese kann verworfen werden. "]
[5,6.91980773548085]
[6,6.930526790916694]
[7,6.942279842555603]
[8,6.946396431729367]
[9,6.950675993597974]
[10,6.964135527549006]
[11,6.972852597677427]
[12,6.977609082348008]
[13,6.986343058789665]
[14,7.01858718262711]
[15,7.025631906408976]
[16,7.049216170077232]
[17,7.068510120066192]
[18,7.086507373307111]
[19,7.089208617956905]
[20,7.094313144952682]
[21,7.108952963299231]
[22,7.138189677505312]
[23,7.219642872718403]
[24,7.228572885134549]
[25,7.23837956175363]
[26,7.29193372591357]
[27,7.292449197176282]
[28,7.31012473978533]
[29,7.323979967435355]
[30,7.329163954769465]
[31,7.3370029824037]
[32,7.341660738582492]
[33,7.354618519573921]
[34,7.354892468266555]
[35,7.370813718114008]
[36,7.372149779670599]
[37,7.421029107288209]
[38,7.435572020010951]
[39,7.460723580295524]
[40,7.521151027901436]
[41,7.553630964474828]
[42,7.563333328497237]
[43,7.566021548311099]
[44,7.596688790013839]
[45,7.610257845836928]
[46,7.643097157430003]
[47,7.6614406186613095]
[48,7.707946171366826]
[49,7.756047580849157]
[50,7.770683014114444]

{"sheet":"7","index":15,"n_rows":1,"n_cols":8,"rows_kept":1,"flags":["formulas_cached_only"]}
["Übung 7",{"$nulls":3},"Bregy","Zeiter",null,"WS 03"]

{"sheet":"L7","index":16,"n_rows":26,"n_cols":4,"rows_kept":26,"flags":["formulas_cached_only"]}
{"$rows_empty":17}
[null,"Anzahl Defekte","P(X=xi)"]
[null,3,{"v":0.0019725404781121615,"d":"0.0019725404781"}]
[null,4,{"v":7.032384627072407e-05,"d":"0.0000703238463"}]
[null,5,{"v":1.2853567683928476e-06,"d":"0.0000012853568"}]
[null,6,{"v":9.395882809889236e-09,"d":"0.0000000093959"}]
[]
[null,"Summe",{"v":0.0020441590770340886,"d":"0.0020441590770"},"< 0.05"]
[]
["è Die Abweichung ist signifikant. Die Produktion entspricht den Produktionsbedingungen nicht."]

{"sheet":"8a","index":17,"n_rows":13,"n_cols":7,"rows_kept":13,"flags":["formulas_cached_only"]}
["Übung 8a",{"$nulls":3},"Moreillon","Andres","SS 03"]
[]
[]
[]
[]
["Die durchschnittliche Lebensdauer von Bremsscheiben beträgt 12 Monate"]
["Standartabweichung = 1"]
["Die Werbung für die etwas teuereren neuen Bremschscheiben verspricht eine längere Lebensdauer"]
["Getestet werden 20 Bremsscheiben die durchschnittlich 16.3 Monate halten"]
[]
["H0 = Die durchschnittliche Lebensdauer unterscheidet sich nicht"]
["HA = Die Lebensdauer ist länger"]
["(Signifikanzniveau 0.01)"]

{"sheet":"L8a","index":18,"n_rows":8,"n_cols":2,"rows_kept":8,"flags":["formulas_cached_only"]}
["Lösung Übung 8a"]
[]
["z-Test"]
["z-Wert",19.230184606498195]
[]
["Normverteilung:",{"v":1,"d":"1.0000"}]
[]
["1-1 = 0  ,   0 < 0.01 folglich signifikant"]

{"sheet":"8","index":19,"n_rows":44,"n_cols":9,"rows_kept":44,"flags":["formulas_cached_only"]}
["Übung 8",{"$nulls":4},"Bregy","Zeiter",null,"WS 03"]
[]
[]
[]
["Wir wollen testen, ob sich nach der Einführung einer neuen Futterung das durchschnittliche Alter von n Hasen signifikant erhöht hat"]
["wobei die Standartabweichung und der Mittelwert der Ergebnisse der traditionellen Futterung bekannt ist. "]
["Mittelwert = ",5.126666666666668]
["Stabw = ",1.6579865922949657]
["Testen Sie: "]
["Signifikanzniveau 0.01"]
["Folgende Daten wurden erhoben:"]
[]
[]
["Alter von Hasen mit neuem Futter"]
[3]
[6.2]
[8.5]
[4.6]
[7.3]
[6.1]
[5.5]
[4.3]
[5]
[2.8]
[7]
[3.5]
[6]
[7.2]
[8]
[7.6]
[3.5]
[4]
[6.7]
[8.2]
[9.1]
[6]
[4]
[3.1]
[8.2]
[7.1]
[6.8]
[5]
[3.9]
[7]

{"sheet":"L8","index":20,"n_rows":42,"n_cols":3,"rows_kept":42,"flags":["formulas_cached_only"]}
["Ho: Die Ergebnisse der verschiedenen Futter unterscheiden sich nicht."]
["H1: Das Alter bei der neuen Futterung ist grösser als bei der alten."]
[]
[]
["Alter von Hasen mit neuem Futter"]
[3]
[6.2]
[8.5]
[4.6]
[7.3]
[6.1]
[5.5]
[4.3]
[5]
[2.8]
[7]
[3.5]
[6]
[7.2]
[8]
[7.6]
[3.5]
[4]
[6.7]
[8.2]
[9.1]
[6]
[4]
[3.1]
[8.2]
[7.1]
[6.8]
[5]
[3.9]
[7]
[5.839999999999999," = Mittelwert neu"]
[30," = n"]
[5.126666666666668,"Mittelwert alt= "]
[1.6579865922949657,"Stabw alt = "]
["Z",2.3565254357467555]
["Standartnormv.",0.9907766145466429]
["P-Wert",0.009223385453357102,"< 0.01 damit ist der Unterschied signifikant"]

{"sheet":"9","index":21,"n_rows":112,"n_cols":10,"rows_kept":112,"flags":["formulas_cached_only"]}
["Übung 9",null,"Werbekampagne in Siders/ Eröffnung eines Geschäftes",{"$nulls":4},"Rohrer","Robert","WS 03"]
[]
["Von einer Werbeagentur wird eine Werbekampagane lanciert. "]
["1) Ziel der Werbekampagne: Mindestens 30% der Einwohner in Siders sollen sich spontan an den Namen des Geschäftes erinnern."]
["Um nach der Kampagane den Erfolg zu testen, wird eine Zufallsstichprobe von 20 Personen aus der Siderser Bevölkerung gezogen. "]
["2) 20 Personen von 100 können uns spontan den Namen des Geschäftes sagen. Der Auftraggeber behauptet, dass das Ziel nicht erreicht wurde"]
["Hat die Werbekampagne das Ziel nicht erreicht?"]
["Signifikanzniveau",null,0.05]
[]
[]
[]
[]
[1,1.2240771391413508e-14,1.2240771391413508e-14]
[2,2.619168946510514e-13,2.741576660424649e-13]
[3,3.697330197018912e-12,3.971487863061377e-12]
[4,3.8733812514514485e-11,4.270530037757586e-11]
[5,3.211826568695667e-10,3.6388795724714254e-10]
[6,2.1956109275843276e-09,2.5594988848314702e-09]
[7,1.2725839894569577e-08,1.528533877940105e-08]
[8,6.383384055595631e-08,7.911917933535736e-08]
[9,2.8147390287015643e-07,3.605930822055138e-07]
[10,1.1045659194170467e-06,1.4651590016225605e-06]
[11,3.8960437883889665e-06,5.361202790011527e-06]
[12,1.2453321330775545e-05,1.781452412078707e-05]
[13,3.6320125582611385e-05,5.4134649703398456e-05]
[14,9.721462236345814e-05,0.0001513492720668566]
[15,0.00023999490002285086,0.00039134417208970746]
[16,0.0005488255988653423,0.0009401697709550497]
[17,0.0011669931046655137,0.0021071628756205636]
[18,0.0023149818393998563,0.00442214471502042]
[19,0.004296864725589818,0.008719009440610239]
[20,0.007482050946477674,0.016201060387087914]
[21,0.012251109149712773,0.028452169536800687]
[22,0.018903140374898635,0.047355309911699325,null,"P(X >=22)= 0.04735531 <=0.05"]
[23,0.027537526892880533,0.07489283680457987]
[24,0.037940118136017255,0.11283295494059711]
[25,0.04951497463564588,0.162347929576243]
[26,0.06129976317216315,0.22364769274840615]
[27,0.07208270551248083,0.295730398260887]
[28,0.0806065298571435,0.3763369281180305]
[29,0.08581219601611438,0.4621491241341449]
[30,0.0870563315085195,0.5492054556426644]
[31,0.08424049397264445,0.6334459496153089]
[32,0.07781693874397104,0.7112628883592799]
[33,0.0686741278245273,0.7799370161838072]
[34,0.057940597987478616,0.8378776141712858]
[35,0.04676518760805523,0.8846428017793411]
[36,0.03612993826804185,0.920772740047383]
[37,0.026733080280663853,0.9475058203280469]
[38,0.01895305938592992,0.9664588797139768]
[39,0.012881000378295473,0.9793398800922722]
[40,0.008395226685064969,0.9877351067773372]
[41,0.005249072840714813,0.9929841796180521]
[42,0.003149472868188037,0.9961336524862401]
[43,0.0018139266294965543,0.9979475791157366]
[44,0.0010030762409069711,0.9989506553566436]
[45,0.0005326859352937518,0.9994833412919374]
[46,0.00027171121874039125,0.9997550525106778]
[47,0.00013313880317031832,0.9998881913138481]
[48,6.267727912299622e-05,0.9999508685929711]
[49,2.8350316730902652e-05,0.999979218909702]
[50,1.2321632455990033e-05,0.999991540542158]
[51,5.1457403948606265e-06,0.9999966862825529]
[52,2.064857175712637e-06,0.9999987511397286]
[53,7.961124086650906e-07,0.9999995472521372]
[54,2.9489477846323113e-07,0.9999998421469157]
[55,1.0493500420517299e-07,0.99999994708192]
[56,3.586514427359649e-08,0.9999999829470643]
[57,1.1771929439457313e-08,0.9999999947189937]
[58,3.7098374403518713e-09,0.9999999984288311]
[59,1.1222469420749403e-09,0.9999999995510781]
[60,3.2578178441975635e-10,0.9999999998768598]
[61,9.072608854013875e-11,0.9999999999675859]
[62,2.4229798119883964e-11,0.9999999999918158]
[63,6.203074176021398e-12,0.9999999999980188]
[64,1.5216412796671973e-12,0.9999999999995405]
[65,3.5748217522909985e-13,0.999999999999898]
[66,8.038978377249466e-14,0.9999999999999784]
[67,1.7294050082112476e-14,0.9999999999999957]
[68,3.556827790898189e-15,0.9999999999999992]
[69,6.988664165034519e-16,0.9999999999999999]
[70,1.3108638893824372e-16,1]
[71,2.3452524318294992e-17,1]
[72,3.998466699406365e-18,1]
[73,6.489874876128879e-19,1]
[74,1.0017175980019414e-19,1]
[75,1.4686001678996164e-20,1]
[76,2.0424216699452537e-21,1]
[77,2.6906088366963334e-22,1]
[78,3.352259558857447e-23,1]
[79,3.9432676323752005e-24,1]
[80,4.370969324030744e-25,1]
[81,4.5560038931620344e-26,1]
[82,4.45506786892699e-27,1]
[83,4.076133025717347e-28,1]
[84,3.479258541105152e-29,1]
[85,2.761376133767712e-30,1]
[86,2.030136581240683e-31,1]
[87,1.376607020418404e-32,1]
[88,8.56674110390345e-34,1]
[89,4.864306024668271e-35,1]
[90,2.5029610019296385e-36,1]
[91,1.157616483328793e-37,1]
[92,4.7647527911976766e-39,1]
[93,1.7240003989404802e-40,1]
[94,5.398417193927007e-42,1]
[95,1.433249880235283e-43,1]
[96,3.1370209815014935e-45,1]
[97,5.434646687204703e-47,1]
[98,6.987165174336085e-49,1]
[99,5.926512314813141e-51,1]
[100,2.4875477135657654e-53,1]

{"sheet":"L9","index":22,"n_rows":106,"n_cols":7,"rows_kept":106,"flags":["formulas_cached_only"]}
["Nullhypothese","Mit unserer Werbekampagne, erinnern sich 30% der Einwohner in Siders an den Namen des Geschäftes."]
["Alternativhypothese","Mit unserer Werbekampagne, erinnern sich nicht 30% der Einwohner in Siders an den Namen des Geschäftes."]
["d.h. wir testen linksseitig."]
["(Es ist korrekt, wie im Beispiel gemacht, die hypergeometrische Verteilung zu verwenden, da nicht zurückgelegt wird. Näherungsweise könnte man auch die Binomialverteilung brauchen, da die Grundgesamtheit gross ist)"]
[{"$nulls":4},"P(X<=20)=0.01620106",null,"<= 0.05"]
["xi","P(X=xi)","P(X<=xi)",null,"Somit ist die Abweichung signifikant. Das Ziel wurde nicht erreicht."]
[1,1.2240771391413508e-14,1.2240771391413508e-14]
[2,2.619168946510514e-13,2.741576660424649e-13]
[3,3.697330197018912e-12,3.971487863061377e-12]
[4,3.8733812514514485e-11,4.270530037757586e-11]
[5,3.211826568695667e-10,3.6388795724714254e-10]
[6,2.1956109275843276e-09,2.5594988848314702e-09]
[7,1.2725839894569577e-08,1.528533877940105e-08]
[8,6.383384055595631e-08,7.911917933535736e-08]
[9,2.8147390287015643e-07,3.605930822055138e-07]
[10,1.1045659194170467e-06,1.4651590016225605e-06]
[11,3.8960437883889665e-06,5.361202790011527e-06]
[12,1.2453321330775545e-05,1.781452412078707e-05]
[13,3.6320125582611385e-05,5.4134649703398456e-05]
[14,9.721462236345814e-05,0.0001513492720668566]
[15,0.00023999490002285086,0.00039134417208970746]
[16,0.0005488255988653423,0.0009401697709550497]
[17,0.0011669931046655137,0.0021071628756205636]
[18,0.0023149818393998563,0.00442214471502042]
[19,0.004296864725589818,0.008719009440610239]
[20,0.007482050946477674,0.016201060387087914]
[21,0.012251109149712773,0.028452169536800687]
[22,0.018903140374898635,0.047355309911699325]
[23,0.027537526892880533,0.07489283680457987]
[24,0.037940118136017255,0.11283295494059711]
[25,0.04951497463564588,0.162347929576243]
[26,0.06129976317216315,0.22364769274840615]
[27,0.07208270551248083,0.295730398260887]
[28,0.0806065298571435,0.3763369281180305]
[29,0.08581219601611438,0.4621491241341449]
[30,0.0870563315085195,0.5492054556426644]
[31,0.08424049397264445,0.6334459496153089]
[32,0.07781693874397104,0.7112628883592799]
[33,0.0686741278245273,0.7799370161838072]
[34,0.057940597987478616,0.8378776141712858]
[35,0.04676518760805523,0.8846428017793411]
[36,0.03612993826804185,0.920772740047383]
[37,0.026733080280663853,0.9475058203280469]
[38,0.01895305938592992,0.9664588797139768]
[39,0.012881000378295473,0.9793398800922722]
[40,0.008395226685064969,0.9877351067773372]
[41,0.005249072840714813,0.9929841796180521]
[42,0.003149472868188037,0.9961336524862401]
[43,0.0018139266294965543,0.9979475791157366]
[44,0.0010030762409069711,0.9989506553566436]
[45,0.0005326859352937518,0.9994833412919374]
[46,0.00027171121874039125,0.9997550525106778]
[47,0.00013313880317031832,0.9998881913138481]
[48,6.267727912299622e-05,0.9999508685929711]
[49,2.8350316730902652e-05,0.999979218909702]
[50,1.2321632455990033e-05,0.999991540542158]
[51,5.1457403948606265e-06,0.9999966862825529]
[52,2.064857175712637e-06,0.9999987511397286]
[53,7.961124086650906e-07,0.9999995472521372]
[54,2.9489477846323113e-07,0.9999998421469157]
[55,1.0493500420517299e-07,0.99999994708192]
[56,3.586514427359649e-08,0.9999999829470643]
[57,1.1771929439457313e-08,0.9999999947189937]
[58,3.7098374403518713e-09,0.9999999984288311]
[59,1.1222469420749403e-09,0.9999999995510781]
[60,3.2578178441975635e-10,0.9999999998768598]
[61,9.072608854013875e-11,0.9999999999675859]
[62,2.4229798119883964e-11,0.9999999999918158]
[63,6.203074176021398e-12,0.9999999999980188]
[64,1.5216412796671973e-12,0.9999999999995405]
[65,3.5748217522909985e-13,0.999999999999898]
[66,8.038978377249466e-14,0.9999999999999784]
[67,1.7294050082112476e-14,0.9999999999999957]
[68,3.556827790898189e-15,0.9999999999999992]
[69,6.988664165034519e-16,0.9999999999999999]
[70,1.3108638893824372e-16,1]
[71,2.3452524318294992e-17,1]
[72,3.998466699406365e-18,1]
[73,6.489874876128879e-19,1]
[74,1.0017175980019414e-19,1]
[75,1.4686001678996164e-20,1]
[76,2.0424216699452537e-21,1]
[77,2.6906088366963334e-22,1]
[78,3.352259558857447e-23,1]
[79,3.9432676323752005e-24,1]
[80,4.370969324030744e-25,1]
[81,4.5560038931620344e-26,1]
[82,4.45506786892699e-27,1]
[83,4.076133025717347e-28,1]
[84,3.479258541105152e-29,1]
[85,2.761376133767712e-30,1]
[86,2.030136581240683e-31,1]
[87,1.376607020418404e-32,1]
[88,8.56674110390345e-34,1]
[89,4.864306024668271e-35,1]
[90,2.5029610019296385e-36,1]
[91,1.157616483328793e-37,1]
[92,4.7647527911976766e-39,1]
[93,1.7240003989404802e-40,1]
[94,5.398417193927007e-42,1]
[95,1.433249880235283e-43,1]
[96,3.1370209815014935e-45,1]
[97,5.434646687204703e-47,1]
[98,6.987165174336085e-49,1]
[99,5.926512314813141e-51,1]
[100,2.4875477135657654e-53,1]

{"sheet":"10","index":23,"n_rows":26,"n_cols":9,"rows_kept":26,"flags":["formulas_cached_only"]}
["Beispiel 10: ",{"$nulls":4},"Robert","Rohrer",null,"WS 03"]
["Beim Skispringen wurden die Sprungweiten (in Meter) für ein Skityp A ermittelt:"]
["Mittelwert dieser Grundgesamtheit:",null,null,100,"m"]
["Bezüglich des Skityps B werden folgende Daten erhoben, um zu testen, ob der Skityp B besser ist:"]
[]
["Sprungweiten A:"]
[98.2]
[{"v":99,"d":"99.0"}]
[99.7]
[99.9]
[{"v":100.348322245734,"d":"100.3"}]
[{"v":100.452658966095,"d":"100.5"}]
[{"v":100.702667221305,"d":"100.7"}]
[101.6]
[102.3]
[102.4]
[102.7]
[103.4]
[103.7]
[105.2]
[105.8]
[106.7]
[107.2]
[108.6]
[109.5,null,"Testen Sie (Signifikanzniveau = 0.05)"]
[110.1]

{"sheet":"L10","index":24,"n_rows":30,"n_cols":7,"rows_kept":30,"flags":["formulas_cached_only"]}
["Mittelwert Grundgesamtheit",100,null,null,"t-Wert",4.18552729569641]
["Mittelwert Stichprobe",{"v":103.3751824216567,"d":"103.4"},null,null,"p-Wert",0.0002508044130010608,"< 0.01"]
["Standardabweichung Stichprobe",3.6063018100714666]
["Stichprobengrösse",20,null,null,"Die Nullhypothese kann verworfen werden"]
[]
["Ho: Die Mittelwerte unterscheiden sich nicht."]
["Ha: Der neue Mittelwert liegt höher. (rechtsseitiger Test)"]
["Wir verwenden auf Grund der Angaben den t-Test, sofern die Daten normalverteilt sind:"]
[]
["Sprungweiten A:","H(xi)","F(xi)"]
[98.2,0.05,0.1125258406412355]
[{"v":99,"d":"99.0"},0.1,0.15407774400711716]
[99.7,0.15,0.16761281452515187]
[99.9,0.2,0.20064335389817634]
[{"v":100.348322245734,"d":"100.3"},0.25,0.20885697119989222]
[{"v":100.452658966095,"d":"100.5"},0.3,0.22932600430917627]
[{"v":100.702667221305,"d":"100.7"},0.35,0.31127323421339836]
[101.6,0.4,0.38279826356515967]
[102.3,0.45,0.39342223252770725]
[102.4,0.5,0.4257429327273121]
[102.7,0.55,0.502745405567369]
[103.4,0.6,0.5358840460491227]
[103.7,0.65,0.6935744936894208]
[105.2,0.7,0.74933025645074]
[105.8,0.75,0.8217218017506521]
[106.7,0.8,0.85556246400109]
[107.2,0.85,0.9263035280520886]
[108.6,0.9,0.9552806047560607,null,"knapp normalverteilt"]
[109.5,0.95,0.9688911803911965,null,"(es würde sich deshalb empfehlen, noch einen Vorzeichentest durchzuführen)"]
[110.1,1,0]

{"sheet":"11","index":25,"n_rows":17,"n_cols":6,"rows_kept":17,"flags":["formulas_cached_only"]}
["Übung 11",{"$nulls":3},"Moreillon","Andres"]
[]
[]
[]
["Ein Autohersteller wird gebeten die Abgaswerte der Autos zu überprüfen."]
["Der offizielle Grenzwert liegt bei 5 Einheiten pro Liter Luft"]
["Getestet werden 5 mal je ein Liter Luft"]
[]
["H0 = Die tatsächliche Anzahl liegt auf dem Grenzwert"]
["HA = Grenzwert wird überschritten  (Signifikanzniveau: 0.05)"]
[]
["Proben","erhobener Wert"]
[1,3]
[2,2]
[3,6]
[4,3]
[5,4]

{"sheet":"L11","index":26,"n_rows":27,"n_cols":3,"rows_kept":27,"flags":["formulas_cached_only"]}
["Lösung Übung 11"]
[]
["Ein Autohersteller wird gebeten die Abgaswerte der Autos zu überprüfen."]
["Der offizielle Grenzwert liegt bei 5 Einheiten pro Liter Luft"]
["Getestet werden 5 mal je ein Liter Luft"]
[]
["H0 = Die tatsächliche Anzahl liegt auf dem Grenzwert"]
["HA = Grenzwert wird überschritten"]
[]
["Proben","getesteter Wert"]
[1,3]
[2,2]
[3,6]
[4,3]
[5,4]
[]
["(X~P(25))"]
["Summe",18]
[]
["p-Wert",0.907959140801143,">0.05"]
[]
[]
[]
[]
["Das Resultat liegt nicht über dem Grenzwert."]
[]
["(ein Test erübrigt sich eigentlich, da 18 < 25)"]

{"sheet":"12","index":27,"n_rows":27,"n_cols":8,"rows_kept":27,"flags":["formulas_cached_only"]}
["Übung 11",{"$nulls":3},"Von Kimmig und Karlen",null,null,"SS 03"]
[]
[]
[]
[]
["Völkl testet einen neuen Belag. Die Firma misst die Geschwindigkeit nach 50 Metern (n=10)."]
[]
["Belag neu","Belag alt"]
[]
[108,102]
[99,105]
[98,94]
[115,92]
[100,107]
[102,95]
[97,93]
[101,100]
[109,106]
[111,99]
[]
[]
[]
[]
["H0","Der neue Belag unterscheidet sich nicht wesentlîch vom alten Belag"]
["HA","Der neue Belag ist besser"]
[]
[0.05,"Signifikanzniveau"]

{"sheet":"L12","index":28,"n_rows":26,"n_cols":6,"rows_kept":26,"flags":["formulas_cached_only"]}
[]
[]
["Offenbar werden jeweils dieselben Skis verwendet. ",{"$nulls":3},"(sinnvoll?)"]
["Zweistichprobentest: gepaarte Stichproben"]
[]
[]
[]
["Belag neu","Belag alt","Differenzen"]
[]
[108,102,6]
[99,105,-6,null,null," "]
[98,94,4]
[115,92,23]
[100,107,-7]
[102,95,7]
[97,93,4]
[101,100,1]
[109,106,3,null,"Normalverteilungsannahme ist wohl nicht haltbar."]
[111,99,12,null,"Trotzdem verwenden die Autoren den t-Test (fragwürdig)"]
[]
[104,99.3,4.7,"Mittlere Geschwindigkeit"]
[38.888888888888886,31.566666666667313,73.78888888888889,"Varianz"]
[]
["Testwert",1.7302241621412355]
["p-Wert",0.05882182522765865,">0.05"]
[null,"nicht signifikant"]

{"sheet":"13","index":29,"n_rows":21,"n_cols":7,"rows_kept":21,"flags":["formulas_cached_only"]}
["Übung 13",{"$nulls":3},"Sonja Borter und Anja Kimmig",null,"SS 03"]
[]
["Eine Lebensmittelfirma hat Absatzprobleme mit ihren Produkten."]
["Darum organisieren sie einen Degustationstag, an dem die Einkäufer einige Produkte probieren können."]
["Bei 10 Produkten wird nun untersucht ob sie durch die Degustation einen höheren Absatz erlangt haben. (gekaufte Produkte pro Woche)"]
["Signifikanzniveau = 0.025"]
[]
["Ho = Der Degustationstag bewirkt nichts"]
["Ha = Der Degustationstag lässt den Absatz steigern"]
[]
["Produkt:","Absatz vorher","Absatz nachher"]
[1,5,7]
[2,8,11]
[3,6,5]
[4,12,9]
[5,18,20]
[6,4,7]
[7,22,25]
[8,7,6]
[9,9,14]
[10,26,29]

{"sheet":"L13","index":30,"n_rows":30,"n_cols":8,"rows_kept":30,"flags":["formulas_cached_only"]}
["Die Autorinnen verwenden einen Wilcoxon-Test (wieso?)"]
[]
["Man könnte es hier vorgängig mit einem parametrischen Test versuchen."]
[]
[]
[]
[]
["Ho = Der Degustationstag bewirkt nichts"]
["Ha = Der Degustationstag lässt den Absatz steigern"]
[]
["Produkt:","Absatz vorher","Absatz nachher","Differenz","Beträge","Beträge geordnet","no(d1)","r(d1)"]
[1,5,7,-2,2,1,1,1.5]
[2,8,11,-3,3,1,2,1.5]
[3,6,5,1,1,2,3,3.5]
[4,12,9,3,3,2,4,3.5]
[5,18,20,-2,2,3,5,7]
[6,4,7,-3,3,3,6,7]
[7,22,25,-3,3,3,7,7]
[8,7,6,1,1,3,8,7]
[9,9,14,-5,5,3,9,7]
[10,26,29,-3,3,5,10,10]
[55,{"$nulls":6},55]
[]
["Negative Differenzen",null,"Positive Differenzen"]
[41,null,14]
[]
["Kritischer Wert = 8"]
["14 > 8"]
[]
["Somit kann die Nullhypothese nicht verworfen werden. "]

{"sheet":"14","index":31,"n_rows":37,"n_cols":8,"rows_kept":37,"flags":["formulas_cached_only"]}
["Übung 14",{"$nulls":4},"Ingeborg Zeiter",null,"SS 03"]
["Test eines neuen Düngemittels"]
[]
["H0: Die Höhe der Pflanzen ändert sich nicht."]
["H1: Die Pflanzen werden höher. (=> linksseitiger Test)"]
[]
["Proband","vorher (cm)","nachher (cm)"]
[1,2.5,5.65]
[2,3.6,8.65]
[3,7.63,8.67]
[4,6.37,13.26]
[5,1.98,6.32]
[6,3.54,9.45]
[7,8.54,15.23]
[8,3.54,7.55]
[9,1.87,4.25]
[10,6.23,10.5]
[11,7.1,12.56]
[12,6.3,9.25]
[13,6.84,9.26]
[14,8.13,10.23]
[15,3.75,5.24]
[16,9.25,15.69]
[17,8.31,9.58]
[18,5.14,6.32]
[19,9.35,14.65]
[20,7.24,13.65]
[21,10.01,12.25]
[22,5.5,7.58]
[23,3.84,8.25]
[24,5.25,6.89]
[25,6.2,8.25]
[26,4.51,9.35]
[27,4.01,8.25]
[28,11.02,14.25]
[29,7.9,12.33]
[30,9.85,14.63]

{"sheet":"L14","index":32,"n_rows":57,"n_cols":10,"rows_kept":57,"flags":["formulas_cached_only"]}
[]
["Zweistichprobentest: verbundene Stichprobe"]
[]
["H0: Die Höhe der Pflanzen ändert sich nicht."]
["H1: Die Pflanzen werden höher. (=> linksseitiger Test)"]
[]
["Proband","vorher (cm)","nachher (cm)","Differenzen","Diff. sortiert","H(x)","F(x)"]
[1,2.5,5.65,-3.1500000000000004,-6.89,0.03333333333333333,0.04073934300629134]
[2,3.6,8.65,-5.050000000000001,-6.69,0.06666666666666667,0.05144735026081426,null,-3.756333333333333,"Mittelwert"]
[3,7.63,8.67,-1.04,-6.44,0.1,0.06785077956386776,null,1.7987150266583194,"Stabw"]
[4,6.37,13.26,-6.89,-6.41,0.133333333333333,0.07006431516804301,null,30,"n"]
[5,1.98,6.32,-4.34,-5.91,0.166666666666666,0.11558782560463787,null,0.01,"Signifikanzniveau"]
[6,3.54,9.45,-5.909999999999999,-5.46,0.2,0.17177921511681338]
[7,8.54,15.23,-6.690000000000001,-5.3,0.233333333333333,0.19538952226869]
[8,3.54,7.55,-4.01,-5.05,0.266666666666666,0.23600349772056362,null,-11.438323857212453,"t"]
[9,1.87,4.25,-2.38,-4.84,0.3,0.2734315670839591,null,{"v":2.7443858651285248e-06,"d":"0.0000027444"},"t(-11.4383239)"]
[10,6.23,10.5,-4.27,-4.78,0.333333333333333,0.28464071367254573]
[11,7.1,12.56,-5.460000000000001,-4.43,0.366666666666666,0.3540063307660575]
[12,6.3,9.25,-2.95,-4.41,0.4,0.3581502797954509,null,"Ergebnis ist signifikant! "]
[13,6.84,9.26,-2.42,-4.34,0.433333333333333,0.37278326832906106,null,"Nullhypothese muss verworfen werden."]
[14,8.13,10.23,-2.0999999999999996,-4.27,0.466666666666666,0.38760218275617864]
[15,3.75,5.24,-1.4900000000000002,-4.24,0.5,0.39400504668523983]
[16,9.25,15.69,-6.4399999999999995,-4.01,0.533333333333333,0.4439244369209039]
[17,8.31,9.58,-1.2699999999999996,-3.23,0.566666666666666,0.6150922089258389]
[18,5.14,6.32,-1.1800000000000006,-3.15,0.6,0.6319763484819216]
[19,9.35,14.65,-5.300000000000001,-2.95,0.633333333333333,0.6730254871622859]
[20,7.24,13.65,-6.41,-2.42,0.666666666666666,0.771240395062235]
[21,10.01,12.25,-2.24,-2.38,0.7,0.7779166573942482]
[22,5.5,7.58,-2.08,-2.24,0.733333333333333,0.8003884067500755]
[23,3.84,8.25,-4.41,-2.1,0.766666666666666,0.8214337076587114]
[24,5.25,6.89,-1.6399999999999997,-2.08,0.8,0.824321835707114]
[25,6.2,8.25,-2.05,-2.05,0.833333333333333,0.8285981886894569]
[26,4.51,9.35,-4.84,-1.64,0.866666666666666,0.8803184837259217]
[27,4.01,8.25,-4.24,-1.49,0.9,0.8961604798855797]
[28,11.02,14.25,-3.2300000000000004,-1.27,0.933333333333333,0.9165575439345243]
[29,7.9,12.33,-4.43,-1.18,0.966666666666666,0.9239736511394958]
[30,9.85,14.63,-4.780000000000001,-1.04,1,0.9344976705677902]
{"$rows_empty":19}
[null,"Die Differenzen können als normalverteilt angesehen werden."]

{"sheet":"15","index":33,"n_rows":14,"n_cols":8,"rows_kept":14,"flags":["formulas_cached_only"]}
["Übung 15",{"$nulls":5},"Ivan, Renato","Salzgeber, Del Buono"]
[]
[]
[null,"In einer Schule wird ein neuer Spezialunterricht angeboten. Dieser wird von 15 Prozent der gesamten"]
[null,"Schülerschaft genutzt. "]
[null,"Die Schulleitung möchte die Teilname steigern. Der Nutzen des neuen Spezialunterrichts soll durch diverse Informationen hervorgehoben werden."]
[null,"Nach der Informationskampagne ist der Anteil auf 25% gestiegen."]
[null,"H0","Die Anteile unterscheiden sich nicht"]
[null,"HA","Der Anteil der Besucher des Spezialunterrichts ist gestiegen (rechtsseitiger Test, alpha = 0.05)"]
[]
[]
[null,"Hier braucht man nicht zu testen, da sich ja die Anteile unterscheiden. "]
[null,"Wir haben ja nicht Stichproben, mit hilfe derer wir die Veränderungen der Grundgesamtheit beurteilen wollen. "]
[null,"Wir haben vielmehr direkt die Anteile der Grundgesamtheit"]

{"sheet":"29","index":34,"n_rows":18,"n_cols":6,"rows_kept":18,"flags":["formulas_cached_only"]}
["Übung 29",null,null,"Escher Christian",null,"SS 03"]
[]
["In einer Untersuchung zur häuslichen Arbeitsteilung in Ehen, in denen beide Partner voll "]
["erwerbstätig sind, wurden folgende Angaben zur Anzahl der jeweils vom Mann bzw. der Frau in einer Woche für Hausarbeit aufgewendeten Stunden ermittelt:"]
[]
["Std. Mann","Std. Frau"]
[5,10]
[8,8]
[14,2]
[7,9]
[6,15]
[1,9]
[2,5]
[5,4]
[12,13]
[]
[]
["Unterscheiden sich die Beiträge an den Haushalt?"]

{"sheet":"L29","index":35,"n_rows":24,"n_cols":4,"rows_kept":24,"flags":["formulas_cached_only"]}
["In einer Untersuchung zur häuslichen Arbeitsteilung in Ehen, in denen beide Partner voll erwerbstätig sind, wurden folgende Angaben zur Anzahl der jeweils vom Mann bzw. der Frau in einer Woche für Hausarbeit aufgewendeten Stunden ermittelt:"]
[]
["Std. Mann","Std. Frau",null,"Richtung des Unterschiedes"]
[5,10,0,"minus"]
[8,8]
[14,2,1,"plus"]
[7,9,0,"minus"]
[6,15,0,"minus"]
[1,9,0,"minus"]
[2,5,0,"minus"]
[5,4,1,"plus"]
[12,13,0,"minus"]
["Summe",null,2]
[]
["Binomialtest:"]
["p-Wert",0.08984375000000001,"> 0.05"]
[]
[]
[]
[]
["Da die Anzahl positiver Differenzen mit einem Wert von 2"]
[" im Annahmebereich liegt, kann die Nullhypothese nicht abgelehnt werden."]
[]
["(ist eine arg kleine Stichprobe. Man sollte wohl über 14 Haushalte untersuchen)"]

{"sheet":"30","index":36,"n_rows":29,"n_cols":7,"rows_kept":29,"merged":[[85,2,85,3]],"flags":["formulas_cached_only"]}
["Übung 30",{"$nulls":3},"Claudia Sofia Paiva Lima",null,"SS 03"]
["Für ein Getriebe wird ein neues Schmiermittel getestet,"]
["welches sich positiv auf die Lebensdauer des Getriebes in Stunden auswirken soll."]
["H0","Das Schmiermittel hat keine Wirkung."]
["HA","Das Schmiermittel verlängert die Lebensdauer des Getriebes. --> rechtsseitiger Test a=0.025"]
[]
[]
[]
[null,"Lebensdauer ohne neues Produkt (1)",{"$nulls":3},"Lebensdauer mit neuem Produkt (2)"]
[]
[1,482.65,{"$nulls":3},785.57]
[2,716.9,{"$nulls":3},788.78]
[3,729.76,{"$nulls":3},865.76]
[4,824.13,{"$nulls":3},873.89]
[5,840.3,{"$nulls":3},888.65]
[6,888.19,{"$nulls":3},891]
[7,908.31,{"$nulls":3},895.14]
[8,910.07,{"$nulls":3},897.56]
[9,959.16,{"$nulls":3},898.12]
[10,996.51,{"$nulls":3},922.04]
[11,1000.83,{"$nulls":3},923.43]
[12,1053.96,{"$nulls":3},928.43]
[13,1100.92,{"$nulls":3},928.51]
[14,1144.13,{"$nulls":3},930.04]
[15,1163.34,{"$nulls":3},940.9]
[16,1178.56,{"$nulls":3},945.18]
[17,1201.43]
[18,1217.08]
[19,1256.84]

{"sheet":"L30","index":37,"n_rows":90,"n_cols":16,"rows_kept":90,"merged":[[85,2,85,3]],"flags":["formulas_cached_only"]}
["Zweistichprobentest"]
[]
[]
[]
[]
[]
[]
[{"$nulls":8},"Überprüfung auf Normalverteilung: "]
[null,"Lebensdauer ohne neues Produkt (1)",{"$nulls":3},"Lebensdauer mit neuem Produkt (2)"]
[]
[1,482.65,0.0074780617328740195,0.05263157894736842,null,785.57,0.011664431816280407,0.0625]
[2,716.9,0.09999539437986371,0.10526315789473684,null,788.78,0.01387423234152052,0.125]
[3,729.76,0.11154697139678815,0.15789473684210525,null,865.76,0.27768848253449274,0.1875]
[4,824.13,0.22533346056757164,0.21052631578947367,null,873.89,0.3373996129377621,0.25]
[5,840.3,0.24990396963567885,0.2631578947368421,null,888.65,0.4559424708787163,0.3125,{"$nulls":5},"nicht normalverteilt",null,"somit Mann-Withney-Test (U-Test)"]
[6,888.19,0.3302201179178028,0.3157894736842105,null,891,0.47548902847727526,0.375]
[7,908.31,0.3667887155067353,0.3684210526315789,null,895.14,0.5100391329647991,0.4375]
[8,910.07,0.37005174476158187,0.42105263157894735,null,897.56,0.5302167960982118,0.5]
[9,959.16,0.46401260487255946,0.47368421052631576,null,898.12,0.5348768566599833,0.5625]
[10,996.51,0.5371789904021425,0.5263157894736842,null,922.04,0.7217850157469435,0.625]
[11,1000.83,0.5456076655468074,0.5789473684210527,null,923.43,0.7314629538574099,0.6875]
[12,1053.96,0.6464760900004358,0.631578947368421,null,928.43,0.7648182510874589,0.75]
[13,1100.92,0.7279874096816762,0.6842105263157895,null,928.51,0.7653326761707335,0.8125]
[14,1144.13,0.7936669987737401,0.7368421052631579,null,930.04,0.7750504192611003,0.875]
[15,1163.34,0.8195551242649556,0.7894736842105263,null,940.9,0.8371642765967725,0.9375]
[16,1178.56,0.8385488114609996,0.8421052631578947,null,945.18,0.8582399378196275,1]
[17,1201.43,0.8645447213855005,0.8947368421052632]
[18,1217.08,0.8805862756451868,0.9473684210526315]
[19,1256.84,0.915190911475303,1]
["Mittelwert",977.53,{"$nulls":3},893.9375000000001]
["Standartabweichung",203.3664457464786,{"$nulls":3},47.780990711088535]
[]
["Daten geordnet","Gruppe","Rang","Nummer","Rang1","Rang2"]
[]
[482.65,1,1,1,1,0]
[716.9,1,2,2,2,0]
[729.76,1,3,3,3,0]
[785.57,2,4,4,0,4]
[788.78,2,5,5,0,5]
[824.13,1,6,6,6,0]
[840.3,1,7,7,7,0]
[865.76,2,8,8,0,8]
[873.89,2,9,9,0,9]
[888.19,1,10,10,10,0]
[888.65,2,11,11,0,11]
[891,2,12,12,0,12]
[895.14,2,13,13,0,13]
[897.56,2,14,14,0,14]
[898.12,2,15,15,0,15]
[908.31,1,16,16,16,0]
[910.07,1,17,17,17,0]
[922.04,2,18,18,0,18]
[923.43,2,19,19,0,19]
[928.43,2,20,20,0,20]
[928.51,2,21,21,0,21]
[930.04,2,22,22,0,22]
[940.9,2,23,23,0,23]
[945.18,2,24,24,0,24]
[959.16,1,25,25,25,0]
[996.51,1,26,26,26,0]
[1000.83,1,27,27,27,0]
[1053.96,1,28,28,28,0]
[1100.92,1,29,29,29,0]
[1144.13,1,30,30,30,0]
[1163.34,1,31,31,31,0]
[1178.56,1,32,32,32,0]
[1201.43,1,33,33,33,0]
[1217.08,1,34,34,34,0]
[1256.84,1,35,35,35,0]
[{"$nulls":4},392,238]
[]
[null,"R1",392]
[null,"U1",102]
[]
[null,"R2",238]
[null,"U2",202]
[]
[null,"Gemäss Tabelle,"]
[null,"kritischer Wert:",92," liegt darüber; somit nicht signifikant"]
{"$rows_empty":10}
["Mt SPSS "]

{"sheet":"31","index":38,"n_rows":9,"n_cols":7,"rows_kept":9,"flags":["formulas_cached_only"]}
["Übung 31",null,null,"Zeiter Ingeborg","Marco Volken",null,"SS 03"]
[]
[]
[]
[]
[]
[]
["H0: Die Jugendanteile unterscheiden sich nicht."]
["HA: Die Jugendanteile unterscheiden sich. (=> zweiseitiger Test, Signifikantsniveau=0.05)"]

{"sheet":"L31","index":39,"n_rows":17,"n_cols":5,"rows_kept":17,"flags":["formulas_cached_only"]}
{"$rows_empty":7}
["H0: Die Jugendanteile unterscheiden sich nicht."]
["HA: Die Jugendanteile unterscheiden sich. (=> zweiseitiger Test, Signifikantsniveau=0.05)"]
[]
["X1/n1",0.5,null,"Z",-2.255254012288006]
["X2/n2",0.72,null,"Standarndnormvert.(-2.25525401)",0.012058656505205767]
["n1",50]
["n2",50,null,"Da wir zweiseitig testen gilt: 0.01205866 < 0.025"]
["X1",25,null,"Der Unterschied ist somit signifikant."]
["X2",36]
["X1+X2 / n1+n2",0.61]

{"sheet":"32","index":40,"n_rows":71,"n_cols":7,"rows_kept":71,"flags":["formulas_cached_only"]}
["Übung 32",null,null,"Sonja Borter, Ingrid Bregy",null,null,"SS 03"]
[]
[]
[]
[null,"Beispiel: Schwimmbad A erfasst durchschnittlich x Eintritte pro Tag, Schwimmbad B durchschnittlich x Eintritte."]
[]
[null,"Ho: Die durchschnittlichen Eintritte pro Tag unterscheiden sich nicht"]
[null,"Ha: Die durchschnittlichen Eintritte pro Tag unterscheiden sich (beidseitiger Test, a = 0.05)"]
[]
[]
[null,"Schwimmbad A","Schwimmbad B"]
[1,50,50]
[2,65,49]
[3,55,43]
[4,57,52]
[5,59,46]
[6,53,51]
[7,51,55]
[8,49,53]
[9,65,59]
[10,68,59]
[11,50,58]
[12,54,52]
[13,45,53]
[14,54,51]
[15,57,48]
[16,51,61]
[17,53,62]
[18,70,58]
[19,46,51]
[20,57,46]
[21,52,41]
[22,75,42]
[23,58,45]
[24,61,56]
[25,61,52]
[26,57,51]
[27,51,53]
[28,53,57]
[29,48,54]
[30,43,52]
[31,61,56]
[32,63,54]
[33,51,52]
[34,48,59]
[35,64,50]
[36,67,52]
[37,61,49]
[38,54,52]
[39,52,53]
[40,39,57]
[41,45,50]
[42,46,61]
[43,70,52]
[44,46,53]
[45,45,57]
[46,70,51]
[47,62,52]
[48,48,59]
[49,51,54]
[50,59,49]
[51,53,46]
[52,63,43]
[53,null,51]
[54,null,52]
[55,null,51]
[56,null,50]
[57,null,49]
[58,null,54]
[59,null,51]
[60,null,55]

{"sheet":"L32","index":41,"n_rows":71,"n_cols":9,"rows_kept":71,"flags":["formulas_cached_only"]}
[]
["Es handelt sich um einen Zweistichprobentest: "]
["Die Varianzen untescheiden sich signifikant."]
["Somit muss der Z-Test verwendet werden (oder dann bei nicht normalverteilten Daten der Mann-Withney-Test)"]
[]
[]
[null,"Ho: Die durchschnittlichen Eintritte pro Tag unterscheiden sich nicht"]
[null,"Ha: Die durchschnittlichen Eintritte pro Tag unterscheiden sich (beidseitiger Test, a = 0.05)"]
[]
[]
[null,"Schwimmbad A","Schwimmbad B"]
[1,50,50,null,"Mittelwert A",55.5]
[2,65,49,null,"Mittelwert B",52.32692307692308]
[3,55,43,null,"Varianz A",65.23529411764706,"Hier fehlt der Varianztest!!!!!!",null,"Die Varianzen sind vermutlich signifikant verschieden"]
[4,57,52,null,"Varianz B",24.65573152337867]
[5,59,46]
[6,53,51,null,"n A",52]
[7,51,55,null,"n B",60]
[8,49,53]
[9,65,59,null,"Z",2.4587496594755254]
[10,68,59,null,"Mit Excel",0.012121486397000026,"(zweiseitig!)"]
[11,50,58]
[12,54,52,null,"Standartnormvert.",0.0069710957901542026,"< 0.05 "]
[13,45,53]
[14,54,51,null,"Der Unterschied ist signifikant!"]
[15,57,48]
[16,51,61]
[17,53,62]
[18,70,58]
[19,46,51]
[20,57,46]
[21,52,41]
[22,75,42]
[23,58,45]
[24,61,56]
[25,61,52]
[26,57,51]
[27,51,53]
[28,53,57]
[29,48,54]
[30,43,52]
[31,61,56]
[32,63,54]
[33,51,52]
[34,48,59]
[35,64,50]
[36,67,52]
[37,61,49]
[38,54,52]
[39,52,53]
[40,39,57]
[41,45,50]
[42,46,61]
[43,70,52]
[44,46,53]
[45,45,57]
[46,70,51]
[47,62,52]
[48,48,59]
[49,51,54]
[50,59,49]
[51,53,46]
[52,63,43]
[53,null,51]
[54,null,52]
[55,null,51]
[56,null,50]
[57,null,49]
[58,null,54]
[59,null,51]
[60,null,55]

{"sheet":"40","index":42,"n_rows":124,"n_cols":5,"rows_kept":124,"flags":["formulas_cached_only"]}
["Übung 40",{"$nulls":3},"Claudia Sofia Paiva Lima"]
[]
["Es werden die Tagesumsätze zweier Vertreter verglichen"]
[]
[]
[]
[]
[]
[null,"Ho:","Die durchschnittlichen Umsätze der zwei Vertreter unterscheiden sich nicht"]
[null,"HA:","Die durchschnittlichen Umsätze der zwei Vertreter unterscheiden sich (beidseitiger Test, a = 0.05)"]
[]
[null,null,"Vertreter 1","Vertreter 2"]
[null,1,109.35,129.35]
[null,2,111.18,130.18]
[null,3,113.02,130.19]
[null,4,114.18,130.31]
[null,5,114.32,130.41]
[null,6,114.39,130.43]
[null,7,114.78,130.6]
[null,8,114.99,130.77]
[null,9,115.1,130.82]
[null,10,115.97,130.83]
[null,11,115.99,130.9]
[null,12,116.07,130.93]
[null,13,116.69,130.99]
[null,14,116.71,131.1]
[null,15,116.75,131.24]
[null,16,116.84,131.34]
[null,17,116.91,131.4]
[null,18,117.07,131.66]
[null,19,117.2,131.86]
[null,20,117.45,132.13]
[null,21,117.46,132.13]
[null,22,117.59,132.28]
[null,23,117.71,132.31]
[null,24,118.18,132.31]
[null,25,118.28,132.41]
[null,26,118.53,132.42]
[null,27,118.84,132.7]
[null,28,118.93,132.75]
[null,29,118.96,132.76]
[null,30,119.1,132.85]
[null,31,119.12,132.85]
[null,32,119.18,132.88]
[null,33,119.2,132.95]
[null,34,119.2,133.01]
[null,35,119.27,133.02]
[null,36,119.36,133.06]
[null,37,119.63,133.1]
[null,38,119.88,133.2]
[null,39,119.96,133.22]
[null,40,120,133.26]
[null,41,120.06,133.42]
[null,42,120.11,133.5]
[null,43,120.17,133.61]
[null,44,120.22,133.62]
[null,45,120.23,133.85]
[null,46,120.27,134.04]
[null,47,120.28,134.08]
[null,48,120.5,134.2]
[null,49,120.54,134.23]
[null,50,120.64,134.24]
[null,51,120.85,134.27]
[null,52,120.88,134.32]
[null,53,120.93,134.33]
[null,54,121.29,134.4]
[null,55,121.3,134.5]
[null,56,121.37,134.54]
[null,57,121.42,134.6]
[null,58,121.43,134.79]
[null,59,121.62,134.87]
[null,60,121.79,135.01]
[null,61,121.84,135.05]
[null,62,121.86,135.13]
[null,63,121.94,135.21]
[null,64,122.4,135.27]
[null,65,122.54,135.29]
[null,66,122.59,135.36]
[null,67,122.59,135.38]
[null,68,122.64,135.41]
[null,69,122.7,135.45]
[null,70,122.79,135.48]
[null,71,122.82,135.48]
[null,72,123.08,135.58]
[null,73,123.12,135.63]
[null,74,123.21,135.64]
[null,75,123.21,135.78]
[null,76,123.25,135.85]
[null,77,123.28,135.85]
[null,78,124.35,135.91]
[null,79,124.37,135.95]
[null,80,124.44,136.01]
[null,81,124.53,136.1]
[null,82,124.6,136.39]
[null,83,124.75,136.48]
[null,84,124.94,136.55]
[null,85,125.2,136.56]
[null,86,125.51,136.65]
[null,87,126.77,136.69]
[null,88,127.32,136.79]
[null,89,128.46,136.86]
[null,90,129.37,137.1]
[null,91,129.48,137.2]
[null,92,129.71,137.36]
[null,93,129.9,137.4]
[null,94,129.94,137.51]
[null,95,130.15,137.9]
[null,96,null,138.04]
[null,97,null,138.1]
[null,98,null,138.25]
[null,99,null,138.31]
[null,100,null,138.55]
[null,101,null,138.67]
[null,102,null,138.94]
[null,103,null,139.41]
[null,104,null,139.62]
[null,105,null,139.86]
[null,106,null,139.93]
[null,107,null,140.17]
[null,108,null,140.77]
[null,109,null,140.87]
[null,110,null,140.98]
[null,111,null,141.49]
[null,112,null,142.44]

{"sheet":"L40","index":43,"n_rows":126,"n_cols":13,"rows_kept":126,"flags":["formulas_cached_only"]}
["Übung 40",{"$nulls":4},"Claudia Lima Paiva",null,"SS 03"]
[]
["Vertreter 1 erzielt einen durchschnittlichen Tagesumsatz von sFr. 120.725157894737 in 95 Tage, "]
["die Standartabweichung beträgt = 4.14282534467699"]
[{"$nulls":8},134.785535714286]
["Vertreter 2 erzielt einen durchschnittlichen Tagesumsatz von sFr. 134.785535714286 in 112 Tage, ",{"$nulls":7},2.88585642019375]
["die Standartabweichung beträgt hier = 2.88585642019375"]
["Zweistichprobentest:"]
[null,"Ho:","Die durchschnittlichen Umsätze der zwei Vertreter unterscheiden sich nicht"]
[null,"HA:","Die durchschnittlichen Umsätze der zwei Vertreter unterscheiden sich (beidseitiger Test, a = 0.05)"]
[]
[null,null,"Vertreter 1",{"$nulls":3},"Vertreter 2",null,"Überprüfung Normalverteilung:"]
[null,1,109.35,0.0030187030162397432,0.010526315789473684,0.008928571428571428,129.35,0.029815664571839706]
[null,2,111.18,0.010610695470730902,0.021052631578947368,0.017857142857142856,130.18,0.055255658295306875]
[null,3,113.02,0.03145119178422873,0.031578947368421054,0.026785714285714284,130.19,0.05564361748170288]
[null,4,114.18,0.05706742806904652,0.042105263157894736,0.03571428571428571,130.31,0.06046861067290554]
[null,5,114.32,0.061042099463162414,0.05263157894736842,0.044642857142857144,130.41,0.06473440772640882]
[null,6,114.39,0.06310896854806802,0.06315789473684211,0.05357142857142857,130.43,0.06561495949934637]
[null,7,114.78,0.07563659384333221,0.07368421052631578,0.0625,130.6,0.07347887717212465]
[null,8,114.99,0.08312432053096985,0.08421052631578947,0.07142857142857142,130.77,0.08204399248600436]
[null,9,115.1,0.08726250120337464,0.09473684210526316,0.08035714285714286,130.82,0.08470105213238155]
[null,10,115.97,0.12552447690175372,0.10526315789473684,0.08928571428571429,130.83,0.08524012309545459]
[null,11,115.99,0.12652393092360992,0.11578947368421053,0.09821428571428571,130.9,0.08908579579055087]
[null,12,116.07,0.1305771169247053,0.12631578947368421,0.10714285714285714,130.93,0.09077291267422127]
[null,13,116.69,0.1650255080677524,0.1368421052631579,0.11607142857142858,130.99,0.09421807296450124]
[null,14,116.71,0.16622681902314074,0.14736842105263157,0.125,131.1,0.10078301947440127]
[null,15,116.75,0.16864634086297636,0.15789473684210525,0.13392857142857142,131.24,0.10961275826422312]
[null,16,116.84,0.17417257129028196,0.16842105263157894,0.14285714285714285,131.34,0.11625103108918267]
[null,17,116.91,0.17854940100479078,0.17894736842105263,0.15178571428571427,131.4,0.12036835544931213]
[null,18,117.07,0.1888109712380026,0.18947368421052632,0.16071428571428573,131.66,0.13939246485244183]
[null,19,117.2,0.197410537085419,0.2,0.16964285714285715,131.86,0.15535114253858506]
[null,20,117.45,0.21459991660725086,0.21052631578947367,0.17857142857142858,132.13,0.17873675940264022]
[null,21,117.46,0.21530511755447546,0.22105263157894736,0.1875,132.13,0.17873675940264022]
[null,22,117.59,0.2245943440776681,0.23157894736842105,0.19642857142857142,132.28,0.19263904679417176]
[null,23,117.71,0.23336722821347722,0.24210526315789474,0.20535714285714285,132.31,0.19549680600111574]
[null,24,118.18,0.2694909285832767,0.25263157894736843,0.21428571428571427,132.31,0.19549680600111574]
[null,25,118.28,0.27752319038872586,0.2631578947368421,0.22321428571428573,132.41,0.20520705386927252]
[null,26,118.53,0.2981010931545697,0.2736842105263158,0.23214285714285715,132.42,0.20619359351315691]
[null,27,118.84,0.32453967194354205,0.28421052631578947,0.24107142857142858,132.7,0.23493977612885175]
[null,28,118.93,0.332392165163927,0.29473684210526313,0.25,132.75,0.24029648729191921,"Normalverteilung ist i.O."]
[null,29,118.96,0.3350263159470599,0.30526315789473685,0.25892857142857145,132.76,0.24137575931627953]
[null,30,119.1,0.34742479340142307,0.3157894736842105,0.26785714285714285,132.85,0.2512066643950537,null,"n1:",95,"> 50"]
[null,31,119.12,0.34920979115485284,0.3263157894736842,0.2767857142857143,132.85,0.2512066643950537,null,"n2:",112,"> 50"]
[null,32,119.18,0.35458469323577446,0.3368421052631579,0.2857142857142857,132.88,0.2545300712340137]
[null,33,119.2,0.3563828444586218,0.3473684210526316,0.29464285714285715,132.95,0.26237335031926223,null,null,0.4852395494279576,"~ F(111, 94)"]
[null,34,119.2,0.3563828444586218,0.35789473684210527,0.30357142857142855,133.01,0.2691933221690832,null,null,0.9998644850629436,"> 0.05"]
[null,35,119.27,0.3627013228476297,0.3684210526315789,0.3125,133.02,0.27033856997022676,null,null,"Somit sind die Varianzen verschieden. "]
[null,36,119.36,0.370880119319305,0.37894736842105264,0.32142857142857145,133.06,0.2749437790795002]
[null,37,119.63,0.3957549878181792,0.3894736842105263,0.33035714285714285,133.1,0.2795873132806379,null,null,"Also z-Test"]
[null,38,119.88,0.4191747445930931,0.4,0.3392857142857143,133.2,0.29135996389872654]
[null,39,119.96,0.4267342611366447,0.4105263157894737,0.3482142857142857,133.22,0.2937419648693751,null,null,-28.64660611474933]
[null,40,120,0.4305243178179121,0.42105263157894735,0.35714285714285715,133.26,0.29853280222979883,null,null,"p-Wert",0,"< 0.05"]
[null,41,120.06,0.4362213152323393,0.43157894736842106,0.36607142857142855,133.42,0.31804162811845593,null,null,"hochsignifikanter Unterschied"]
[null,42,120.11,0.44097899354598913,0.4421052631578947,0.375,133.5,0.3279934389498511]
[null,43,120.17,0.44669941253693657,0.45263157894736844,0.38392857142857145,133.61,0.34187779141003216]
[null,44,120.22,0.4514749678015282,0.4631578947368421,0.39285714285714285,133.62,0.34315103212624853]
[null,45,120.23,0.4524309448575178,0.47368421052631576,0.4017857142857143,133.85,0.3729011063408989]
[null,46,120.27,0.45625755694771464,0.4842105263157895,0.4107142857142857,134.04,0.39807183744916874]
[null,47,120.28,0.45721485845102583,0.49473684210526314,0.41964285714285715,134.08,0.40342938813951834]
[null,48,120.5,0.4783285365156873,0.5052631578947369,0.42857142857142855,134.2,0.4196072381711671]
[null,49,120.54,0.48217569138187755,0.5157894736842106,0.4375,134.23,0.42367416696852556]
[null,50,120.64,0.49180007378289614,0.5263157894736842,0.44642857142857145,134.24,0.42503164109966085]
[null,51,120.85,0.5120201731246874,0.5368421052631579,0.45535714285714285,134.27,0.42910933724891076]
[null,52,120.88,0.5149074428098438,0.5473684210526316,0.4642857142857143,134.32,0.43592212897306837]
[null,53,120.93,0.5197177438861327,0.5578947368421052,0.4732142857142857,134.33,0.4372870392228789]
[null,54,121.29,0.5542246661474474,0.5684210526315789,0.48214285714285715,134.4,0.4468614234081256]
[null,55,121.3,0.5551785687316625,0.5789473684210527,0.49107142857142855,134.5,0.46059164665303953]
[null,56,121.37,0.5618466376480383,0.5894736842105263,0.5,134.54,0.46609785824689975]
[null,57,121.42,0.566598929378733,0.6,0.5089285714285714,134.6,0.474369035185087]
[null,58,121.43,0.5675482560554814,0.6105263157894737,0.5178571428571429,134.79,0.5006171485910036]
[null,59,121.62,0.5855053242666668,0.6210526315789474,0.5267857142857143,134.87,0.5116747718636065]
[null,60,121.79,0.6014232288526254,0.631578947368421,0.5357142857142857,135.01,0.5309988674584506]
[null,61,121.84,0.6060743008088563,0.6421052631578947,0.5446428571428571,135.05,0.5365086341813363]
[null,62,121.86,0.6079305422652599,0.6526315789473685,0.5535714285714286,135.13,0.5475061314230791]
[null,63,121.94,0.6153305802986149,0.6631578947368421,0.5625,135.21,0.5584672963526598]
[null,64,122.4,0.6569948264292,0.6736842105263158,0.5714285714285714,135.27,0.5666593498505266]
[null,65,122.54,0.669331730616773,0.6842105263157895,0.5803571428571429,135.29,0.5693838613199754]
[null,66,122.59,0.6736944221568224,0.6947368421052632,0.5892857142857143,135.36,0.5788928466519943]
[null,67,122.59,0.6736944221568224,0.7052631578947368,0.5982142857142857,135.38,0.5816015217717933]
[null,68,122.64,0.6780334770862501,0.7157894736842105,0.6071428571428571,135.41,0.585657250850576]
[null,69,122.7,0.6832084385747375,0.7263157894736842,0.6160714285714286,135.45,0.5910506430422919]
[null,70,122.79,0.690903865760055,0.7368421052631579,0.625,135.48,0.595084463932011]
[null,71,122.82,0.6934507259860166,0.7473684210526316,0.6339285714285714,135.48,0.595084463932011]
[null,72,123.08,0.7151232756165475,0.7578947368421053,0.6428571428571429,135.58,0.6084554617754747]
[null,73,123.12,0.7183915374279358,0.7684210526315789,0.6517857142857143,135.63,0.6150942832761852]
[null,74,123.21,0.72567831225797,0.7789473684210526,0.6607142857142857,135.64,0.6164180772571799]
[null,75,123.21,0.72567831225797,0.7894736842105263,0.6696428571428571,135.78,0.6348021455370116]
[null,76,123.25,0.7288867296514401,0.8,0.6785714285714286,135.85,0.6438822619313491]
[null,77,123.28,0.7312806995076261,0.8105263157894737,0.6875,135.85,0.6438822619313491]
[null,78,124.35,0.8092045481137757,0.8210526315789474,0.6964285714285714,135.91,0.6516010249633973]
[null,79,124.37,0.8105151863975872,0.8315789473684211,0.7053571428571429,135.95,0.6567124432403922]
[null,80,124.44,0.8150586318270018,0.8421052631578947,0.7142857142857143,136.01,0.6643258660680584]
[null,81,124.53,0.820799785195484,0.8526315789473684,0.7232142857142857,136.1,0.6756198004895154]
[null,82,124.6,0.8251867413837592,0.8631578947368421,0.7321428571428571,136.39,0.7108860930232226]
[null,83,124.75,0.8343555720279002,0.8736842105263158,0.7410714285714286,136.48,0.7214524829727442]
[null,84,124.94,0.845514470864534,0.8842105263157894,0.75,136.55,0.7295385806013122]
[null,85,125.2,0.8599606214869789,0.8947368421052632,0.7589285714285714,136.56,0.7306840892226798]
[null,86,125.51,0.8759487439842208,0.9052631578947369,0.7678571428571429,136.65,0.7408829457764521]
[null,87,126.77,0.9277326843277771,0.9157894736842105,0.7767857142857143,136.69,0.7453508110878768]
[null,88,127.32,0.9442931148785793,0.9263157894736842,0.7857142857142857,136.79,0.7563414647443759]
[null,89,128.46,0.9690524244908832,0.9368421052631579,0.7946428571428571,136.86,0.7638798134458649]
[null,90,129.37,0.9815425262434299,0.9473684210526315,0.8035714285714286,137.1,0.7887243304012974]
[null,91,129.48,0.9827105435059208,0.9578947368421052,0.8125,137.2,0.7986066081176915]
[null,92,129.71,0.9849500410446962,0.968421052631579,0.8214285714285714,137.36,0.8138296051864072]
[null,93,129.9,0.9866074498065579,0.9789473684210527,0.8303571428571429,137.4,0.817520950755563]
[null,94,129.94,0.9869355512765936,0.9894736842105263,0.8392857142857143,137.51,0.8274343002430518]
[null,95,130.15,0.9885464498547083,1,0.8482142857142857,137.9,0.8597543852935159]
[null,96,{"$nulls":3},0.8571428571428571,138.04,0.8702827815727668]
[null,97,{"$nulls":3},0.8660714285714286,138.1,0.8746230000728856]
[null,98,{"$nulls":3},0.875,138.25,0.8850269053138091]
[null,99,{"$nulls":3},0.8839285714285714,138.31,0.889011600622215]
[null,100,{"$nulls":3},0.8928571428571429,138.55,0.9039603611112782]
[null,101,{"$nulls":3},0.9017857142857143,138.67,0.9108543546876757]
[null,102,{"$nulls":3},0.9107142857142857,138.94,0.9250089398993105]
[null,103,{"$nulls":3},0.9196428571428571,139.41,0.9454728411440485]
[null,104,{"$nulls":3},0.9285714285714286,139.62,0.953055162822704]
[null,105,{"$nulls":3},0.9375,139.86,0.9606595531594804]
[null,106,{"$nulls":3},0.9464285714285714,139.93,0.9626781864342044]
[null,107,{"$nulls":3},0.9553571428571429,140.17,0.9689661967294646]
[null,108,{"$nulls":3},0.9642857142857143,140.77,0.9809475028117792]
[null,109,{"$nulls":3},0.9732142857142857,140.87,0.9825007310320564]
[null,110,{"$nulls":3},0.9821428571428571,140.98,0.9840831366132099]
[null,111,{"$nulls":3},0.9910714285714286,141.49,0.9899162153658606]
[null,112,{"$nulls":3},1,142.44,0.9960039444589928]
["Mittelwert:",null,120.72515789473688,{"$nulls":3},134.78553571428577]
["Standartabweichung:",null,4.142825344676987,{"$nulls":3},2.8858564201937518]