{"text_format":"3","workbook":"xlsx","n_sheets":8,"sheets":["U1","LU1","U2","LU2","U3","LU3","U4","LU4"],"not_rendered":{"charts":4,"images":4},"read":"whole","date_system":"1900"}

{"sheet":"U1","index":0,"n_rows":73,"n_cols":2,"rows_kept":73}
["Seien n i.i.d. Zufallsvariablen Xi gegeben und die folgende Statistik, "]
["die auf das kartesische Produkt der Bilder dieser Zufallsvariablen definiert ist: "]
[]
[]
[null,"Y="]
[]
[]
[]
["x0quer ist der Mittelwert der Grundgesamtheit, der als Schätzer für den Erwartungswert der Zufallsvariablen Xi betrachtet wird. (x0quer = 49)"]
["s0 ist die Standardabweichung der Grundgesamtheit, die als Schätzer für die Standardabweichung der Zufallsvariablen Xi betrachtet wird. (s0 = 4)"]
["Xquer ist die Statistik, welche Stichprobenmittel annimmt. "]
["n ist die Stichprobengrösse. "]
["Wie hoch ist die Wahrscheinlichkeit, dass die Statistik Y den Werte Y(x) oder einen grösseren Wert zufälliger weise annimmt? (x = Stichprobe)"]
[]
[]
[]
[]
["Daten (Werte der Xi)"]
[46.19717992241851]
[50.435520938062446]
[53.82051594273283]
[49.08687546411736]
[53.07099149514209]
[47.440677777103176]
[48.8644469534828]
[47.730790668801895]
[53.447073311301686]
[53.50895440991537]
[57.116094097218166]
[48.9856458516521]
[50.30900915992773]
[52.237535305078495]
[53.259760288820786]
[46.23483495467716]
[48.71287177199705]
[56.930600822238816]
[49.253697647839225]
[51.86924616503463]
[46.75938450350805]
[51.436922271356096]
[51.09390795838175]
[45.92625685196024]
[52.215452353587715]
[44.07787185563551]
[47.89146208472085]
[56.69207801702496]
[43.36223413202278]
[54.19716349294661]
[53.38316131534252]
[51.724776392554716]
[50.20515473004973]
[50.35640476213734]
[51.38137869928308]
[51.506875123050065]
[53.28859845783083]
[51.104186056884465]
[49.23097146913074]
[46.883865950861484]
[53.29509739638628]
[52.606115374400396]
[52.855157257875014]
[46.9051584821356]
[50.12468578659679]
[39.06583630386602]
[45.873757298336386]
[48.847115138332974]
[43.89436654086168]
[42.3231521614377]
[53.504545312431574]
[50.58161829771595]
[48.75280897103817]
[51.13795879145406]
[51.4252929627431]

{"sheet":"LU1","index":1,"n_rows":73,"n_cols":6,"rows_kept":73}
[]
["Y="]
[]
[]
["Y stellt eine Standardisierung der Statistik Mittelwert dar (Vergleichen Sie die Formel, "]
["in welche die geschätzten Grössen ersetzt werden, mit der Formel im Zentralen Grenzwertsatz.)"]
["Da der standardisierte Mittelwert gemäss zentralem Grenzwertsatz standardnormalverteilt ist"]
["berechnen wir:"]
[null,null,"Mittelwert:",{"$f":"AVERAGE(A19:A73)","v":50.04405628184441},"(Stichprobenmittel = Wert den die Statistik Mittelwert für den vorliegenden Datensatz annimmt = Xquer(x))"]
[null,null,"n",{"$f":"COUNT(A19:A73)","v":55},"(Anzahl Daten)"]
[]
[null,null,"Y(x) =",{"$f":"(D9-49)/(4/SQRT(55))","v":1.935732154464313},"Wert der Statistik Y für die Stichprobe x."]
[null,null,"P(Y > 1.93573215) =",null,{"$f":"1-NORMDIST(D9,49,4/SQRT(55),1)","v":0.026450257075749772},"=1-NORMVERT(D15;49;4/WURZEL(55);1)"]
[null,null,{"$f":"1-NORMDIST(D12,0,1,1)","v":0.026450257075749772}]
["Wichtige Zusatzüberlegung:",null,"Wie hoch ist die Wahrscheinlichkeit, dass die Statistik Xquer den Stichprobenmittelwert oder einen höheren Wert annimmt."]
[null,null,"P(Xquer > 50.044056) mit Xquer ~ N(49, 4^2/55) ="]
[null,null,{"$f":"1-NORMDIST(D9,49,4/SQRT(55),1)","v":0.026450257075749772}]
["Daten (Werte der Xi) = Stichprobe x"]
[46.19717992241851]
[50.435520938062446]
[53.82051594273283]
[49.08687546411736]
[53.07099149514209]
[47.440677777103176]
[48.8644469534828]
[47.730790668801895]
[53.447073311301686]
[53.50895440991537]
[57.116094097218166]
[48.9856458516521]
[50.30900915992773]
[52.237535305078495]
[53.259760288820786]
[46.23483495467716]
[48.71287177199705]
[56.930600822238816]
[49.253697647839225]
[51.86924616503463]
[46.75938450350805]
[51.436922271356096]
[51.09390795838175]
[45.92625685196024]
[52.215452353587715]
[44.07787185563551]
[47.89146208472085]
[56.69207801702496]
[43.36223413202278]
[54.19716349294661]
[53.38316131534252]
[51.724776392554716]
[50.20515473004973]
[50.35640476213734]
[51.38137869928308]
[51.506875123050065]
[53.28859845783083]
[51.104186056884465]
[49.23097146913074]
[46.883865950861484]
[53.29509739638628]
[52.606115374400396]
[52.855157257875014]
[46.9051584821356]
[50.12468578659679]
[39.06583630386602]
[45.873757298336386]
[48.847115138332974]
[43.89436654086168]
[42.3231521614377]
[53.504545312431574]
[50.58161829771595]
[48.75280897103817]
[51.13795879145406]
[51.4252929627431]

{"sheet":"U2","index":2,"n_rows":92,"n_cols":2,"rows_kept":92}
["Seien n i.i.d. Zufallsvariablen Xi gegeben und die folgende Statistik, "]
["die auf das kartesische Produkt der Bilder dieser Zufallsvariablen definiert ist: "]
[]
[]
[null,"Y="]
[]
[]
[]
[]
["s0 ist die Standardabweichung der Zufallsvariablen Xi. (s0 = 9)"]
["n ist die Stichprobengrösse. "]
["S^2 ist die Statistik, welche Stichprobenvarianzen als Werte annimmt. "]
["Wie hoch ist die Wahrscheinlichkeit, dass die Statistik Y den Wert Y(x) oder einen grösseren Wert zufälliger weise annimmt (x ist die vorliegende Stichprobe)?"]
["Wenn die Zufallsvariablen Xi normalverteilt sind, ist die Statistik Y chiquadrat verteilt mit n-1 Freiheitsgraden."]
["(Überprüfen Sie vor der Berechnung die Voraussetzung)"]
[]
["Daten (Werte der Xi)"]
[147.29832467222587]
[164.59881379163096]
[132.24555350341194]
[153.5915575569228]
[145.5832605037666]
[155.45492594993252]
[124.5249538523685]
[168.80237149262783]
[170.80623187176792]
[145.14065490231982]
[145.09573767571422]
[136.59805930737687]
[141.54655575403618]
[149.16669159393285]
[142.12206492827548]
[130.52444083860772]
[137.2804888435679]
[166.36490308411]
[168.43963972779306]
[160.11577193963623]
[167.82987516086766]
[149.16529431828462]
[150.39016417575468]
[143.90900961809257]
[127.05309483805988]
[137.16934446689177]
[162.8731145185201]
[150.18563320256126]
[135.28302385690375]
[150.08450765410433]
[153.7417830274607]
[132.31002467267083]
[164.88442650720881]
[132.41345219944407]
[180.4734192940876]
[174.18217000518618]
[143.4847841677396]
[156.30210829582796]
[143.00374684730002]
[157.96150976627302]
[143.4947023961718]
[167.9270291205626]
[128.0668281184821]
[151.88261826065911]
[147.027840385341]
[173.65868882972705]
[160.65762064878794]
[144.87460835697956]
[159.164934154005]
[160.83527196697736]
[177.68526687953567]
[153.25361967136107]
[143.3611007535384]
[153.12495532207546]
[132.32045322492894]
[159.43852815380174]
[153.03719452073892]
[148.3079406277408]
[160.67579396246174]
[137.77865172505705]
[146.95173773250468]
[134.73380120902394]
[166.6964127895036]
[136.77798569536986]
[132.19759554308905]
[134.92709579649323]
[156.40075682364065]
[166.89397243265975]
[134.3993271869336]
[126.67759984968741]
[135.48182164915747]
[154.0827961828574]
[142.1200974339755]
[146.61378907152948]
[114.0818714684695]

{"sheet":"LU2","index":3,"n_rows":92,"n_cols":6,"rows_kept":92}
[]
[]
[]
[]
[null,"Y="]
[]
[]
[]
[]
["n=",{"$f":"COUNT(A18:A92)","v":75}]
["S^2(x)=",{"$f":"VAR(A18:A92)","v":199.90831669608298}]
["Y(x)=",{"$f":"(75-1)*B11/9^2","v":182.6322893272857}]
["Xquer(x)=",{"$f":"AVERAGE(A18:A92)","v":149.11482395102783}]
["P(Y > 182.632289)=",null,{"$f":"CHIDIST(B12,74)","v":3.6641020497183334E-11},"=CHIVERT(B12;74)"]
[]
[{"$nulls":4},"x","y"]
["Daten (Werte der Xi)","i/n","F(xi)",null,0,0]
[114.0818714684695,0.013333333333333334,{"$f":"NORMDIST(A18,$B$13,SQRT($B$11),1)","v":0.006610283231039653},null,1,1]
[124.5249538523685,0.02666666666666667,{"$f":"NORMDIST(A19,$B$13,SQRT($B$11),1)","v":0.04100286614863322},null,"Überprüfung aus Normalverteilung der Daten mit P-P-Plot"]
[126.67759984968741,0.04,0.05626593645669834]
[127.05309483805988,0.0533333333333333,0.059337709500892885]
[128.0668281184821,0.0666666666666666,0.06828855242634906]
[130.52444083860772,0.08,0.09428184000469185]
[132.19759554308905,0.0933333333333333,0.11575016966365087]
[132.24555350341194,0.106666666666667,0.11641294125882713]
[132.31002467267083,0.12,0.11730815851069719]
[132.32045322492894,0.133333333333333,0.11745342153426125]
[132.41345219944407,0.146666666666666,0.11875447156950525]
[134.3993271869336,0.16,0.14898852158050363]
[134.73380120902394,0.173333333333333,0.1545469771853446]
[134.92709579649323,0.186666666666666,0.15782095330919385]
[135.28302385690375,0.2,0.16396787506513003]
[135.48182164915747,0.213333333333333,0.1674678522201843]
[136.59805930737687,0.226666666666666,0.18800501414024703]
[136.77798569536986,0.24,0.19145523337748305]
[137.16934446689177,0.253333333333333,0.19909265463240927,null,"Die Daten, die wir als Werte von Zufallsvariablen betrachten, sind normalverteilt."]
[137.2804888435679,0.266666666666666,0.20129467328387554]
[137.77865172505705,0.28,0.21134236567452713]
[141.54655575403618,0.293333333333333,0.29622809900280817]
[142.1200974339755,0.306666666666666,0.31040056370448177]
[142.12206492827548,0.32,0.3104496858985676]
[143.00374684730002,0.333333333333333,0.33279167612336613]
[143.3611007535384,0.346666666666666,0.3420249432850152]
[143.4847841677396,0.36,0.34524314789338384]
[143.4947023961718,0.373333333333333,0.34550170627483956]
[143.90900961809257,0.386666666666666,0.3563653865705279]
[144.87460835697956,0.4,0.3821277595922674]
[145.09573767571422,0.413333333333333,0.38810653526129757]
[145.14065490231982,0.426666666666666,0.38932428191870727]
[145.5832605037666,0.44,0.40138009567234195]
[146.61378907152948,0.453333333333333,0.42979723117027185]
[146.95173773250468,0.466666666666666,0.4392037258996531]
[147.027840385341,0.48,0.44132691526909756]
[147.29832467222587,0.493333333333333,0.4488864034681712]
[148.3079406277408,0.506666666666666,0.4772453745828118]
[149.16529431828462,0.52,0.5014240661957761]
[149.16669159393285,0.533333333333333,0.5014634913935564]
[150.08450765410433,0.546666666666666,0.5273391105459204]
[150.18563320256126,0.56,0.5301850387495355]
[150.39016417575468,0.573333333333333,0.5359361952708095]
[151.88261826065911,0.586666666666666,0.5776000066347755]
[153.03719452073892,0.6,0.6092700645314066]
[153.12495532207546,0.613333333333333,0.6116507765455803]
[153.25361967136107,0.626666666666666,0.6151334971907335]
[153.5915575569228,0.64,0.6242360890394052]
[153.7417830274607,0.653333333333333,0.6282607598111333]
[154.0827961828574,0.666666666666666,0.6373443187690899]
[155.45492594993252,0.68,0.6730733948887991]
[156.30210829582796,0.693333333333333,0.6943905324395366]
[156.40075682364065,0.706666666666666,0.69683227647347]
[157.96150976627302,0.72,0.7342436691651358]
[159.164934154005,0.733333333333333,0.7613999538086639]
[159.43852815380174,0.746666666666666,0.7673548758878971]
[160.11577193963623,0.76,0.781734019175495]
[160.65762064878794,0.773333333333333,0.7928603353383339]
[160.67579396246174,0.786666666666666,0.7932275966110192]
[160.83527196697736,0.8,0.7964338904854571]
[162.8731145185201,0.813333333333333,0.8347435065596658]
[164.59881379163096,0.826666666666666,0.8632711341093076]
[164.88442650720881,0.84,0.8676465460629015]
[166.36490308411,0.853333333333333,0.8887759911989912]
[166.6964127895036,0.866666666666666,0.8931565444439777]
[166.89397243265975,0.88,{"$f":"NORMDIST(A83,$B$13,SQRT($B$11),1)","v":0.8957071483520016}]
[167.82987516086766,0.893333333333333,0.9071915720937043]
[167.9270291205626,0.906666666666666,0.9083279460376893]
[168.43963972779306,0.92,0.9141535126340153]
[168.80237149262783,0.933333333333333,0.918105254147147]
[170.80623187176792,0.946666666666666,0.9375055713314105]
[173.65868882972705,0.96,0.9587102367420759]
[174.18217000518618,0.973333333333333,0.961880298691498]
[177.68526687953567,0.986666666666666,0.9783445129613043]
[180.4734192940876,1,0.986719036475665]

{"sheet":"U3","index":4,"n_rows":88,"n_cols":2,"rows_kept":88}
["Seien n i.i.d. Zufallsvariablen Xi gegeben und die folgende Statistik Y, "]
["die auf das kartesische Produkt der Bilder dieser Zufallsvariablen definiert ist: "]
[]
[]
[null,"Y="]
[]
[]
[]
[]
["xquer0 ist der Erwartungswert der Zufallsvariablen Xi. (xquer0 = 500)"]
["n ist die Stichprobengrösse. "]
["S^2 ist die Statistik, welche Stichprobenvarianzen als Werte annimmt. "]
["Wie hoch ist die Wahrscheinlichkeit, dass die Statistik Y den Wert Y(x) oder einen grösseren Wert zufälliger weise annimmt?"]
["Wenn die Zufallsvariablen Xi normalverteilt sind, ist die Statistik Y t-verteilt mit n-1 Freiheitsgraden."]
["(Überprüfen Sie vor der Berechnung die Voraussetzung)"]
[]
["Daten (Werte der Xi)"]
[533.3603522541457]
[542.4598435624977]
[548.7222928870134]
[540.1773864112374]
[548.5672071450216]
[528.5518098436579]
[538.8423747224924]
[552.6509980516057]
[535.2606768227012]
[554.4496886517512]
[533.3212013979763]
[550.4947955806566]
[558.4751319874798]
[530.9755409433892]
[532.3939578140638]
[536.6124434811377]
[532.1411026919387]
[557.8104268526102]
[527.4853441423721]
[552.4971060060114]
[527.0918862203914]
[551.1462844114143]
[546.7600818368401]
[521.2842129110893]
[530.0401218543889]
[527.8126346195041]
[541.9069952180843]
[520.0232845418178]
[536.453623107365]
[533.0146053018681]
[530.6794637330746]
[541.5388958590515]
[548.5438064264712]
[542.368925852884]
[535.0152392358659]
[541.5733328444331]
[542.343292249937]
[546.3063399165621]
[552.4583156615038]
[540.9352072964067]
[518.6335451268292]
[530.763024197037]
[537.7565431116234]
[543.0870695208389]
[539.398912878998]
[539.1684125993098]
[525.0756042995062]
[520.0317916678088]
[547.5240763645644]
[539.8744285502338]
[536.5324867971641]
[526.4529268345457]
[544.0115507077961]
[526.7081614974084]
[558.7265331289819]
[534.561260186741]
[544.9146788333993]
[537.7989638027798]
[550.3836268795875]
[545.9766546411936]
[535.7553201921768]
[543.5666848590417]
[521.5266903341277]
[522.8309216126887]
[531.8170080314005]
[532.0277539957037]
[537.8567962924841]
[538.2438705081184]
[521.1440307181532]
[527.4544490308292]
[548.3454767846108]

{"sheet":"LU3","index":5,"n_rows":88,"n_cols":5,"rows_kept":88}
[]
[]
[]
[]
[null,"Y="]
[]
[]
[]
["Xquer(x)=",{"$f":"AVERAGE(A18:A88)","v":538.0351476666815}]
["n=",{"$f":"COUNT(A18:A88)","v":71}]
["S(x)=",{"$f":"STDEV(A18:A88)","v":10.104631670178547}]
["Y(x)=",{"$f":"(B9-500)*SQRT(71)/B11","v":31.717123527638154}]
["P(Y > 31.7171235) =",null,{"$f":"TDIST(B12,70,1)","v":1.4333121883134991E-43},"=TVERT(B12;70;1)"]
[]
[]
[]
["Daten (Werte der Xi)","i/n","F(xi)",null,"Überprüfung der Daten auf Normalverteilung"]
[518.6335451268292,0.014084507042253521,{"$f":"NORMDIST(A18,$B$9,$B$11,1)","v":0.027424513987440235},0,0]
[520.0232845418178,0.028169014084507043,{"$f":"NORMDIST(A19,$B$9,$B$11,1)","v":0.03733098615415067},1,1]
[520.0317916678088,0.0422535211267605,0.037399618313133126]
[521.1440307181532,0.0563380281690141,0.047299516605172294]
[521.2842129110893,0.0704225352112676,0.04868415238639253]
[521.5266903341277,0.0845070422535211,0.051155518005422874]
[522.8309216126887,0.0985915492957746,0.06620332534112848]
[525.0756042995062,0.112676056338028,0.09982752478136425]
[526.4529268345457,0.126760563380282,0.12585022671705218]
[526.7081614974084,0.140845070422536,0.13115037508116345]
[527.0918862203914,0.154929577464789,0.13940541187993113]
[527.4544490308292,0.169014084507043,0.14752356202762917]
[527.4853441423721,0.183098591549296,0.14822969027761773]
[527.8126346195041,0.19718309859155,0.15584887104993314]
[528.5518098436579,0.211267605633803,0.17399017464565633]
[530.0401218543889,0.225352112676057,0.21440668122007492]
[530.6794637330746,0.23943661971831,0.23332157276737975]
[530.763024197037,0.253521126760564,0.2358603465686452,null,"Die Daten sind normalverteilt"]
[530.9755409433892,0.267605633802816,0.24238521453140782]
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{"sheet":"U4","index":6,"n_rows":139,"n_cols":5,"rows_kept":139}
["Seien n i.i.d. Zufallsvariablen X1i und m i.i.d. Zufallsvariablen X2i gegeben und die folgende Statistik "]
[]
[]
["Y="]
[]
[]
[]
[]
["S^2 tief i ist die Statistik, welche Varianzen der Stichprobe i als Werte annimmt. "]
["Wie hoch ist die Wahrscheinlichkeit, dass die Statistik Y den Quotienten der Stichprobenvarianzen oder einen kleineren Wert zufälliger weise annimmt?"]
["Wenn die Zufallsvariablen Xi für jede Stichprobe isoliert betrachtet normalverteilt sind, ist die Statistik "]
["Y F-verteilt mit n-1 Zählerfreiheitsgraden und m-1 Nennerfreiheitsgraden."]
["(Überprüfen Sie vor der Berechnung die Voraussetzung)"]
[]
[]
[]
[]
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{"sheet":"LU4","index":7,"n_rows":139,"n_cols":6,"rows_kept":139}
[]
["Y="]
[]
[]
[]
[]
["S^2tief1(x1)=",{"$f":"VAR(A19:A75)","v":99.46310697007782},null,"x1 = Stichprobe 1",null,"19:75"]
["S^2tief^2(x2)=",{"$f":"VAR(A76:A139)","v":309.0085379311018},null,"x2 = Stichprobe 2",null,"76:139"]
["Xquer(x1)=",{"$f":"AVERAGE(A19:A75)","v":599.9379169943852}]
["Xquer(x2)=",{"$f":"AVERAGE(A76:A139)","v":601.0634846588425}]
["n1",{"$f":"COUNT(A19:A75)","v":57}]
["n2",{"$f":"COUNT(A76:A139)","v":64}]
[]
[{"$nulls":3},"Wahrscheinlichkeit:"]
[{"$nulls":3},{"$f":"_xlfn.F.DIST(B7/B8,56,63,1)","v":1.3961154644663896E-5},"=F.VERT(B7/B8;56;63;1)"]
[]
[{"$nulls":4},"Überprüfung der Daten pro Stichprobe auf Normalverteilung"]
["Daten (Werte der ZV Xi)","Stichprobe","i/n","F(xi)","Stichprobe 1"]
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[595.2958897614408,1,0.333333333333334,0.3208032215300901,"Die Daten der Stichprobe 1 sind normalverteilt."]
[595.3737412159082,1,0.350877192982456,0.3236027585889704]
[595.6575486758798,1,0.368421052631579,0.33389228724390163,"Stichprobe 2:"]
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[603.2330236186887,1,0.666666666666667,0.6294506760032438,"Die Daten der Stichprobe 2 sind nicht normalverteilt"]
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