[{"data":1,"prerenderedAt":3480},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ffehler-erster-und-zweiter-art":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ffehler-erster-und-zweiter-art":3470},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":556,"category":441,"checks":3409,"conditions":3425,"conditionsHtml":3426,"deprecated":3427,"description":3403,"extension":3428,"figure":3427,"figureCaption":3427,"figureHtml":3427,"formulaId":3429,"latex":3430,"latexHtml":3431,"level":3432,"meta":3433,"navigation":3434,"path":3435,"redirectFrom":3436,"related":3437,"seo":3441,"stem":3442,"subject":592,"summary":3443,"tags":3444,"variables":3449,"__hash__":3469},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Ffehler-erster-und-zweiter-art.md","Fehler 1. und 2. Art",[550,551,552,553,554,555],"Alpha-Fehler","Beta-Fehler","Fehler erster Art","Fehler zweiter Art","Irrtumswahrscheinlichkeit","Fehler 2. Art berechnen",{"type":557,"value":558,"toc":3402},"minimark",[559,564,568,926,1274,1429,1433,1840,1872,2094,2138,2317,2547,3013,3017],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567],"p",{},"Bei einem Hypothesentest kann man sich auf zwei Arten irren:",[569,570,571,763],"table",{},[572,573,574],"thead",{},[575,576,577,580,691],"tr",{},[578,579],"th",{},[578,581,582,690],{},[583,584,587,617],"span",{"className":585},[586],"katex",[583,588,591],{"className":589},[590],"katex-mathml",[592,593,595],"math",{"xmlns":594},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[596,597,598,612],"semantics",{},[599,600,601],"mrow",{},[602,603,604,608],"msub",{},[605,606,607],"mi",{},"H",[609,610,611],"mn",{},"0",[613,614,616],"annotation",{"encoding":615},"application\u002Fx-tex","H_0",[583,618,622],{"className":619,"ariaHidden":621},[620],"katex-html","true",[583,623,626,631],{"className":624},[625],"base",[583,627],{"className":628,"style":630},[629],"strut","height:0.8333em;vertical-align:-0.15em;",[583,632,635,640],{"className":633},[634],"mord",[583,636,607],{"className":637,"style":639},[634,638],"mathnormal","margin-right:0.0813em;",[583,641,644],{"className":642},[643],"msupsub",[583,645,649,681],{"className":646},[647,648],"vlist-t","vlist-t2",[583,650,653,676],{"className":651},[652],"vlist-r",[583,654,658],{"className":655,"style":657},[656],"vlist","height:0.3011em;",[583,659,661,666],{"style":660},"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;",[583,662],{"className":663,"style":665},[664],"pstrut","height:2.7em;",[583,667,673],{"className":668},[669,670,671,672],"sizing","reset-size6","size3","mtight",[583,674,611],{"className":675},[634,672],[583,677,680],{"className":678},[679],"vlist-s","​",[583,682,684],{"className":683},[652],[583,685,688],{"className":686,"style":687},[656],"height:0.15em;",[583,689],{}," ist wahr",[578,692,693,762],{},[583,694,696,713],{"className":695},[586],[583,697,699],{"className":698},[590],[592,700,701],{"xmlns":594},[596,702,703,711],{},[599,704,705],{},[602,706,707,709],{},[605,708,607],{},[609,710,611],{},[613,712,616],{"encoding":615},[583,714,716],{"className":715,"ariaHidden":621},[620],[583,717,719,722],{"className":718},[625],[583,720],{"className":721,"style":630},[629],[583,723,725,728],{"className":724},[634],[583,726,607],{"className":727,"style":639},[634,638],[583,729,731],{"className":730},[643],[583,732,734,754],{"className":733},[647,648],[583,735,737,751],{"className":736},[652],[583,738,740],{"className":739,"style":657},[656],[583,741,742,745],{"style":660},[583,743],{"className":744,"style":665},[664],[583,746,748],{"className":747},[669,670,671,672],[583,749,611],{"className":750},[634,672],[583,752,680],{"className":753},[679],[583,755,757],{"className":756},[652],[583,758,760],{"className":759,"style":687},[656],[583,761],{}," ist falsch",[764,765,766,847],"tbody",{},[575,767,768,841,844],{},[769,770,771,840],"td",{},[583,772,774,791],{"className":773},[586],[583,775,777],{"className":776},[590],[592,778,779],{"xmlns":594},[596,780,781,789],{},[599,782,783],{},[602,784,785,787],{},[605,786,607],{},[609,788,611],{},[613,790,616],{"encoding":615},[583,792,794],{"className":793,"ariaHidden":621},[620],[583,795,797,800],{"className":796},[625],[583,798],{"className":799,"style":630},[629],[583,801,803,806],{"className":802},[634],[583,804,607],{"className":805,"style":639},[634,638],[583,807,809],{"className":808},[643],[583,810,812,832],{"className":811},[647,648],[583,813,815,829],{"className":814},[652],[583,816,818],{"className":817,"style":657},[656],[583,819,820,823],{"style":660},[583,821],{"className":822,"style":665},[664],[583,824,826],{"className":825},[669,670,671,672],[583,827,611],{"className":828},[634,672],[583,830,680],{"className":831},[679],[583,833,835],{"className":834},[652],[583,836,838],{"className":837,"style":687},[656],[583,839],{}," wird verworfen",[769,842,843],{},"Fehler 1. Art",[769,845,846],{},"richtig",[575,848,849,921,923],{},[769,850,851,920],{},[583,852,854,871],{"className":853},[586],[583,855,857],{"className":856},[590],[592,858,859],{"xmlns":594},[596,860,861,869],{},[599,862,863],{},[602,864,865,867],{},[605,866,607],{},[609,868,611],{},[613,870,616],{"encoding":615},[583,872,874],{"className":873,"ariaHidden":621},[620],[583,875,877,880],{"className":876},[625],[583,878],{"className":879,"style":630},[629],[583,881,883,886],{"className":882},[634],[583,884,607],{"className":885,"style":639},[634,638],[583,887,889],{"className":888},[643],[583,890,892,912],{"className":891},[647,648],[583,893,895,909],{"className":894},[652],[583,896,898],{"className":897,"style":657},[656],[583,899,900,903],{"style":660},[583,901],{"className":902,"style":665},[664],[583,904,906],{"className":905},[669,670,671,672],[583,907,611],{"className":908},[634,672],[583,910,680],{"className":911},[679],[583,913,915],{"className":914},[652],[583,916,918],{"className":917,"style":687},[656],[583,919],{}," wird nicht verworfen",[769,922,846],{},[769,924,925],{},"Fehler 2. Art",[927,928,929,1136],"ul",{},[930,931,932,933,936,937,969,970,1042,1043,1135],"li",{},"Die Wahrscheinlichkeit für den ",[934,935,843],"strong",{}," (",[583,938,940,955],{"className":939},[586],[583,941,943],{"className":942},[590],[592,944,945],{"xmlns":594},[596,946,947,952],{},[599,948,949],{},[605,950,951],{},"α",[613,953,954],{"encoding":615},"\\alpha",[583,956,958],{"className":957,"ariaHidden":621},[620],[583,959,961,965],{"className":960},[625],[583,962],{"className":963,"style":964},[629],"height:0.4306em;",[583,966,951],{"className":967,"style":968},[634,638],"margin-right:0.0037em;","-Fehler) berechnet man mit ",[583,971,973,991],{"className":972},[586],[583,974,976],{"className":975},[590],[592,977,978],{"xmlns":594},[596,979,980,988],{},[599,981,982],{},[602,983,984,986],{},[605,985,565],{},[609,987,611],{},[613,989,990],{"encoding":615},"p_0",[583,992,994],{"className":993,"ariaHidden":621},[620],[583,995,997,1001],{"className":996},[625],[583,998],{"className":999,"style":1000},[629],"height:0.625em;vertical-align:-0.1944em;",[583,1002,1004,1007],{"className":1003},[634],[583,1005,565],{"className":1006},[634,638],[583,1008,1010],{"className":1009},[643],[583,1011,1013,1034],{"className":1012},[647,648],[583,1014,1016,1031],{"className":1015},[652],[583,1017,1019],{"className":1018,"style":657},[656],[583,1020,1022,1025],{"style":1021},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[583,1023],{"className":1024,"style":665},[664],[583,1026,1028],{"className":1027},[669,670,671,672],[583,1029,611],{"className":1030},[634,672],[583,1032,680],{"className":1033},[679],[583,1035,1037],{"className":1036},[652],[583,1038,1040],{"className":1039,"style":687},[656],[583,1041],{},". Sie ist durch das Signifikanzniveau begrenzt: ",[583,1044,1046,1072],{"className":1045},[586],[583,1047,1049],{"className":1048},[590],[592,1050,1051],{"xmlns":594},[596,1052,1053,1069],{},[599,1054,1055,1064,1067],{},[1056,1057,1058,1060],"msup",{},[605,1059,951],{},[1061,1062,1063],"mo",{},"∗",[1061,1065,1066],{},"≤",[605,1068,951],{},[613,1070,1071],{"encoding":615},"\\alpha^* \\leq \\alpha",[583,1073,1075,1126],{"className":1074,"ariaHidden":621},[620],[583,1076,1078,1082,1114,1119,1123],{"className":1077},[625],[583,1079],{"className":1080,"style":1081},[629],"height:0.8247em;vertical-align:-0.136em;",[583,1083,1085,1088],{"className":1084},[634],[583,1086,951],{"className":1087,"style":968},[634,638],[583,1089,1091],{"className":1090},[643],[583,1092,1094],{"className":1093},[647],[583,1095,1097],{"className":1096},[652],[583,1098,1101],{"className":1099,"style":1100},[656],"height:0.6887em;",[583,1102,1104,1107],{"style":1103},"top:-3.063em;margin-right:0.05em;",[583,1105],{"className":1106,"style":665},[664],[583,1108,1110],{"className":1109},[669,670,671,672],[583,1111,1063],{"className":1112},[1113,672],"mbin",[583,1115],{"className":1116,"style":1118},[1117],"mspace","margin-right:0.2778em;",[583,1120,1066],{"className":1121},[1122],"mrel",[583,1124],{"className":1125,"style":1118},[1117],[583,1127,1129,1132],{"className":1128},[625],[583,1130],{"className":1131,"style":964},[629],[583,1133,951],{"className":1134,"style":968},[634,638],".",[930,1137,932,1138,936,1140,1172,1173,1201,1202,1273],{},[934,1139,925],{},[583,1141,1143,1158],{"className":1142},[586],[583,1144,1146],{"className":1145},[590],[592,1147,1148],{"xmlns":594},[596,1149,1150,1155],{},[599,1151,1152],{},[605,1153,1154],{},"β",[613,1156,1157],{"encoding":615},"\\beta",[583,1159,1161],{"className":1160,"ariaHidden":621},[620],[583,1162,1164,1168],{"className":1163},[625],[583,1165],{"className":1166,"style":1167},[629],"height:0.8889em;vertical-align:-0.1944em;",[583,1169,1154],{"className":1170,"style":1171},[634,638],"margin-right:0.0528em;","-Fehler) hängt vom wahren Wert ",[583,1174,1176,1189],{"className":1175},[586],[583,1177,1179],{"className":1178},[590],[592,1180,1181],{"xmlns":594},[596,1182,1183,1187],{},[599,1184,1185],{},[605,1186,565],{},[613,1188,565],{"encoding":615},[583,1190,1192],{"className":1191,"ariaHidden":621},[620],[583,1193,1195,1198],{"className":1194},[625],[583,1196],{"className":1197,"style":1000},[629],[583,1199,565],{"className":1200},[634,638]," ab, den man nicht kennt. Man berechnet sie deshalb für einen angenommenen Wert ",[583,1203,1205,1224],{"className":1204},[586],[583,1206,1208],{"className":1207},[590],[592,1209,1210],{"xmlns":594},[596,1211,1212,1221],{},[599,1213,1214],{},[602,1215,1216,1218],{},[605,1217,565],{},[609,1219,1220],{},"1",[613,1222,1223],{"encoding":615},"p_1",[583,1225,1227],{"className":1226,"ariaHidden":621},[620],[583,1228,1230,1233],{"className":1229},[625],[583,1231],{"className":1232,"style":1000},[629],[583,1234,1236,1239],{"className":1235},[634],[583,1237,565],{"className":1238},[634,638],[583,1240,1242],{"className":1241},[643],[583,1243,1245,1265],{"className":1244},[647,648],[583,1246,1248,1262],{"className":1247},[652],[583,1249,1251],{"className":1250,"style":657},[656],[583,1252,1253,1256],{"style":1021},[583,1254],{"className":1255,"style":665},[664],[583,1257,1259],{"className":1258},[669,670,671,672],[583,1260,1220],{"className":1261},[634,672],[583,1263,680],{"className":1264},[679],[583,1266,1268],{"className":1267},[652],[583,1269,1271],{"className":1270,"style":687},[656],[583,1272],{}," aus der Alternative.",[565,1275,1276,1277,1336,1337,1365,1366,1420,1421,1424,1425,1428],{},"Die beiden Fehler hängen zusammen: Ein kleinerer Ablehnungsbereich senkt ",[583,1278,1280,1298],{"className":1279},[586],[583,1281,1283],{"className":1282},[590],[592,1284,1285],{"xmlns":594},[596,1286,1287,1295],{},[599,1288,1289],{},[1056,1290,1291,1293],{},[605,1292,951],{},[1061,1294,1063],{},[613,1296,1297],{"encoding":615},"\\alpha^*",[583,1299,1301],{"className":1300,"ariaHidden":621},[620],[583,1302,1304,1307],{"className":1303},[625],[583,1305],{"className":1306,"style":1100},[629],[583,1308,1310,1313],{"className":1309},[634],[583,1311,951],{"className":1312,"style":968},[634,638],[583,1314,1316],{"className":1315},[643],[583,1317,1319],{"className":1318},[647],[583,1320,1322],{"className":1321},[652],[583,1323,1325],{"className":1324,"style":1100},[656],[583,1326,1327,1330],{"style":1103},[583,1328],{"className":1329,"style":665},[664],[583,1331,1333],{"className":1332},[669,670,671,672],[583,1334,1063],{"className":1335},[1113,672],", erhöht aber ",[583,1338,1340,1353],{"className":1339},[586],[583,1341,1343],{"className":1342},[590],[592,1344,1345],{"xmlns":594},[596,1346,1347,1351],{},[599,1348,1349],{},[605,1350,1154],{},[613,1352,1157],{"encoding":615},[583,1354,1356],{"className":1355,"ariaHidden":621},[620],[583,1357,1359,1362],{"className":1358},[625],[583,1360],{"className":1361,"style":1167},[629],[583,1363,1154],{"className":1364,"style":1171},[634,638],". Beide zugleich verkleinert nur ein größerer Stichprobenumfang. Die Wahrscheinlichkeit ",[583,1367,1369,1388],{"className":1368},[586],[583,1370,1372],{"className":1371},[590],[592,1373,1374],{"xmlns":594},[596,1375,1376,1385],{},[599,1377,1378,1380,1383],{},[609,1379,1220],{},[1061,1381,1382],{},"−",[605,1384,1154],{},[613,1386,1387],{"encoding":615},"1 - \\beta",[583,1389,1391,1411],{"className":1390,"ariaHidden":621},[620],[583,1392,1394,1398,1401,1405,1408],{"className":1393},[625],[583,1395],{"className":1396,"style":1397},[629],"height:0.7278em;vertical-align:-0.0833em;",[583,1399,1220],{"className":1400},[634],[583,1402],{"className":1403,"style":1404},[1117],"margin-right:0.2222em;",[583,1406,1382],{"className":1407},[1113],[583,1409],{"className":1410,"style":1404},[1117],[583,1412,1414,1417],{"className":1413},[625],[583,1415],{"className":1416,"style":1167},[629],[583,1418,1154],{"className":1419,"style":1171},[634,638],", eine falsche Nullhypothese zu erkennen, heißt ",[934,1422,1423],{},"Güte"," oder ",[934,1426,1427],{},"Trennschärfe"," des Tests.",[560,1430,1432],{"id":1431},"beispiele","Beispiele",[565,1434,1435,1436,1482,1483,1641,1642,1697,1698,1135],{},"Ein neues Medikament soll besser wirken als das alte mit ",[583,1437,1439,1462],{"className":1438},[586],[583,1440,1442],{"className":1441},[590],[592,1443,1444],{"xmlns":594},[596,1445,1446,1459],{},[599,1447,1448,1451,1455],{},[609,1449,1450],{},"60",[1452,1453,1454],"mtext",{}," ",[605,1456,1458],{"mathvariant":1457},"normal","%",[613,1460,1461],{"encoding":615},"60\\,\\%",[583,1463,1465],{"className":1464,"ariaHidden":621},[620],[583,1466,1468,1472,1475,1479],{"className":1467},[625],[583,1469],{"className":1470,"style":1471},[629],"height:0.8056em;vertical-align:-0.0556em;",[583,1473,1450],{"className":1474},[634],[583,1476],{"className":1477,"style":1478},[1117],"margin-right:0.1667em;",[583,1480,1458],{"className":1481},[634],". Getestet wird ",[583,1484,1486,1529],{"className":1485},[586],[583,1487,1489],{"className":1488},[590],[592,1490,1491],{"xmlns":594},[596,1492,1493,1526],{},[599,1494,1495,1501,1503,1506,1510,1513,1516,1519,1521,1523],{},[602,1496,1497,1499],{},[605,1498,607],{},[609,1500,611],{},[1117,1502],{},[1117,1504],{"width":1505},"0.1111em",[1061,1507],{"lspace":1508,"rspace":1509},"0em","0.17em",[1452,1511,1512],{}," ⁣",[1061,1514,1515],{"lspace":1508,"rspace":1508},":",[1117,1517],{"width":1518},"0.3333em",[605,1520,565],{},[1061,1522,1066],{},[609,1524,1525],{},"0,6",[613,1527,1528],{"encoding":615},"H_0\\colon p \\leq 0{,}6",[583,1530,1532,1620],{"className":1531,"ariaHidden":621},[620],[583,1533,1535,1539,1579,1583,1587,1591,1595,1598,1604,1608,1611,1614,1617],{"className":1534},[625],[583,1536],{"className":1537,"style":1538},[629],"height:0.8778em;vertical-align:-0.1944em;",[583,1540,1542,1545],{"className":1541},[634],[583,1543,607],{"className":1544,"style":639},[634,638],[583,1546,1548],{"className":1547},[643],[583,1549,1551,1571],{"className":1550},[647,648],[583,1552,1554,1568],{"className":1553},[652],[583,1555,1557],{"className":1556,"style":657},[656],[583,1558,1559,1562],{"style":660},[583,1560],{"className":1561,"style":665},[664],[583,1563,1565],{"className":1564},[669,670,671,672],[583,1566,611],{"className":1567},[634,672],[583,1569,680],{"className":1570},[679],[583,1572,1574],{"className":1573},[652],[583,1575,1577],{"className":1576,"style":687},[656],[583,1578],{},[583,1580],{"className":1581},[1117,1582],"nobreak",[583,1584],{"className":1585,"style":1586},[1117],"margin-right:0.1111em;",[583,1588],{"className":1589},[1590],"mpunct",[583,1592],{"className":1593,"style":1594},[1117],"margin-right:-0.1667em;",[583,1596],{"className":1597,"style":1478},[1117],[583,1599,1601],{"className":1600},[634],[583,1602,1515],{"className":1603},[1122],[583,1605],{"className":1606,"style":1607},[1117],"margin-right:0.3333em;",[583,1609,565],{"className":1610},[634,638],[583,1612],{"className":1613,"style":1118},[1117],[583,1615,1066],{"className":1616},[1122],[583,1618],{"className":1619,"style":1118},[1117],[583,1621,1623,1627,1630,1637],{"className":1622},[625],[583,1624],{"className":1625,"style":1626},[629],"height:0.8389em;vertical-align:-0.1944em;",[583,1628,611],{"className":1629},[634],[583,1631,1633],{"className":1632},[634],[583,1634,1636],{"className":1635},[1590],",",[583,1638,1640],{"className":1639},[634],"6"," an ",[583,1643,1645,1666],{"className":1644},[586],[583,1646,1648],{"className":1647},[590],[592,1649,1650],{"xmlns":594},[596,1651,1652,1663],{},[599,1653,1654,1657,1660],{},[605,1655,1656],{},"n",[1061,1658,1659],{},"=",[609,1661,1662],{},"50",[613,1664,1665],{"encoding":615},"n = 50",[583,1667,1669,1687],{"className":1668,"ariaHidden":621},[620],[583,1670,1672,1675,1678,1681,1684],{"className":1671},[625],[583,1673],{"className":1674,"style":964},[629],[583,1676,1656],{"className":1677},[634,638],[583,1679],{"className":1680,"style":1118},[1117],[583,1682,1659],{"className":1683},[1122],[583,1685],{"className":1686,"style":1118},[1117],[583,1688,1690,1694],{"className":1689},[625],[583,1691],{"className":1692,"style":1693},[629],"height:0.6444em;",[583,1695,1662],{"className":1696},[634]," Personen, Ablehnungsbereich ",[583,1699,1701,1744],{"className":1700},[586],[583,1702,1704],{"className":1703},[590],[592,1705,1706],{"xmlns":594},[596,1707,1708,1741],{},[599,1709,1710,1719,1721,1725,1728,1731,1734,1736,1738],{},[1711,1712,1713,1716],"mover",{"accent":621},[605,1714,1715],{},"A",[1061,1717,1718],{"stretchy":621},"‾",[1061,1720,1659],{},[1061,1722,1724],{"stretchy":1723},"false","{",[609,1726,1727],{},"37",[1061,1729,1730],{"separator":621},";",[1061,1732,1733],{},"…",[1061,1735,1730],{"separator":621},[609,1737,1662],{},[1061,1739,1740],{"stretchy":1723},"}",[613,1742,1743],{"encoding":615},"\\overline{A} = \\{37; \\ldots; 50\\}",[583,1745,1747,1800],{"className":1746,"ariaHidden":621},[620],[583,1748,1750,1754,1791,1794,1797],{"className":1749},[625],[583,1751],{"className":1752,"style":1753},[629],"height:0.8833em;",[583,1755,1758],{"className":1756},[634,1757],"overline",[583,1759,1761],{"className":1760},[647],[583,1762,1764],{"className":1763},[652],[583,1765,1767,1780],{"className":1766,"style":1753},[656],[583,1768,1770,1774],{"style":1769},"top:-3em;",[583,1771],{"className":1772,"style":1773},[664],"height:3em;",[583,1775,1777],{"className":1776},[634],[583,1778,1715],{"className":1779},[634,638],[583,1781,1783,1786],{"style":1782},"top:-3.8033em;",[583,1784],{"className":1785,"style":1773},[664],[583,1787],{"className":1788,"style":1790},[1789],"overline-line","border-bottom-width:0.04em;",[583,1792],{"className":1793,"style":1118},[1117],[583,1795,1659],{"className":1796},[1122],[583,1798],{"className":1799,"style":1118},[1117],[583,1801,1803,1807,1811,1814,1817,1820,1824,1827,1830,1833,1836],{"className":1802},[625],[583,1804],{"className":1805,"style":1806},[629],"height:1em;vertical-align:-0.25em;",[583,1808,1724],{"className":1809},[1810],"mopen",[583,1812,1727],{"className":1813},[634],[583,1815,1730],{"className":1816},[1590],[583,1818],{"className":1819,"style":1478},[1117],[583,1821,1733],{"className":1822},[1823],"minner",[583,1825],{"className":1826,"style":1478},[1117],[583,1828,1730],{"className":1829},[1590],[583,1831],{"className":1832,"style":1478},[1117],[583,1834,1662],{"className":1835},[634],[583,1837,1740],{"className":1838},[1839],"mclose",[565,1841,1842,1843,1871],{},"Fehler 1. Art: Das Mittel ist nicht besser, trotzdem wirkt es zufällig bei mindestens ",[583,1844,1846,1859],{"className":1845},[586],[583,1847,1849],{"className":1848},[590],[592,1850,1851],{"xmlns":594},[596,1852,1853,1857],{},[599,1854,1855],{},[609,1856,1727],{},[613,1858,1727],{"encoding":615},[583,1860,1862],{"className":1861,"ariaHidden":621},[620],[583,1863,1865,1868],{"className":1864},[625],[583,1866],{"className":1867,"style":1693},[629],[583,1869,1727],{"className":1870},[634]," Personen.",[583,1873,1876],{"className":1874},[1875],"katex-display",[583,1877,1879,1927],{"className":1878},[586],[583,1880,1882],{"className":1881},[590],[592,1883,1885],{"xmlns":594,"display":1884},"block",[596,1886,1887,1924],{},[599,1888,1889,1895,1897,1904,1907,1910,1913,1915,1918,1921],{},[1056,1890,1891,1893],{},[605,1892,951],{},[1061,1894,1063],{},[1061,1896,1659],{},[602,1898,1899,1902],{},[605,1900,1901],{},"P",[609,1903,1525],{},[1061,1905,1906],{"stretchy":1723},"(",[605,1908,1909],{},"X",[1061,1911,1912],{},"≥",[609,1914,1727],{},[1061,1916,1917],{"stretchy":1723},")",[1061,1919,1920],{},"≈",[609,1922,1923],{},"0,0280",[613,1925,1926],{"encoding":615},"\\alpha^* = P_{0{,}6}(X \\geq 37) \\approx 0{,}0280",[583,1928,1930,1976,2054,2075],{"className":1929,"ariaHidden":621},[620],[583,1931,1933,1937,1967,1970,1973],{"className":1932},[625],[583,1934],{"className":1935,"style":1936},[629],"height:0.7387em;",[583,1938,1940,1943],{"className":1939},[634],[583,1941,951],{"className":1942,"style":968},[634,638],[583,1944,1946],{"className":1945},[643],[583,1947,1949],{"className":1948},[647],[583,1950,1952],{"className":1951},[652],[583,1953,1955],{"className":1954,"style":1936},[656],[583,1956,1958,1961],{"style":1957},"top:-3.113em;margin-right:0.05em;",[583,1959],{"className":1960,"style":665},[664],[583,1962,1964],{"className":1963},[669,670,671,672],[583,1965,1063],{"className":1966},[1113,672],[583,1968],{"className":1969,"style":1118},[1117],[583,1971,1659],{"className":1972},[1122],[583,1974],{"className":1975,"style":1118},[1117],[583,1977,1979,1983,2038,2041,2045,2048,2051],{"className":1978},[625],[583,1980],{"className":1981,"style":1982},[629],"height:1.0361em;vertical-align:-0.2861em;",[583,1984,1986,1990],{"className":1985},[634],[583,1987,1901],{"className":1988,"style":1989},[634,638],"margin-right:0.1389em;",[583,1991,1993],{"className":1992},[643],[583,1994,1996,2029],{"className":1995},[647,648],[583,1997,1999,2026],{"className":1998},[652],[583,2000,2002],{"className":2001,"style":657},[656],[583,2003,2005,2008],{"style":2004},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[583,2006],{"className":2007,"style":665},[664],[583,2009,2011],{"className":2010},[669,670,671,672],[583,2012,2014,2017,2023],{"className":2013},[634,672],[583,2015,611],{"className":2016},[634,672],[583,2018,2020],{"className":2019},[634,672],[583,2021,1636],{"className":2022},[1590,672],[583,2024,1640],{"className":2025},[634,672],[583,2027,680],{"className":2028},[679],[583,2030,2032],{"className":2031},[652],[583,2033,2036],{"className":2034,"style":2035},[656],"height:0.2861em;",[583,2037],{},[583,2039,1906],{"className":2040},[1810],[583,2042,1909],{"className":2043,"style":2044},[634,638],"margin-right:0.0785em;",[583,2046],{"className":2047,"style":1118},[1117],[583,2049,1912],{"className":2050},[1122],[583,2052],{"className":2053,"style":1118},[1117],[583,2055,2057,2060,2063,2066,2069,2072],{"className":2056},[625],[583,2058],{"className":2059,"style":1806},[629],[583,2061,1727],{"className":2062},[634],[583,2064,1917],{"className":2065},[1839],[583,2067],{"className":2068,"style":1118},[1117],[583,2070,1920],{"className":2071},[1122],[583,2073],{"className":2074,"style":1118},[1117],[583,2076,2078,2081,2084,2090],{"className":2077},[625],[583,2079],{"className":2080,"style":1626},[629],[583,2082,611],{"className":2083},[634],[583,2085,2087],{"className":2086},[634],[583,2088,1636],{"className":2089},[1590],[583,2091,2093],{"className":2092},[634],"0280",[565,2095,2096,2097,2137],{},"Fehler 2. Art: Das Mittel wirkt in Wahrheit bei ",[583,2098,2100,2119],{"className":2099},[586],[583,2101,2103],{"className":2102},[590],[592,2104,2105],{"xmlns":594},[596,2106,2107,2116],{},[599,2108,2109,2112,2114],{},[609,2110,2111],{},"75",[1452,2113,1454],{},[605,2115,1458],{"mathvariant":1457},[613,2117,2118],{"encoding":615},"75\\,\\%",[583,2120,2122],{"className":2121,"ariaHidden":621},[620],[583,2123,2125,2128,2131,2134],{"className":2124},[625],[583,2126],{"className":2127,"style":1471},[629],[583,2129,2111],{"className":2130},[634],[583,2132],{"className":2133,"style":1478},[1117],[583,2135,1458],{"className":2136},[634],", der Test erkennt das aber nicht.",[583,2139,2141],{"className":2140},[1875],[583,2142,2144,2183],{"className":2143},[586],[583,2145,2147],{"className":2146},[590],[592,2148,2149],{"xmlns":594,"display":1884},[596,2150,2151,2180],{},[599,2152,2153,2155,2157,2164,2166,2168,2170,2173,2175,2177],{},[605,2154,1154],{},[1061,2156,1659],{},[602,2158,2159,2161],{},[605,2160,1901],{},[609,2162,2163],{},"0,75",[1061,2165,1906],{"stretchy":1723},[605,2167,1909],{},[1061,2169,1066],{},[609,2171,2172],{},"36",[1061,2174,1917],{"stretchy":1723},[1061,2176,1920],{},[609,2178,2179],{},"0,3630",[613,2181,2182],{"encoding":615},"\\beta = P_{0{,}75}(X \\leq 36) \\approx 0{,}3630",[583,2184,2186,2204,2277,2298],{"className":2185,"ariaHidden":621},[620],[583,2187,2189,2192,2195,2198,2201],{"className":2188},[625],[583,2190],{"className":2191,"style":1167},[629],[583,2193,1154],{"className":2194,"style":1171},[634,638],[583,2196],{"className":2197,"style":1118},[1117],[583,2199,1659],{"className":2200},[1122],[583,2202],{"className":2203,"style":1118},[1117],[583,2205,2207,2210,2262,2265,2268,2271,2274],{"className":2206},[625],[583,2208],{"className":2209,"style":1982},[629],[583,2211,2213,2216],{"className":2212},[634],[583,2214,1901],{"className":2215,"style":1989},[634,638],[583,2217,2219],{"className":2218},[643],[583,2220,2222,2254],{"className":2221},[647,648],[583,2223,2225,2251],{"className":2224},[652],[583,2226,2228],{"className":2227,"style":657},[656],[583,2229,2230,2233],{"style":2004},[583,2231],{"className":2232,"style":665},[664],[583,2234,2236],{"className":2235},[669,670,671,672],[583,2237,2239,2242,2248],{"className":2238},[634,672],[583,2240,611],{"className":2241},[634,672],[583,2243,2245],{"className":2244},[634,672],[583,2246,1636],{"className":2247},[1590,672],[583,2249,2111],{"className":2250},[634,672],[583,2252,680],{"className":2253},[679],[583,2255,2257],{"className":2256},[652],[583,2258,2260],{"className":2259,"style":2035},[656],[583,2261],{},[583,2263,1906],{"className":2264},[1810],[583,2266,1909],{"className":2267,"style":2044},[634,638],[583,2269],{"className":2270,"style":1118},[1117],[583,2272,1066],{"className":2273},[1122],[583,2275],{"className":2276,"style":1118},[1117],[583,2278,2280,2283,2286,2289,2292,2295],{"className":2279},[625],[583,2281],{"className":2282,"style":1806},[629],[583,2284,2172],{"className":2285},[634],[583,2287,1917],{"className":2288},[1839],[583,2290],{"className":2291,"style":1118},[1117],[583,2293,1920],{"className":2294},[1122],[583,2296],{"className":2297,"style":1118},[1117],[583,2299,2301,2304,2307,2313],{"className":2300},[625],[583,2302],{"className":2303,"style":1626},[629],[583,2305,611],{"className":2306},[634],[583,2308,2310],{"className":2309},[634],[583,2311,1636],{"className":2312},[1590],[583,2314,2316],{"className":2315},[634],"3630",[565,2318,2319,2320,2421,2422,2506,2507,2546],{},"Die Güte für ",[583,2321,2323,2345],{"className":2322},[586],[583,2324,2326],{"className":2325},[590],[592,2327,2328],{"xmlns":594},[596,2329,2330,2342],{},[599,2331,2332,2338,2340],{},[602,2333,2334,2336],{},[605,2335,565],{},[609,2337,1220],{},[1061,2339,1659],{},[609,2341,2163],{},[613,2343,2344],{"encoding":615},"p_1 = 0{,}75",[583,2346,2348,2403],{"className":2347,"ariaHidden":621},[620],[583,2349,2351,2354,2394,2397,2400],{"className":2350},[625],[583,2352],{"className":2353,"style":1000},[629],[583,2355,2357,2360],{"className":2356},[634],[583,2358,565],{"className":2359},[634,638],[583,2361,2363],{"className":2362},[643],[583,2364,2366,2386],{"className":2365},[647,648],[583,2367,2369,2383],{"className":2368},[652],[583,2370,2372],{"className":2371,"style":657},[656],[583,2373,2374,2377],{"style":1021},[583,2375],{"className":2376,"style":665},[664],[583,2378,2380],{"className":2379},[669,670,671,672],[583,2381,1220],{"className":2382},[634,672],[583,2384,680],{"className":2385},[679],[583,2387,2389],{"className":2388},[652],[583,2390,2392],{"className":2391,"style":687},[656],[583,2393],{},[583,2395],{"className":2396,"style":1118},[1117],[583,2398,1659],{"className":2399},[1122],[583,2401],{"className":2402,"style":1118},[1117],[583,2404,2406,2409,2412,2418],{"className":2405},[625],[583,2407],{"className":2408,"style":1626},[629],[583,2410,611],{"className":2411},[634],[583,2413,2415],{"className":2414},[634],[583,2416,1636],{"className":2417},[1590],[583,2419,2111],{"className":2420},[634]," beträgt also nur ",[583,2423,2425,2448],{"className":2424},[586],[583,2426,2428],{"className":2427},[590],[592,2429,2430],{"xmlns":594},[596,2431,2432,2445],{},[599,2433,2434,2436,2438,2440,2442],{},[609,2435,1220],{},[1061,2437,1382],{},[605,2439,1154],{},[1061,2441,1920],{},[609,2443,2444],{},"0,637",[613,2446,2447],{"encoding":615},"1 - \\beta \\approx 0{,}637",[583,2449,2451,2469,2487],{"className":2450,"ariaHidden":621},[620],[583,2452,2454,2457,2460,2463,2466],{"className":2453},[625],[583,2455],{"className":2456,"style":1397},[629],[583,2458,1220],{"className":2459},[634],[583,2461],{"className":2462,"style":1404},[1117],[583,2464,1382],{"className":2465},[1113],[583,2467],{"className":2468,"style":1404},[1117],[583,2470,2472,2475,2478,2481,2484],{"className":2471},[625],[583,2473],{"className":2474,"style":1167},[629],[583,2476,1154],{"className":2477,"style":1171},[634,638],[583,2479],{"className":2480,"style":1118},[1117],[583,2482,1920],{"className":2483},[1122],[583,2485],{"className":2486,"style":1118},[1117],[583,2488,2490,2493,2496,2502],{"className":2489},[625],[583,2491],{"className":2492,"style":1626},[629],[583,2494,611],{"className":2495},[634],[583,2497,2499],{"className":2498},[634],[583,2500,1636],{"className":2501},[1590],[583,2503,2505],{"className":2504},[634],"637",". Ein deutlich wirksameres Medikament bleibt mit etwa ",[583,2508,2510,2528],{"className":2509},[586],[583,2511,2513],{"className":2512},[590],[592,2514,2515],{"xmlns":594},[596,2516,2517,2525],{},[599,2518,2519,2521,2523],{},[609,2520,2172],{},[1452,2522,1454],{},[605,2524,1458],{"mathvariant":1457},[613,2526,2527],{"encoding":615},"36\\,\\%",[583,2529,2531],{"className":2530,"ariaHidden":621},[620],[583,2532,2534,2537,2540,2543],{"className":2533},[625],[583,2535],{"className":2536,"style":1471},[629],[583,2538,2172],{"className":2539},[634],[583,2541],{"className":2542,"style":1478},[1117],[583,2544,1458],{"className":2545},[634]," Wahrscheinlichkeit unentdeckt.",[565,2548,2549,2550,2578,2579,2607,2608,2761,2762,2607,2820,2972,2973,1135],{},"Würde man schon ab ",[583,2551,2553,2566],{"className":2552},[586],[583,2554,2556],{"className":2555},[590],[592,2557,2558],{"xmlns":594},[596,2559,2560,2564],{},[599,2561,2562],{},[609,2563,2172],{},[613,2565,2172],{"encoding":615},[583,2567,2569],{"className":2568,"ariaHidden":621},[620],[583,2570,2572,2575],{"className":2571},[625],[583,2573],{"className":2574,"style":1693},[629],[583,2576,2172],{"className":2577},[634]," Erfolgen verwerfen, sänke ",[583,2580,2582,2595],{"className":2581},[586],[583,2583,2585],{"className":2584},[590],[592,2586,2587],{"xmlns":594},[596,2588,2589,2593],{},[599,2590,2591],{},[605,2592,1154],{},[613,2594,1157],{"encoding":615},[583,2596,2598],{"className":2597,"ariaHidden":621},[620],[583,2599,2601,2604],{"className":2600},[625],[583,2602],{"className":2603,"style":1167},[629],[583,2605,1154],{"className":2606,"style":1171},[634,638]," auf ",[583,2609,2611,2645],{"className":2610},[586],[583,2612,2614],{"className":2613},[590],[592,2615,2616],{"xmlns":594},[596,2617,2618,2642],{},[599,2619,2620,2626,2628,2630,2632,2635,2637,2639],{},[602,2621,2622,2624],{},[605,2623,1901],{},[609,2625,2163],{},[1061,2627,1906],{"stretchy":1723},[605,2629,1909],{},[1061,2631,1066],{},[609,2633,2634],{},"35",[1061,2636,1917],{"stretchy":1723},[1061,2638,1920],{},[609,2640,2641],{},"0,2519",[613,2643,2644],{"encoding":615},"P_{0{,}75}(X \\leq 35) \\approx 0{,}2519",[583,2646,2648,2721,2742],{"className":2647,"ariaHidden":621},[620],[583,2649,2651,2654,2706,2709,2712,2715,2718],{"className":2650},[625],[583,2652],{"className":2653,"style":1982},[629],[583,2655,2657,2660],{"className":2656},[634],[583,2658,1901],{"className":2659,"style":1989},[634,638],[583,2661,2663],{"className":2662},[643],[583,2664,2666,2698],{"className":2665},[647,648],[583,2667,2669,2695],{"className":2668},[652],[583,2670,2672],{"className":2671,"style":657},[656],[583,2673,2674,2677],{"style":2004},[583,2675],{"className":2676,"style":665},[664],[583,2678,2680],{"className":2679},[669,670,671,672],[583,2681,2683,2686,2692],{"className":2682},[634,672],[583,2684,611],{"className":2685},[634,672],[583,2687,2689],{"className":2688},[634,672],[583,2690,1636],{"className":2691},[1590,672],[583,2693,2111],{"className":2694},[634,672],[583,2696,680],{"className":2697},[679],[583,2699,2701],{"className":2700},[652],[583,2702,2704],{"className":2703,"style":2035},[656],[583,2705],{},[583,2707,1906],{"className":2708},[1810],[583,2710,1909],{"className":2711,"style":2044},[634,638],[583,2713],{"className":2714,"style":1118},[1117],[583,2716,1066],{"className":2717},[1122],[583,2719],{"className":2720,"style":1118},[1117],[583,2722,2724,2727,2730,2733,2736,2739],{"className":2723},[625],[583,2725],{"className":2726,"style":1806},[629],[583,2728,2634],{"className":2729},[634],[583,2731,1917],{"className":2732},[1839],[583,2734],{"className":2735,"style":1118},[1117],[583,2737,1920],{"className":2738},[1122],[583,2740],{"className":2741,"style":1118},[1117],[583,2743,2745,2748,2751,2757],{"className":2744},[625],[583,2746],{"className":2747,"style":1626},[629],[583,2749,611],{"className":2750},[634],[583,2752,2754],{"className":2753},[634],[583,2755,1636],{"className":2756},[1590],[583,2758,2760],{"className":2759},[634],"2519",". Dafür stiege ",[583,2763,2765,2782],{"className":2764},[586],[583,2766,2768],{"className":2767},[590],[592,2769,2770],{"xmlns":594},[596,2771,2772,2780],{},[599,2773,2774],{},[1056,2775,2776,2778],{},[605,2777,951],{},[1061,2779,1063],{},[613,2781,1297],{"encoding":615},[583,2783,2785],{"className":2784,"ariaHidden":621},[620],[583,2786,2788,2791],{"className":2787},[625],[583,2789],{"className":2790,"style":1100},[629],[583,2792,2794,2797],{"className":2793},[634],[583,2795,951],{"className":2796,"style":968},[634,638],[583,2798,2800],{"className":2799},[643],[583,2801,2803],{"className":2802},[647],[583,2804,2806],{"className":2805},[652],[583,2807,2809],{"className":2808,"style":1100},[656],[583,2810,2811,2814],{"style":1103},[583,2812],{"className":2813,"style":665},[664],[583,2815,2817],{"className":2816},[669,670,671,672],[583,2818,1063],{"className":2819},[1113,672],[583,2821,2823,2856],{"className":2822},[586],[583,2824,2826],{"className":2825},[590],[592,2827,2828],{"xmlns":594},[596,2829,2830,2853],{},[599,2831,2832,2838,2840,2842,2844,2846,2848,2850],{},[602,2833,2834,2836],{},[605,2835,1901],{},[609,2837,1525],{},[1061,2839,1906],{"stretchy":1723},[605,2841,1909],{},[1061,2843,1912],{},[609,2845,2172],{},[1061,2847,1917],{"stretchy":1723},[1061,2849,1920],{},[609,2851,2852],{},"0,0540",[613,2854,2855],{"encoding":615},"P_{0{,}6}(X \\geq 36) \\approx 0{,}0540",[583,2857,2859,2932,2953],{"className":2858,"ariaHidden":621},[620],[583,2860,2862,2865,2917,2920,2923,2926,2929],{"className":2861},[625],[583,2863],{"className":2864,"style":1982},[629],[583,2866,2868,2871],{"className":2867},[634],[583,2869,1901],{"className":2870,"style":1989},[634,638],[583,2872,2874],{"className":2873},[643],[583,2875,2877,2909],{"className":2876},[647,648],[583,2878,2880,2906],{"className":2879},[652],[583,2881,2883],{"className":2882,"style":657},[656],[583,2884,2885,2888],{"style":2004},[583,2886],{"className":2887,"style":665},[664],[583,2889,2891],{"className":2890},[669,670,671,672],[583,2892,2894,2897,2903],{"className":2893},[634,672],[583,2895,611],{"className":2896},[634,672],[583,2898,2900],{"className":2899},[634,672],[583,2901,1636],{"className":2902},[1590,672],[583,2904,1640],{"className":2905},[634,672],[583,2907,680],{"className":2908},[679],[583,2910,2912],{"className":2911},[652],[583,2913,2915],{"className":2914,"style":2035},[656],[583,2916],{},[583,2918,1906],{"className":2919},[1810],[583,2921,1909],{"className":2922,"style":2044},[634,638],[583,2924],{"className":2925,"style":1118},[1117],[583,2927,1912],{"className":2928},[1122],[583,2930],{"className":2931,"style":1118},[1117],[583,2933,2935,2938,2941,2944,2947,2950],{"className":2934},[625],[583,2936],{"className":2937,"style":1806},[629],[583,2939,2172],{"className":2940},[634],[583,2942,1917],{"className":2943},[1839],[583,2945],{"className":2946,"style":1118},[1117],[583,2948,1920],{"className":2949},[1122],[583,2951],{"className":2952,"style":1118},[1117],[583,2954,2956,2959,2962,2968],{"className":2955},[625],[583,2957],{"className":2958,"style":1626},[629],[583,2960,611],{"className":2961},[634],[583,2963,2965],{"className":2964},[634],[583,2966,1636],{"className":2967},[1590],[583,2969,2971],{"className":2970},[634],"0540"," und läge über ",[583,2974,2976,2995],{"className":2975},[586],[583,2977,2979],{"className":2978},[590],[592,2980,2981],{"xmlns":594},[596,2982,2983,2992],{},[599,2984,2985,2988,2990],{},[609,2986,2987],{},"5",[1452,2989,1454],{},[605,2991,1458],{"mathvariant":1457},[613,2993,2994],{"encoding":615},"5\\,\\%",[583,2996,2998],{"className":2997,"ariaHidden":621},[620],[583,2999,3001,3004,3007,3010],{"className":3000},[625],[583,3002],{"className":3003,"style":1471},[629],[583,3005,2987],{"className":3006},[634],[583,3008],{"className":3009,"style":1478},[1117],[583,3011,1458],{"className":3012},[634],[560,3014,3016],{"id":3015},"typische-fehler","Typische Fehler",[927,3018,3019,3189,3326],{},[930,3020,3021,3049,3050,3119,3120,1273],{},[583,3022,3024,3037],{"className":3023},[586],[583,3025,3027],{"className":3026},[590],[592,3028,3029],{"xmlns":594},[596,3030,3031,3035],{},[599,3032,3033],{},[605,3034,1154],{},[613,3036,1157],{"encoding":615},[583,3038,3040],{"className":3039,"ariaHidden":621},[620],[583,3041,3043,3046],{"className":3042},[625],[583,3044],{"className":3045,"style":1167},[629],[583,3047,1154],{"className":3048,"style":1171},[634,638]," mit ",[583,3051,3053,3070],{"className":3052},[586],[583,3054,3056],{"className":3055},[590],[592,3057,3058],{"xmlns":594},[596,3059,3060,3068],{},[599,3061,3062],{},[602,3063,3064,3066],{},[605,3065,565],{},[609,3067,611],{},[613,3069,990],{"encoding":615},[583,3071,3073],{"className":3072,"ariaHidden":621},[620],[583,3074,3076,3079],{"className":3075},[625],[583,3077],{"className":3078,"style":1000},[629],[583,3080,3082,3085],{"className":3081},[634],[583,3083,565],{"className":3084},[634,638],[583,3086,3088],{"className":3087},[643],[583,3089,3091,3111],{"className":3090},[647,648],[583,3092,3094,3108],{"className":3093},[652],[583,3095,3097],{"className":3096,"style":657},[656],[583,3098,3099,3102],{"style":1021},[583,3100],{"className":3101,"style":665},[664],[583,3103,3105],{"className":3104},[669,670,671,672],[583,3106,611],{"className":3107},[634,672],[583,3109,680],{"className":3110},[679],[583,3112,3114],{"className":3113},[652],[583,3115,3117],{"className":3116,"style":687},[656],[583,3118],{}," berechnen. Für den Fehler 2. Art braucht man einen Wert ",[583,3121,3123,3140],{"className":3122},[586],[583,3124,3126],{"className":3125},[590],[592,3127,3128],{"xmlns":594},[596,3129,3130,3138],{},[599,3131,3132],{},[602,3133,3134,3136],{},[605,3135,565],{},[609,3137,1220],{},[613,3139,1223],{"encoding":615},[583,3141,3143],{"className":3142,"ariaHidden":621},[620],[583,3144,3146,3149],{"className":3145},[625],[583,3147],{"className":3148,"style":1000},[629],[583,3150,3152,3155],{"className":3151},[634],[583,3153,565],{"className":3154},[634,638],[583,3156,3158],{"className":3157},[643],[583,3159,3161,3181],{"className":3160},[647,648],[583,3162,3164,3178],{"className":3163},[652],[583,3165,3167],{"className":3166,"style":657},[656],[583,3168,3169,3172],{"style":1021},[583,3170],{"className":3171,"style":665},[664],[583,3173,3175],{"className":3174},[669,670,671,672],[583,3176,1220],{"className":3177},[634,672],[583,3179,680],{"className":3180},[679],[583,3182,3184],{"className":3183},[652],[583,3185,3187],{"className":3186,"style":687},[656],[583,3188],{},[930,3190,3191,3296,3297,3325],{},[583,3192,3194,3221],{"className":3193},[586],[583,3195,3197],{"className":3196},[590],[592,3198,3199],{"xmlns":594},[596,3200,3201,3218],{},[599,3202,3203,3209,3212,3214,3216],{},[1056,3204,3205,3207],{},[605,3206,951],{},[1061,3208,1063],{},[1061,3210,3211],{},"+",[605,3213,1154],{},[1061,3215,1659],{},[609,3217,1220],{},[613,3219,3220],{"encoding":615},"\\alpha^* + \\beta = 1",[583,3222,3224,3269,3287],{"className":3223,"ariaHidden":621},[620],[583,3225,3227,3231,3260,3263,3266],{"className":3226},[625],[583,3228],{"className":3229,"style":3230},[629],"height:0.772em;vertical-align:-0.0833em;",[583,3232,3234,3237],{"className":3233},[634],[583,3235,951],{"className":3236,"style":968},[634,638],[583,3238,3240],{"className":3239},[643],[583,3241,3243],{"className":3242},[647],[583,3244,3246],{"className":3245},[652],[583,3247,3249],{"className":3248,"style":1100},[656],[583,3250,3251,3254],{"style":1103},[583,3252],{"className":3253,"style":665},[664],[583,3255,3257],{"className":3256},[669,670,671,672],[583,3258,1063],{"className":3259},[1113,672],[583,3261],{"className":3262,"style":1404},[1117],[583,3264,3211],{"className":3265},[1113],[583,3267],{"className":3268,"style":1404},[1117],[583,3270,3272,3275,3278,3281,3284],{"className":3271},[625],[583,3273],{"className":3274,"style":1167},[629],[583,3276,1154],{"className":3277,"style":1171},[634,638],[583,3279],{"className":3280,"style":1118},[1117],[583,3282,1659],{"className":3283},[1122],[583,3285],{"className":3286,"style":1118},[1117],[583,3288,3290,3293],{"className":3289},[625],[583,3291],{"className":3292,"style":1693},[629],[583,3294,1220],{"className":3295},[634]," annehmen. Die beiden Wahrscheinlichkeiten gehören zu verschiedenen Werten von ",[583,3298,3300,3313],{"className":3299},[586],[583,3301,3303],{"className":3302},[590],[592,3304,3305],{"xmlns":594},[596,3306,3307,3311],{},[599,3308,3309],{},[605,3310,565],{},[613,3312,565],{"encoding":615},[583,3314,3316],{"className":3315,"ariaHidden":621},[620],[583,3317,3319,3322],{"className":3318},[625],[583,3320],{"className":3321,"style":1000},[629],[583,3323,565],{"className":3324},[634,638]," und ergänzen sich nicht.",[930,3327,3328,3329,3398,3399,1135],{},"Die Fehlerarten im Sachzusammenhang vertauschen. Fehler 1. Art bedeutet immer: ",[583,3330,3332,3349],{"className":3331},[586],[583,3333,3335],{"className":3334},[590],[592,3336,3337],{"xmlns":594},[596,3338,3339,3347],{},[599,3340,3341],{},[602,3342,3343,3345],{},[605,3344,607],{},[609,3346,611],{},[613,3348,616],{"encoding":615},[583,3350,3352],{"className":3351,"ariaHidden":621},[620],[583,3353,3355,3358],{"className":3354},[625],[583,3356],{"className":3357,"style":630},[629],[583,3359,3361,3364],{"className":3360},[634],[583,3362,607],{"className":3363,"style":639},[634,638],[583,3365,3367],{"className":3366},[643],[583,3368,3370,3390],{"className":3369},[647,648],[583,3371,3373,3387],{"className":3372},[652],[583,3374,3376],{"className":3375,"style":657},[656],[583,3377,3378,3381],{"style":660},[583,3379],{"className":3380,"style":665},[664],[583,3382,3384],{"className":3383},[669,670,671,672],[583,3385,611],{"className":3386},[634,672],[583,3388,680],{"className":3389},[679],[583,3391,3393],{"className":3392},[652],[583,3394,3396],{"className":3395,"style":687},[656],[583,3397],{}," wird ",[934,3400,3401],{},"zu Unrecht verworfen",{"title":3403,"searchDepth":3404,"depth":3404,"links":3405},"",2,[3406,3407,3408],{"id":562,"depth":3404,"text":563},{"id":1431,"depth":3404,"text":1432},{"id":3015,"depth":3404,"text":3016},[3410,3413,3416,3419,3422],{"lhs":3411,"rhs":3412},"round(sum(map(37:50, f(k) = combinations(50, k) * 0.6^k * 0.4^(50 - k))), 4)","0.028",{"lhs":3414,"rhs":3415},"round(sum(map(0:36, f(k) = combinations(50, k) * 0.75^k * 0.25^(50 - k))), 4)","0.363",{"lhs":3417,"rhs":3418},"round(1 - sum(map(0:36, f(k) = combinations(50, k) * 0.75^k * 0.25^(50 - k))), 3)","0.637",{"lhs":3420,"rhs":3421},"round(sum(map(0:35, f(k) = combinations(50, k) * 0.75^k * 0.25^(50 - k))), 4)","0.2519",{"lhs":3423,"rhs":3424},"round(sum(map(36:50, f(k) = combinations(50, k) * 0.6^k * 0.4^(50 - k))), 4)","0.054","X \\text{ binomialverteilt},\\ p_0 \\text{ laut } H_0,\\ p_1 \\text{ ein Wert aus } H_1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">binomialverteilt\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">laut\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>H\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">H_0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0813em;\">H\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">ein Wert aus\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>H\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">H_1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0813em;\">H\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","type-errors","\\alpha^* = P_{p_0}(X \\in \\overline{A}), \\qquad \\beta = P_{p_1}(X \\in A)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>∗\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>P\u003C\u002Fmi>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>β\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>P\u003C\u002Fmi>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\alpha^* = P_{p_0}(X \\in \\overline{A}), \\qquad \\beta = P_{p_1}(X \\in A)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7387em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7387em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∗\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0361em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3173em;\">\u003Cspan style=\"top:-2.357em;margin-left:0em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.143em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1333em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0528em;\">β\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0361em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3173em;\">\u003Cspan style=\"top:-2.357em;margin-left:0em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.143em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Ffehler-erster-und-zweiter-art",[],[3438,3439,3440],"hypothesis-test","rejection-region","binomial-distribution",{"title":548,"description":3403},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ffehler-erster-und-zweiter-art","Fehler 1. Art heißt, eine richtige Nullhypothese zu verwerfen, Fehler 2. Art, eine falsche beizubehalten.",[3445,3446,3447,3448],"alpha-fehler","beta-fehler","hypothesentest","irrtumswahrscheinlichkeit",[3450,3453,3456,3459,3463,3466],{"symbol":1297,"meaning":3451,"symbolHtml":3452},"Wahrscheinlichkeit für den Fehler 1. Art, H₀ wird verworfen, obwohl sie stimmt","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>∗\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\alpha^*\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6887em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6887em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∗\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1157,"meaning":3454,"symbolHtml":3455},"Wahrscheinlichkeit für den Fehler 2. Art, H₀ wird nicht verworfen, obwohl sie falsch ist","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>β\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\beta\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0528em;\">β\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1909,"meaning":3457,"symbolHtml":3458},"Testgröße, die Anzahl der Treffer in der Stichprobe","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3460,"meaning":3461,"symbolHtml":3462},"A,\\ \\overline{A}","Annahmebereich und Ablehnungsbereich von H₀","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmover accent=\"true\">\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A,\\ \\overline{A}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\"> \u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":990,"meaning":3464,"symbolHtml":3465},"Trefferwahrscheinlichkeit laut Nullhypothese","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1223,"meaning":3467,"symbolHtml":3468},"angenommene wahre Trefferwahrscheinlichkeit, für die β berechnet wird","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","reWxWds8qwTuHbTtMq1lzc3jOibeaTh96OL-yfBRUAs",[3471,3474,3477],{"stem":3472,"title":3473,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fablehnungsbereich","Ablehnungsbereich bei der Binomialverteilung",{"stem":3475,"title":3476,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialverteilung","Binomialverteilung",{"stem":3478,"title":3479,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fhypothesentest","Hypothesentest",1793824285502]