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1 - m \\ \\text{Freiheitsgraden},",[573,1068,1070,1092,1111],{"className":1069,"ariaHidden":603},[602],[573,1071,1073,1077,1080,1085,1089],{"className":1072},[607],[573,1074],{"className":1075,"style":1076},[611],"height:0.7778em;vertical-align:-0.0833em;",[573,1078,633],{"className":1079,"style":649},[616,617],[573,1081],{"className":1082,"style":1084},[1083],"mspace","margin-right:0.2222em;",[573,1086,1048],{"className":1087},[1088],"mbin",[573,1090],{"className":1091,"style":1084},[1083],[573,1093,1095,1099,1102,1105,1108],{"className":1094},[607],[573,1096],{"className":1097,"style":1098},[611],"height:0.7278em;vertical-align:-0.0833em;",[573,1100,1051],{"className":1101},[616],[573,1103],{"className":1104,"style":1084},[1083],[573,1106,1048],{"className":1107},[1088],[573,1109],{"className":1110,"style":1084},[1083],[573,1112,1114,1118,1121,1125,1133],{"className":1113},[607],[573,1115],{"className":1116,"style":1117},[611],"height:0.8889em;vertical-align:-0.1944em;",[573,1119,1056],{"className":1120},[616,617],[573,1122,1124],{"className":1123},[1083]," ",[573,1126,1129],{"className":1127},[616,1128],"text",[573,1130,1132],{"className":1131},[616],"Freiheitsgraden",[573,1134,1063],{"className":1135},[1136],"mpunct",[565,1138,1139,1140,1168,1169,926,1239,1294,1295,1364,1365,1423,1424,1566,1567,1570,1571,1640],{},"wobei ",[573,1141,1143,1156],{"className":1142},[576],[573,1144,1146],{"className":1145},[580],[582,1147,1148],{"xmlns":584},[586,1149,1150,1154],{},[589,1151,1152],{},[592,1153,1056],{},[596,1155,1056],{"encoding":598},[573,1157,1159],{"className":1158,"ariaHidden":603},[602],[573,1160,1162,1165],{"className":1161},[607],[573,1163],{"className":1164,"style":612},[611],[573,1166,1056],{"className":1167},[616,617]," die Anzahl der aus den Daten geschätzten Parameter ist (bei vollständig vorgegebenen ",[573,1170,1172,1190],{"className":1171},[576],[573,1173,1175],{"className":1174},[580],[582,1176,1177],{"xmlns":584},[586,1178,1179,1187],{},[589,1180,1181],{},[664,1182,1183,1185],{},[592,1184,565],{},[592,1186,758],{},[596,1188,1189],{"encoding":598},"p_i",[573,1191,1193],{"className":1192,"ariaHidden":603},[602],[573,1194,1196,1199],{"className":1195},[607],[573,1197],{"className":1198,"style":807},[611],[573,1200,1202,1205],{"className":1201},[616],[573,1203,565],{"className":1204},[616,617],[573,1206,1208],{"className":1207},[696],[573,1209,1211,1231],{"className":1210},[700,701],[573,1212,1214,1228],{"className":1213},[705],[573,1215,1217],{"className":1216,"style":829},[709],[573,1218,1219,1222],{"style":832},[573,1220],{"className":1221,"style":718},[717],[573,1223,1225],{"className":1224},[722,723,724,725],[573,1226,758],{"className":1227},[616,617,725],[573,1229,733],{"className":1230},[732],[573,1232,1234],{"className":1233},[705],[573,1235,1237],{"className":1236,"style":740},[709],[573,1238],{},[573,1240,1242,1261],{"className":1241},[576],[573,1243,1245],{"className":1244},[580],[582,1246,1247],{"xmlns":584},[586,1248,1249,1258],{},[589,1250,1251,1253,1256],{},[592,1252,1056],{},[1046,1254,1255],{},"=",[670,1257,672],{},[596,1259,1260],{"encoding":598},"m = 0",[573,1262,1264,1284],{"className":1263,"ariaHidden":603},[602],[573,1265,1267,1270,1273,1277,1281],{"className":1266},[607],[573,1268],{"className":1269,"style":612},[611],[573,1271,1056],{"className":1272},[616,617],[573,1274],{"className":1275,"style":1276},[1083],"margin-right:0.2778em;",[573,1278,1255],{"className":1279},[1280],"mrel",[573,1282],{"className":1283,"style":1276},[1083],[573,1285,1287,1291],{"className":1286},[607],[573,1288],{"className":1289,"style":1290},[611],"height:0.6444em;",[573,1292,672],{"className":1293},[616],"). Man verwirft ",[573,1296,1298,1315],{"className":1297},[576],[573,1299,1301],{"className":1300},[580],[582,1302,1303],{"xmlns":584},[586,1304,1305,1313],{},[589,1306,1307],{},[664,1308,1309,1311],{},[592,1310,668],{},[670,1312,672],{},[596,1314,675],{"encoding":598},[573,1316,1318],{"className":1317,"ariaHidden":603},[602],[573,1319,1321,1324],{"className":1320},[607],[573,1322],{"className":1323,"style":685},[611],[573,1325,1327,1330],{"className":1326},[616],[573,1328,668],{"className":1329,"style":692},[616,617],[573,1331,1333],{"className":1332},[696],[573,1334,1336,1356],{"className":1335},[700,701],[573,1337,1339,1353],{"className":1338},[705],[573,1340,1342],{"className":1341,"style":710},[709],[573,1343,1344,1347],{"style":713},[573,1345],{"className":1346,"style":718},[717],[573,1348,1350],{"className":1349},[722,723,724,725],[573,1351,672],{"className":1352},[616,725],[573,1354,733],{"className":1355},[732],[573,1357,1359],{"className":1358},[705],[573,1360,1362],{"className":1361,"style":740},[709],[573,1363],{},", wenn ",[573,1366,1368,1385],{"className":1367},[576],[573,1369,1371],{"className":1370},[580],[582,1372,1373],{"xmlns":584},[586,1374,1375,1383],{},[589,1376,1377],{},[940,1378,1379,1381],{},[592,1380,944],{},[670,1382,947],{},[596,1384,950],{"encoding":598},[573,1386,1388],{"className":1387,"ariaHidden":603},[602],[573,1389,1391,1394],{"className":1390},[607],[573,1392],{"className":1393,"style":960},[611],[573,1395,1397,1400],{"className":1396},[616],[573,1398,944],{"className":1399},[616,617],[573,1401,1403],{"className":1402},[696],[573,1404,1406],{"className":1405},[700],[573,1407,1409],{"className":1408},[705],[573,1410,1412],{"className":1411,"style":979},[709],[573,1413,1414,1417],{"style":982},[573,1415],{"className":1416,"style":718},[717],[573,1418,1420],{"className":1419},[722,723,724,725],[573,1421,947],{"className":1422},[616,725]," das Quantil ",[573,1425,1427,1471],{"className":1426},[576],[573,1428,1430],{"className":1429},[580],[582,1431,1432],{"xmlns":584},[586,1433,1434,1468],{},[589,1435,1436],{},[1437,1438,1439,1441,1466],"msubsup",{},[592,1440,944],{},[589,1442,1443,1445,1447,1449,1451,1453,1456,1459,1461,1463],{},[592,1444,633],{},[1046,1446,1048],{},[670,1448,1051],{},[1046,1450,1048],{},[592,1452,1056],{},[1046,1454,1455],{"separator":603},";",[1058,1457,1458],{}," ",[670,1460,1051],{},[1046,1462,1048],{},[592,1464,1465],{},"α",[670,1467,947],{},[596,1469,1470],{"encoding":598},"\\chi^2_{k-1-m;\\,1-\\alpha}",[573,1472,1474],{"className":1473,"ariaHidden":603},[602],[573,1475,1477,1481],{"className":1476},[607],[573,1478],{"className":1479,"style":1480},[611],"height:1.2333em;vertical-align:-0.4192em;",[573,1482,1484,1487],{"className":1483},[616],[573,1485,944],{"className":1486},[616,617],[573,1488,1490],{"className":1489},[696],[573,1491,1493,1557],{"className":1492},[700,701],[573,1494,1496,1554],{"className":1495},[705],[573,1497,1499,1543],{"className":1498,"style":979},[709],[573,1500,1502,1505],{"style":1501},"top:-2.4169em;margin-left:0em;margin-right:0.05em;",[573,1503],{"className":1504,"style":718},[717],[573,1506,1508],{"className":1507},[722,723,724,725],[573,1509,1511,1514,1517,1520,1523,1526,1529,1533,1536,1539],{"className":1510},[616,725],[573,1512,633],{"className":1513,"style":649},[616,617,725],[573,1515,1048],{"className":1516},[1088,725],[573,1518,1051],{"className":1519},[616,725],[573,1521,1048],{"className":1522},[1088,725],[573,1524,1056],{"className":1525},[616,617,725],[573,1527,1455],{"className":1528},[1136,725],[573,1530],{"className":1531,"style":1532},[1083,725],"margin-right:0.1952em;",[573,1534,1051],{"className":1535},[616,725],[573,1537,1048],{"className":1538},[1088,725],[573,1540,1465],{"className":1541,"style":1542},[616,617,725],"margin-right:0.0037em;",[573,1544,1545,1548],{"style":982},[573,1546],{"className":1547,"style":718},[717],[573,1549,1551],{"className":1550},[722,723,724,725],[573,1552,947],{"className":1553},[616,725],[573,1555,733],{"className":1556},[732],[573,1558,1560],{"className":1559},[705],[573,1561,1564],{"className":1562,"style":1563},[709],"height:0.4192em;",[573,1565],{}," überschreitet. Der Test ist immer ",[569,1568,1569],{},"rechtsseitig",": Nur große Abweichungen sprechen gegen ",[573,1572,1574,1591],{"className":1573},[576],[573,1575,1577],{"className":1576},[580],[582,1578,1579],{"xmlns":584},[586,1580,1581,1589],{},[589,1582,1583],{},[664,1584,1585,1587],{},[592,1586,668],{},[670,1588,672],{},[596,1590,675],{"encoding":598},[573,1592,1594],{"className":1593,"ariaHidden":603},[602],[573,1595,1597,1600],{"className":1596},[607],[573,1598],{"className":1599,"style":685},[611],[573,1601,1603,1606],{"className":1602},[616],[573,1604,668],{"className":1605,"style":692},[616,617],[573,1607,1609],{"className":1608},[696],[573,1610,1612,1632],{"className":1611},[700,701],[573,1613,1615,1629],{"className":1614},[705],[573,1616,1618],{"className":1617,"style":710},[709],[573,1619,1620,1623],{"style":713},[573,1621],{"className":1622,"style":718},[717],[573,1624,1626],{"className":1625},[722,723,724,725],[573,1627,672],{"className":1628},[616,725],[573,1630,733],{"className":1631},[732],[573,1633,1635],{"className":1634},[705],[573,1636,1638],{"className":1637,"style":740},[709],[573,1639],{},".",[565,1642,1643,1644,1710,1711,1753,1754,1794,1795,1836,1837,1878,1879,1920],{},"Kritische Werte für ",[573,1645,1647,1672],{"className":1646},[576],[573,1648,1650],{"className":1649},[580],[582,1651,1652],{"xmlns":584},[586,1653,1654,1669],{},[589,1655,1656,1658,1660,1663,1665],{},[592,1657,1465],{},[1046,1659,1255],{},[670,1661,1662],{},"5",[1058,1664,1458],{},[592,1666,1668],{"mathvariant":1667},"normal","%",[596,1670,1671],{"encoding":598},"\\alpha = 5\\,\\%",[573,1673,1675,1693],{"className":1674,"ariaHidden":603},[602],[573,1676,1678,1681,1684,1687,1690],{"className":1677},[607],[573,1679],{"className":1680,"style":612},[611],[573,1682,1465],{"className":1683,"style":1542},[616,617],[573,1685],{"className":1686,"style":1276},[1083],[573,1688,1255],{"className":1689},[1280],[573,1691],{"className":1692,"style":1276},[1083],[573,1694,1696,1700,1703,1707],{"className":1695},[607],[573,1697],{"className":1698,"style":1699},[611],"height:0.8056em;vertical-align:-0.0556em;",[573,1701,1662],{"className":1702},[616],[573,1704],{"className":1705,"style":1706},[1083],"margin-right:0.1667em;",[573,1708,1668],{"className":1709},[616],": ",[573,1712,1714,1729],{"className":1713},[576],[573,1715,1717],{"className":1716},[580],[582,1718,1719],{"xmlns":584},[586,1720,1721,1726],{},[589,1722,1723],{},[670,1724,1725],{},"3,841",[596,1727,1728],{"encoding":598},"3{,}841",[573,1730,1732],{"className":1731,"ariaHidden":603},[602],[573,1733,1735,1739,1743,1749],{"className":1734},[607],[573,1736],{"className":1737,"style":1738},[611],"height:0.8389em;vertical-align:-0.1944em;",[573,1740,1742],{"className":1741},[616],"3",[573,1744,1746],{"className":1745},[616],[573,1747,1063],{"className":1748},[1136],[573,1750,1752],{"className":1751},[616],"841"," (1 Freiheitsgrad), ",[573,1755,1757,1772],{"className":1756},[576],[573,1758,1760],{"className":1759},[580],[582,1761,1762],{"xmlns":584},[586,1763,1764,1769],{},[589,1765,1766],{},[670,1767,1768],{},"5,991",[596,1770,1771],{"encoding":598},"5{,}991",[573,1773,1775],{"className":1774,"ariaHidden":603},[602],[573,1776,1778,1781,1784,1790],{"className":1777},[607],[573,1779],{"className":1780,"style":1738},[611],[573,1782,1662],{"className":1783},[616],[573,1785,1787],{"className":1786},[616],[573,1788,1063],{"className":1789},[1136],[573,1791,1793],{"className":1792},[616],"991"," (2), ",[573,1796,1798,1813],{"className":1797},[576],[573,1799,1801],{"className":1800},[580],[582,1802,1803],{"xmlns":584},[586,1804,1805,1810],{},[589,1806,1807],{},[670,1808,1809],{},"7,815",[596,1811,1812],{"encoding":598},"7{,}815",[573,1814,1816],{"className":1815,"ariaHidden":603},[602],[573,1817,1819,1822,1826,1832],{"className":1818},[607],[573,1820],{"className":1821,"style":1738},[611],[573,1823,1825],{"className":1824},[616],"7",[573,1827,1829],{"className":1828},[616],[573,1830,1063],{"className":1831},[1136],[573,1833,1835],{"className":1834},[616],"815"," (3), ",[573,1838,1840,1855],{"className":1839},[576],[573,1841,1843],{"className":1842},[580],[582,1844,1845],{"xmlns":584},[586,1846,1847,1852],{},[589,1848,1849],{},[670,1850,1851],{},"9,488",[596,1853,1854],{"encoding":598},"9{,}488",[573,1856,1858],{"className":1857,"ariaHidden":603},[602],[573,1859,1861,1864,1868,1874],{"className":1860},[607],[573,1862],{"className":1863,"style":1738},[611],[573,1865,1867],{"className":1866},[616],"9",[573,1869,1871],{"className":1870},[616],[573,1872,1063],{"className":1873},[1136],[573,1875,1877],{"className":1876},[616],"488"," (4), ",[573,1880,1882,1897],{"className":1881},[576],[573,1883,1885],{"className":1884},[580],[582,1886,1887],{"xmlns":584},[586,1888,1889,1894],{},[589,1890,1891],{},[670,1892,1893],{},"11,070",[596,1895,1896],{"encoding":598},"11{,}070",[573,1898,1900],{"className":1899,"ariaHidden":603},[602],[573,1901,1903,1906,1910,1916],{"className":1902},[607],[573,1904],{"className":1905,"style":1738},[611],[573,1907,1909],{"className":1908},[616],"11",[573,1911,1913],{"className":1912},[616],[573,1914,1063],{"className":1915},[1136],[573,1917,1919],{"className":1918},[616],"070"," (5).",[565,1922,1923,1924,1952],{},"Die Näherung ist nur brauchbar, wenn alle erwarteten Häufigkeiten mindestens ",[573,1925,1927,1940],{"className":1926},[576],[573,1928,1930],{"className":1929},[580],[582,1931,1932],{"xmlns":584},[586,1933,1934,1938],{},[589,1935,1936],{},[670,1937,1662],{},[596,1939,1662],{"encoding":598},[573,1941,1943],{"className":1942,"ariaHidden":603},[602],[573,1944,1946,1949],{"className":1945},[607],[573,1947],{"className":1948,"style":1290},[611],[573,1950,1662],{"className":1951},[616]," sind. Sonst fasst man Klassen zusammen.",[565,1954,1955,1956,1640],{},"Rechenvorteil: ",[573,1957,1959,2012],{"className":1958},[576],[573,1960,1962],{"className":1961},[580],[582,1963,1964],{"xmlns":584},[586,1965,1966,2009],{},[589,1967,1968,1974,1976,1983,2005,2007],{},[940,1969,1970,1972],{},[592,1971,944],{},[670,1973,947],{},[1046,1975,1255],{},[664,1977,1978,1981],{},[1046,1979,1980],{},"∑",[592,1982,758],{},[1984,1985,1986,1995],"mfrac",{},[1437,1987,1988,1991,1993],{},[592,1989,1990],{},"N",[592,1992,758],{},[670,1994,947],{},[589,1996,1997,1999],{},[592,1998,594],{},[664,2000,2001,2003],{},[592,2002,565],{},[592,2004,758],{},[1046,2006,1048],{},[592,2008,594],{},[596,2010,2011],{"encoding":598},"\\chi^2 = \\sum_{i} \\frac{N_i^2}{n p_i} - n",[573,2013,2015,2059,2306],{"className":2014,"ariaHidden":603},[602],[573,2016,2018,2021,2050,2053,2056],{"className":2017},[607],[573,2019],{"className":2020,"style":960},[611],[573,2022,2024,2027],{"className":2023},[616],[573,2025,944],{"className":2026},[616,617],[573,2028,2030],{"className":2029},[696],[573,2031,2033],{"className":2032},[700],[573,2034,2036],{"className":2035},[705],[573,2037,2039],{"className":2038,"style":979},[709],[573,2040,2041,2044],{"style":982},[573,2042],{"className":2043,"style":718},[717],[573,2045,2047],{"className":2046},[722,723,724,725],[573,2048,947],{"className":2049},[616,725],[573,2051],{"className":2052,"style":1276},[1083],[573,2054,1255],{"className":2055},[1280],[573,2057],{"className":2058,"style":1276},[1083],[573,2060,2062,2066,2116,2119,2297,2300,2303],{"className":2061},[607],[573,2063],{"className":2064,"style":2065},[611],"height:1.6152em;vertical-align:-0.4811em;",[573,2067,2070,2076],{"className":2068},[2069],"mop",[573,2071,1980],{"className":2072,"style":2075},[2069,2073,2074],"op-symbol","small-op","position:relative;top:0em;",[573,2077,2079],{"className":2078},[696],[573,2080,2082,2107],{"className":2081},[700,701],[573,2083,2085,2104],{"className":2084},[705],[573,2086,2089],{"className":2087,"style":2088},[709],"height:0.162em;",[573,2090,2092,2095],{"style":2091},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[573,2093],{"className":2094,"style":718},[717],[573,2096,2098],{"className":2097},[722,723,724,725],[573,2099,2101],{"className":2100},[616,725],[573,2102,758],{"className":2103},[616,617,725],[573,2105,733],{"className":2106},[732],[573,2108,2110],{"className":2109},[705],[573,2111,2114],{"className":2112,"style":2113},[709],"height:0.2997em;",[573,2115],{},[573,2117],{"className":2118,"style":1706},[1083],[573,2120,2122,2127,2293],{"className":2121},[616],[573,2123],{"className":2124},[2125,2126],"mopen","nulldelimiter",[573,2128,2130],{"className":2129},[1984],[573,2131,2133,2284],{"className":2132},[700,701],[573,2134,2136,2281],{"className":2135},[705],[573,2137,2140,2202,2213],{"className":2138,"style":2139},[709],"height:1.1341em;",[573,2141,2143,2147],{"style":2142},"top:-2.655em;",[573,2144],{"className":2145,"style":2146},[717],"height:3em;",[573,2148,2150],{"className":2149},[722,723,724,725],[573,2151,2153,2156],{"className":2152},[616,725],[573,2154,594],{"className":2155},[616,617,725],[573,2157,2159,2162],{"className":2158},[616,725],[573,2160,565],{"className":2161},[616,617,725],[573,2163,2165],{"className":2164},[696],[573,2166,2168,2193],{"className":2167},[700,701],[573,2169,2171,2190],{"className":2170},[705],[573,2172,2175],{"className":2173,"style":2174},[709],"height:0.3281em;",[573,2176,2178,2182],{"style":2177},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[573,2179],{"className":2180,"style":2181},[717],"height:2.5em;",[573,2183,2187],{"className":2184},[722,2185,2186,725],"reset-size3","size1",[573,2188,758],{"className":2189},[616,617,725],[573,2191,733],{"className":2192},[732],[573,2194,2196],{"className":2195},[705],[573,2197,2200],{"className":2198,"style":2199},[709],"height:0.143em;",[573,2201],{},[573,2203,2205,2208],{"style":2204},"top:-3.23em;",[573,2206],{"className":2207,"style":2146},[717],[573,2209],{"className":2210,"style":2212},[2211],"frac-line","border-bottom-width:0.04em;",[573,2214,2216,2219],{"style":2215},"top:-3.5102em;",[573,2217],{"className":2218,"style":2146},[717],[573,2220,2222],{"className":2221},[722,723,724,725],[573,2223,2225],{"className":2224},[616,725],[573,2226,2228,2232],{"className":2227},[616,725],[573,2229,1990],{"className":2230,"style":2231},[616,617,725],"margin-right:0.109em;",[573,2233,2235],{"className":2234},[696],[573,2236,2238,2272],{"className":2237},[700,701],[573,2239,2241,2269],{"className":2240},[705],[573,2242,2245,2257],{"className":2243,"style":2244},[709],"height:0.8913em;",[573,2246,2248,2251],{"style":2247},"top:-2.214em;margin-left:-0.109em;margin-right:0.0714em;",[573,2249],{"className":2250,"style":2181},[717],[573,2252,2254],{"className":2253},[722,2185,2186,725],[573,2255,758],{"className":2256},[616,617,725],[573,2258,2260,2263],{"style":2259},"top:-2.931em;margin-right:0.0714em;",[573,2261],{"className":2262,"style":2181},[717],[573,2264,2266],{"className":2265},[722,2185,2186,725],[573,2267,947],{"className":2268},[616,725],[573,2270,733],{"className":2271},[732],[573,2273,2275],{"className":2274},[705],[573,2276,2279],{"className":2277,"style":2278},[709],"height:0.286em;",[573,2280],{},[573,2282,733],{"className":2283},[732],[573,2285,2287],{"className":2286},[705],[573,2288,2291],{"className":2289,"style":2290},[709],"height:0.4811em;",[573,2292],{},[573,2294],{"className":2295},[2296,2126],"mclose",[573,2298],{"className":2299,"style":1084},[1083],[573,2301,1048],{"className":2302},[1088],[573,2304],{"className":2305,"style":1084},[1083],[573,2307,2309,2312],{"className":2308},[607],[573,2310],{"className":2311,"style":612},[611],[573,2313,594],{"className":2314},[616,617],[560,2316,2318],{"id":2317},"beispiele","Beispiele",[565,2320,2321,2322,2351,2352,2421,2422,2571,2572,2672],{},"Ein Würfel wird ",[573,2323,2325,2339],{"className":2324},[576],[573,2326,2328],{"className":2327},[580],[582,2329,2330],{"xmlns":584},[586,2331,2332,2337],{},[589,2333,2334],{},[670,2335,2336],{},"120",[596,2338,2336],{"encoding":598},[573,2340,2342],{"className":2341,"ariaHidden":603},[602],[573,2343,2345,2348],{"className":2344},[607],[573,2346],{"className":2347,"style":1290},[611],[573,2349,2336],{"className":2350},[616],"-mal geworfen. Unter ",[573,2353,2355,2372],{"className":2354},[576],[573,2356,2358],{"className":2357},[580],[582,2359,2360],{"xmlns":584},[586,2361,2362,2370],{},[589,2363,2364],{},[664,2365,2366,2368],{},[592,2367,668],{},[670,2369,672],{},[596,2371,675],{"encoding":598},[573,2373,2375],{"className":2374,"ariaHidden":603},[602],[573,2376,2378,2381],{"className":2377},[607],[573,2379],{"className":2380,"style":685},[611],[573,2382,2384,2387],{"className":2383},[616],[573,2385,668],{"className":2386,"style":692},[616,617],[573,2388,2390],{"className":2389},[696],[573,2391,2393,2413],{"className":2392},[700,701],[573,2394,2396,2410],{"className":2395},[705],[573,2397,2399],{"className":2398,"style":710},[709],[573,2400,2401,2404],{"style":713},[573,2402],{"className":2403,"style":718},[717],[573,2405,2407],{"className":2406},[722,723,724,725],[573,2408,672],{"className":2409},[616,725],[573,2411,733],{"className":2412},[732],[573,2414,2416],{"className":2415},[705],[573,2417,2419],{"className":2418,"style":740},[709],[573,2420],{}," (fairer Würfel) erwartet man je Augenzahl ",[573,2423,2425,2454],{"className":2424},[576],[573,2426,2428],{"className":2427},[580],[582,2429,2430],{"xmlns":584},[586,2431,2432,2451],{},[589,2433,2434,2436,2439,2446,2448],{},[670,2435,2336],{},[1046,2437,2438],{},"⋅",[1984,2440,2441,2443],{},[670,2442,1051],{},[670,2444,2445],{},"6",[1046,2447,1255],{},[670,2449,2450],{},"20",[596,2452,2453],{"encoding":598},"120 \\cdot \\frac{1}{6} = 20",[573,2455,2457,2475,2562],{"className":2456,"ariaHidden":603},[602],[573,2458,2460,2463,2466,2469,2472],{"className":2459},[607],[573,2461],{"className":2462,"style":1290},[611],[573,2464,2336],{"className":2465},[616],[573,2467],{"className":2468,"style":1084},[1083],[573,2470,2438],{"className":2471},[1088],[573,2473],{"className":2474,"style":1084},[1083],[573,2476,2478,2482,2553,2556,2559],{"className":2477},[607],[573,2479],{"className":2480,"style":2481},[611],"height:1.1901em;vertical-align:-0.345em;",[573,2483,2485,2488,2550],{"className":2484},[616],[573,2486],{"className":2487},[2125,2126],[573,2489,2491],{"className":2490},[1984],[573,2492,2494,2541],{"className":2493},[700,701],[573,2495,2497,2538],{"className":2496},[705],[573,2498,2501,2515,2523],{"className":2499,"style":2500},[709],"height:0.8451em;",[573,2502,2503,2506],{"style":2142},[573,2504],{"className":2505,"style":2146},[717],[573,2507,2509],{"className":2508},[722,723,724,725],[573,2510,2512],{"className":2511},[616,725],[573,2513,2445],{"className":2514},[616,725],[573,2516,2517,2520],{"style":2204},[573,2518],{"className":2519,"style":2146},[717],[573,2521],{"className":2522,"style":2212},[2211],[573,2524,2526,2529],{"style":2525},"top:-3.394em;",[573,2527],{"className":2528,"style":2146},[717],[573,2530,2532],{"className":2531},[722,723,724,725],[573,2533,2535],{"className":2534},[616,725],[573,2536,1051],{"className":2537},[616,725],[573,2539,733],{"className":2540},[732],[573,2542,2544],{"className":2543},[705],[573,2545,2548],{"className":2546,"style":2547},[709],"height:0.345em;",[573,2549],{},[573,2551],{"className":2552},[2296,2126],[573,2554],{"className":2555,"style":1276},[1083],[573,2557,1255],{"className":2558},[1280],[573,2560],{"className":2561,"style":1276},[1083],[573,2563,2565,2568],{"className":2564},[607],[573,2566],{"className":2567,"style":1290},[611],[573,2569,2450],{"className":2570},[616],". Beobachtet werden ",[573,2573,2575,2615],{"className":2574},[576],[573,2576,2578],{"className":2577},[580],[582,2579,2580],{"xmlns":584},[586,2581,2582,2612],{},[589,2583,2584,2587,2589,2592,2594,2597,2599,2602,2604,2607,2609],{},[670,2585,2586],{},"15",[1046,2588,1063],{"separator":603},[670,2590,2591],{},"22",[1046,2593,1063],{"separator":603},[670,2595,2596],{},"18",[1046,2598,1063],{"separator":603},[670,2600,2601],{},"25",[1046,2603,1063],{"separator":603},[670,2605,2606],{},"17",[1046,2608,1063],{"separator":603},[670,2610,2611],{},"23",[596,2613,2614],{"encoding":598},"15, 22, 18, 25, 17, 23",[573,2616,2618],{"className":2617,"ariaHidden":603},[602],[573,2619,2621,2624,2627,2630,2633,2636,2639,2642,2645,2648,2651,2654,2657,2660,2663,2666,2669],{"className":2620},[607],[573,2622],{"className":2623,"style":1738},[611],[573,2625,2586],{"className":2626},[616],[573,2628,1063],{"className":2629},[1136],[573,2631],{"className":2632,"style":1706},[1083],[573,2634,2591],{"className":2635},[616],[573,2637,1063],{"className":2638},[1136],[573,2640],{"className":2641,"style":1706},[1083],[573,2643,2596],{"className":2644},[616],[573,2646,1063],{"className":2647},[1136],[573,2649],{"className":2650,"style":1706},[1083],[573,2652,2601],{"className":2653},[616],[573,2655,1063],{"className":2656},[1136],[573,2658],{"className":2659,"style":1706},[1083],[573,2661,2606],{"className":2662},[616],[573,2664,1063],{"className":2665},[1136],[573,2667],{"className":2668,"style":1706},[1083],[573,2670,2611],{"className":2671},[616],":",[573,2674,2676],{"className":2675},[1029],[573,2677,2679,2743],{"className":2678},[576],[573,2680,2682],{"className":2681},[580],[582,2683,2684],{"xmlns":584,"display":1038},[586,2685,2686,2740],{},[589,2687,2688,2694,2696,2726,2728,2735,2737],{},[940,2689,2690,2692],{},[592,2691,944],{},[670,2693,947],{},[1046,2695,1255],{},[1984,2697,2698,2724],{},[589,2699,2700,2702,2705,2708,2710,2712,2714,2716,2718,2720,2722],{},[670,2701,2601],{},[1046,2703,2704],{},"+",[670,2706,2707],{},"4",[1046,2709,2704],{},[670,2711,2707],{},[1046,2713,2704],{},[670,2715,2601],{},[1046,2717,2704],{},[670,2719,1867],{},[1046,2721,2704],{},[670,2723,1867],{},[670,2725,2450],{},[1046,2727,1255],{},[1984,2729,2730,2733],{},[670,2731,2732],{},"76",[670,2734,2450],{},[1046,2736,1255],{},[670,2738,2739],{},"3,8",[596,2741,2742],{"encoding":598},"\\chi^2 = \\frac{25 + 4 + 4 + 25 + 9 + 9}{20} = \\frac{76}{20} = 3{,}8",[573,2744,2746,2793,2935,3012],{"className":2745,"ariaHidden":603},[602],[573,2747,2749,2753,2784,2787,2790],{"className":2748},[607],[573,2750],{"className":2751,"style":2752},[611],"height:1.0585em;vertical-align:-0.1944em;",[573,2754,2756,2759],{"className":2755},[616],[573,2757,944],{"className":2758},[616,617],[573,2760,2762],{"className":2761},[696],[573,2763,2765],{"className":2764},[700],[573,2766,2768],{"className":2767},[705],[573,2769,2772],{"className":2770,"style":2771},[709],"height:0.8641em;",[573,2773,2775,2778],{"style":2774},"top:-3.113em;margin-right:0.05em;",[573,2776],{"className":2777,"style":718},[717],[573,2779,2781],{"className":2780},[722,723,724,725],[573,2782,947],{"className":2783},[616,725],[573,2785],{"className":2786,"style":1276},[1083],[573,2788,1255],{"className":2789},[1280],[573,2791],{"className":2792,"style":1276},[1083],[573,2794,2796,2800,2926,2929,2932],{"className":2795},[607],[573,2797],{"className":2798,"style":2799},[611],"height:2.0074em;vertical-align:-0.686em;",[573,2801,2803,2806,2923],{"className":2802},[616],[573,2804],{"className":2805},[2125,2126],[573,2807,2809],{"className":2808},[1984],[573,2810,2812,2914],{"className":2811},[700,701],[573,2813,2815,2911],{"className":2814},[705],[573,2816,2819,2831,2839],{"className":2817,"style":2818},[709],"height:1.3214em;",[573,2820,2822,2825],{"style":2821},"top:-2.314em;",[573,2823],{"className":2824,"style":2146},[717],[573,2826,2828],{"className":2827},[616],[573,2829,2450],{"className":2830},[616],[573,2832,2833,2836],{"style":2204},[573,2834],{"className":2835,"style":2146},[717],[573,2837],{"className":2838,"style":2212},[2211],[573,2840,2842,2845],{"style":2841},"top:-3.677em;",[573,2843],{"className":2844,"style":2146},[717],[573,2846,2848,2851,2854,2857,2860,2863,2866,2869,2872,2875,2878,2881,2884,2887,2890,2893,2896,2899,2902,2905,2908],{"className":2847},[616],[573,2849,2601],{"className":2850},[616],[573,2852],{"className":2853,"style":1084},[1083],[573,2855,2704],{"className":2856},[1088],[573,2858],{"className":2859,"style":1084},[1083],[573,2861,2707],{"className":2862},[616],[573,2864],{"className":2865,"style":1084},[1083],[573,2867,2704],{"className":2868},[1088],[573,2870],{"className":2871,"style":1084},[1083],[573,2873,2707],{"className":2874},[616],[573,2876],{"className":2877,"style":1084},[1083],[573,2879,2704],{"className":2880},[1088],[573,2882],{"className":2883,"style":1084},[1083],[573,2885,2601],{"className":2886},[616],[573,2888],{"className":2889,"style":1084},[1083],[573,2891,2704],{"className":2892},[1088],[573,2894],{"className":2895,"style":1084},[1083],[573,2897,1867],{"className":2898},[616],[573,2900],{"className":2901,"style":1084},[1083],[573,2903,2704],{"className":2904},[1088],[573,2906],{"className":2907,"style":1084},[1083],[573,2909,1867],{"className":2910},[616],[573,2912,733],{"className":2913},[732],[573,2915,2917],{"className":2916},[705],[573,2918,2921],{"className":2919,"style":2920},[709],"height:0.686em;",[573,2922],{},[573,2924],{"className":2925},[2296,2126],[573,2927],{"className":2928,"style":1276},[1083],[573,2930,1255],{"className":2931},[1280],[573,2933],{"className":2934,"style":1276},[1083],[573,2936,2938,2941,3003,3006,3009],{"className":2937},[607],[573,2939],{"className":2940,"style":2799},[611],[573,2942,2944,2947,3000],{"className":2943},[616],[573,2945],{"className":2946},[2125,2126],[573,2948,2950],{"className":2949},[1984],[573,2951,2953,2992],{"className":2952},[700,701],[573,2954,2956,2989],{"className":2955},[705],[573,2957,2959,2970,2978],{"className":2958,"style":2818},[709],[573,2960,2961,2964],{"style":2821},[573,2962],{"className":2963,"style":2146},[717],[573,2965,2967],{"className":2966},[616],[573,2968,2450],{"className":2969},[616],[573,2971,2972,2975],{"style":2204},[573,2973],{"className":2974,"style":2146},[717],[573,2976],{"className":2977,"style":2212},[2211],[573,2979,2980,2983],{"style":2841},[573,2981],{"className":2982,"style":2146},[717],[573,2984,2986],{"className":2985},[616],[573,2987,2732],{"className":2988},[616],[573,2990,733],{"className":2991},[732],[573,2993,2995],{"className":2994},[705],[573,2996,2998],{"className":2997,"style":2920},[709],[573,2999],{},[573,3001],{"className":3002},[2296,2126],[573,3004],{"className":3005,"style":1276},[1083],[573,3007,1255],{"className":3008},[1280],[573,3010],{"className":3011,"style":1276},[1083],[573,3013,3015,3018,3021,3027],{"className":3014},[607],[573,3016],{"className":3017,"style":1738},[611],[573,3019,1742],{"className":3020},[616],[573,3022,3024],{"className":3023},[616],[573,3025,1063],{"className":3026},[1136],[573,3028,3030],{"className":3029},[616],"8",[565,3032,3033,3034,3107,3108,3148,3149,3219,3220,3289],{},"Mit ",[573,3035,3037,3059],{"className":3036},[576],[573,3038,3040],{"className":3039},[580],[582,3041,3042],{"xmlns":584},[586,3043,3044,3056],{},[589,3045,3046,3048,3050,3052,3054],{},[592,3047,633],{},[1046,3049,1048],{},[670,3051,1051],{},[1046,3053,1255],{},[670,3055,1662],{},[596,3057,3058],{"encoding":598},"k - 1 = 5",[573,3060,3062,3080,3098],{"className":3061,"ariaHidden":603},[602],[573,3063,3065,3068,3071,3074,3077],{"className":3064},[607],[573,3066],{"className":3067,"style":1076},[611],[573,3069,633],{"className":3070,"style":649},[616,617],[573,3072],{"className":3073,"style":1084},[1083],[573,3075,1048],{"className":3076},[1088],[573,3078],{"className":3079,"style":1084},[1083],[573,3081,3083,3086,3089,3092,3095],{"className":3082},[607],[573,3084],{"className":3085,"style":1290},[611],[573,3087,1051],{"className":3088},[616],[573,3090],{"className":3091,"style":1276},[1083],[573,3093,1255],{"className":3094},[1280],[573,3096],{"className":3097,"style":1276},[1083],[573,3099,3101,3104],{"className":3100},[607],[573,3102],{"className":3103,"style":1290},[611],[573,3105,1662],{"className":3106},[616]," Freiheitsgraden ist der kritische Wert ",[573,3109,3111,3126],{"className":3110},[576],[573,3112,3114],{"className":3113},[580],[582,3115,3116],{"xmlns":584},[586,3117,3118,3123],{},[589,3119,3120],{},[670,3121,3122],{},"11,07",[596,3124,3125],{"encoding":598},"11{,}07",[573,3127,3129],{"className":3128,"ariaHidden":603},[602],[573,3130,3132,3135,3138,3144],{"className":3131},[607],[573,3133],{"className":3134,"style":1738},[611],[573,3136,1909],{"className":3137},[616],[573,3139,3141],{"className":3140},[616],[573,3142,1063],{"className":3143},[1136],[573,3145,3147],{"className":3146},[616],"07",". Wegen ",[573,3150,3152,3171],{"className":3151},[576],[573,3153,3155],{"className":3154},[580],[582,3156,3157],{"xmlns":584},[586,3158,3159,3168],{},[589,3160,3161,3163,3166],{},[670,3162,2739],{},[1046,3164,3165],{},"\u003C",[670,3167,3122],{},[596,3169,3170],{"encoding":598},"3{,}8 \u003C 11{,}07",[573,3172,3174,3201],{"className":3173,"ariaHidden":603},[602],[573,3175,3177,3180,3183,3189,3192,3195,3198],{"className":3176},[607],[573,3178],{"className":3179,"style":1738},[611],[573,3181,1742],{"className":3182},[616],[573,3184,3186],{"className":3185},[616],[573,3187,1063],{"className":3188},[1136],[573,3190,3030],{"className":3191},[616],[573,3193],{"className":3194,"style":1276},[1083],[573,3196,3165],{"className":3197},[1280],[573,3199],{"className":3200,"style":1276},[1083],[573,3202,3204,3207,3210,3216],{"className":3203},[607],[573,3205],{"className":3206,"style":1738},[611],[573,3208,1909],{"className":3209},[616],[573,3211,3213],{"className":3212},[616],[573,3214,1063],{"className":3215},[1136],[573,3217,3147],{"className":3218},[616]," wird ",[573,3221,3223,3240],{"className":3222},[576],[573,3224,3226],{"className":3225},[580],[582,3227,3228],{"xmlns":584},[586,3229,3230,3238],{},[589,3231,3232],{},[664,3233,3234,3236],{},[592,3235,668],{},[670,3237,672],{},[596,3239,675],{"encoding":598},[573,3241,3243],{"className":3242,"ariaHidden":603},[602],[573,3244,3246,3249],{"className":3245},[607],[573,3247],{"className":3248,"style":685},[611],[573,3250,3252,3255],{"className":3251},[616],[573,3253,668],{"className":3254,"style":692},[616,617],[573,3256,3258],{"className":3257},[696],[573,3259,3261,3281],{"className":3260},[700,701],[573,3262,3264,3278],{"className":3263},[705],[573,3265,3267],{"className":3266,"style":710},[709],[573,3268,3269,3272],{"style":713},[573,3270],{"className":3271,"style":718},[717],[573,3273,3275],{"className":3274},[722,723,724,725],[573,3276,672],{"className":3277},[616,725],[573,3279,733],{"className":3280},[732],[573,3282,3284],{"className":3283},[705],[573,3285,3287],{"className":3286,"style":740},[709],[573,3288],{}," nicht verworfen.",[565,3291,3292,3293,3333,3334,3333,3374,3413,3414,3443,3444,3333,3473,3333,3502,3531,3532,3333,3561,3333,3589,2672],{},"Ein Vererbungsmodell sagt die Anteile ",[573,3294,3296,3315],{"className":3295},[576],[573,3297,3299],{"className":3298},[580],[582,3300,3301],{"xmlns":584},[586,3302,3303,3312],{},[589,3304,3305,3308,3310],{},[670,3306,3307],{},"50",[1058,3309,1458],{},[592,3311,1668],{"mathvariant":1667},[596,3313,3314],{"encoding":598},"50\\,\\%",[573,3316,3318],{"className":3317,"ariaHidden":603},[602],[573,3319,3321,3324,3327,3330],{"className":3320},[607],[573,3322],{"className":3323,"style":1699},[611],[573,3325,3307],{"className":3326},[616],[573,3328],{"className":3329,"style":1706},[1083],[573,3331,1668],{"className":3332},[616],", ",[573,3335,3337,3356],{"className":3336},[576],[573,3338,3340],{"className":3339},[580],[582,3341,3342],{"xmlns":584},[586,3343,3344,3353],{},[589,3345,3346,3349,3351],{},[670,3347,3348],{},"30",[1058,3350,1458],{},[592,3352,1668],{"mathvariant":1667},[596,3354,3355],{"encoding":598},"30\\,\\%",[573,3357,3359],{"className":3358,"ariaHidden":603},[602],[573,3360,3362,3365,3368,3371],{"className":3361},[607],[573,3363],{"className":3364,"style":1699},[611],[573,3366,3348],{"className":3367},[616],[573,3369],{"className":3370,"style":1706},[1083],[573,3372,1668],{"className":3373},[616],[573,3375,3377,3395],{"className":3376},[576],[573,3378,3380],{"className":3379},[580],[582,3381,3382],{"xmlns":584},[586,3383,3384,3392],{},[589,3385,3386,3388,3390],{},[670,3387,2450],{},[1058,3389,1458],{},[592,3391,1668],{"mathvariant":1667},[596,3393,3394],{"encoding":598},"20\\,\\%",[573,3396,3398],{"className":3397,"ariaHidden":603},[602],[573,3399,3401,3404,3407,3410],{"className":3400},[607],[573,3402],{"className":3403,"style":1699},[611],[573,3405,2450],{"className":3406},[616],[573,3408],{"className":3409,"style":1706},[1083],[573,3411,1668],{"className":3412},[616]," voraus. Bei ",[573,3415,3417,3431],{"className":3416},[576],[573,3418,3420],{"className":3419},[580],[582,3421,3422],{"xmlns":584},[586,3423,3424,3429],{},[589,3425,3426],{},[670,3427,3428],{},"200",[596,3430,3428],{"encoding":598},[573,3432,3434],{"className":3433,"ariaHidden":603},[602],[573,3435,3437,3440],{"className":3436},[607],[573,3438],{"className":3439,"style":1290},[611],[573,3441,3428],{"className":3442},[616]," Pflanzen erwartet man ",[573,3445,3447,3461],{"className":3446},[576],[573,3448,3450],{"className":3449},[580],[582,3451,3452],{"xmlns":584},[586,3453,3454,3459],{},[589,3455,3456],{},[670,3457,3458],{},"100",[596,3460,3458],{"encoding":598},[573,3462,3464],{"className":3463,"ariaHidden":603},[602],[573,3465,3467,3470],{"className":3466},[607],[573,3468],{"className":3469,"style":1290},[611],[573,3471,3458],{"className":3472},[616],[573,3474,3476,3490],{"className":3475},[576],[573,3477,3479],{"className":3478},[580],[582,3480,3481],{"xmlns":584},[586,3482,3483,3488],{},[589,3484,3485],{},[670,3486,3487],{},"60",[596,3489,3487],{"encoding":598},[573,3491,3493],{"className":3492,"ariaHidden":603},[602],[573,3494,3496,3499],{"className":3495},[607],[573,3497],{"className":3498,"style":1290},[611],[573,3500,3487],{"className":3501},[616],[573,3503,3505,3519],{"className":3504},[576],[573,3506,3508],{"className":3507},[580],[582,3509,3510],{"xmlns":584},[586,3511,3512,3517],{},[589,3513,3514],{},[670,3515,3516],{},"40",[596,3518,3516],{"encoding":598},[573,3520,3522],{"className":3521,"ariaHidden":603},[602],[573,3523,3525,3528],{"className":3524},[607],[573,3526],{"className":3527,"style":1290},[611],[573,3529,3516],{"className":3530},[616]," und beobachtet ",[573,3533,3535,3549],{"className":3534},[576],[573,3536,3538],{"className":3537},[580],[582,3539,3540],{"xmlns":584},[586,3541,3542,3547],{},[589,3543,3544],{},[670,3545,3546],{},"118",[596,3548,3546],{"encoding":598},[573,3550,3552],{"className":3551,"ariaHidden":603},[602],[573,3553,3555,3558],{"className":3554},[607],[573,3556],{"className":3557,"style":1290},[611],[573,3559,3546],{"className":3560},[616],[573,3562,3564,3577],{"className":3563},[576],[573,3565,3567],{"className":3566},[580],[582,3568,3569],{"xmlns":584},[586,3570,3571,3575],{},[589,3572,3573],{},[670,3574,3487],{},[596,3576,3487],{"encoding":598},[573,3578,3580],{"className":3579,"ariaHidden":603},[602],[573,3581,3583,3586],{"className":3582},[607],[573,3584],{"className":3585,"style":1290},[611],[573,3587,3487],{"className":3588},[616],[573,3590,3592,3605],{"className":3591},[576],[573,3593,3595],{"className":3594},[580],[582,3596,3597],{"xmlns":584},[586,3598,3599,3603],{},[589,3600,3601],{},[670,3602,2591],{},[596,3604,2591],{"encoding":598},[573,3606,3608],{"className":3607,"ariaHidden":603},[602],[573,3609,3611,3614],{"className":3610},[607],[573,3612],{"className":3613,"style":1290},[611],[573,3615,2591],{"className":3616},[616],[573,3618,3620],{"className":3619},[1029],[573,3621,3623,3696],{"className":3622},[576],[573,3624,3626],{"className":3625},[580],[582,3627,3628],{"xmlns":584,"display":1038},[586,3629,3630,3693],{},[589,3631,3632,3638,3640,3650,3652,3662,3664,3674,3676,3679,3681,3683,3685,3688,3690],{},[940,3633,3634,3636],{},[592,3635,944],{},[670,3637,947],{},[1046,3639,1255],{},[1984,3641,3642,3648],{},[940,3643,3644,3646],{},[670,3645,2596],{},[670,3647,947],{},[670,3649,3458],{},[1046,3651,2704],{},[1984,3653,3654,3660],{},[940,3655,3656,3658],{},[670,3657,672],{},[670,3659,947],{},[670,3661,3487],{},[1046,3663,2704],{},[1984,3665,3666,3672],{},[940,3667,3668,3670],{},[670,3669,2596],{},[670,3671,947],{},[670,3673,3516],{},[1046,3675,1255],{},[670,3677,3678],{},"3,24",[1046,3680,2704],{},[670,3682,672],{},[1046,3684,2704],{},[670,3686,3687],{},"8,1",[1046,3689,1255],{},[670,3691,3692],{},"11,34",[596,3694,3695],{"encoding":598},"\\chi^2 = \\frac{18^2}{100} + \\frac{0^2}{60} + \\frac{18^2}{40} = 3{,}24 + 0 + 8{,}1 = 11{,}34",[573,3697,3699,3743,3851,3954,4060,4088,4106,4133],{"className":3698,"ariaHidden":603},[602],[573,3700,3702,3705,3734,3737,3740],{"className":3701},[607],[573,3703],{"className":3704,"style":2752},[611],[573,3706,3708,3711],{"className":3707},[616],[573,3709,944],{"className":3710},[616,617],[573,3712,3714],{"className":3713},[696],[573,3715,3717],{"className":3716},[700],[573,3718,3720],{"className":3719},[705],[573,3721,3723],{"className":3722,"style":2771},[709],[573,3724,3725,3728],{"style":2774},[573,3726],{"className":3727,"style":718},[717],[573,3729,3731],{"className":3730},[722,723,724,725],[573,3732,947],{"className":3733},[616,725],[573,3735],{"className":3736,"style":1276},[1083],[573,3738,1255],{"className":3739},[1280],[573,3741],{"className":3742,"style":1276},[1083],[573,3744,3746,3750,3842,3845,3848],{"className":3745},[607],[573,3747],{"className":3748,"style":3749},[611],"height:2.1771em;vertical-align:-0.686em;",[573,3751,3753,3756,3839],{"className":3752},[616],[573,3754],{"className":3755},[2125,2126],[573,3757,3759],{"className":3758},[1984],[573,3760,3762,3831],{"className":3761},[700,701],[573,3763,3765,3828],{"className":3764},[705],[573,3766,3769,3780,3788],{"className":3767,"style":3768},[709],"height:1.4911em;",[573,3770,3771,3774],{"style":2821},[573,3772],{"className":3773,"style":2146},[717],[573,3775,3777],{"className":3776},[616],[573,3778,3458],{"className":3779},[616],[573,3781,3782,3785],{"style":2204},[573,3783],{"className":3784,"style":2146},[717],[573,3786],{"className":3787,"style":2212},[2211],[573,3789,3790,3793],{"style":2841},[573,3791],{"className":3792,"style":2146},[717],[573,3794,3796,3799],{"className":3795},[616],[573,3797,1051],{"className":3798},[616],[573,3800,3802,3805],{"className":3801},[616],[573,3803,3030],{"className":3804},[616],[573,3806,3808],{"className":3807},[696],[573,3809,3811],{"className":3810},[700],[573,3812,3814],{"className":3813},[705],[573,3815,3817],{"className":3816,"style":979},[709],[573,3818,3819,3822],{"style":982},[573,3820],{"className":3821,"style":718},[717],[573,3823,3825],{"className":3824},[722,723,724,725],[573,3826,947],{"className":3827},[616,725],[573,3829,733],{"className":3830},[732],[573,3832,3834],{"className":3833},[705],[573,3835,3837],{"className":3836,"style":2920},[709],[573,3838],{},[573,3840],{"className":3841},[2296,2126],[573,3843],{"className":3844,"style":1084},[1083],[573,3846,2704],{"className":3847},[1088],[573,3849],{"className":3850,"style":1084},[1083],[573,3852,3854,3857,3945,3948,3951],{"className":3853},[607],[573,3855],{"className":3856,"style":3749},[611],[573,3858,3860,3863,3942],{"className":3859},[616],[573,3861],{"className":3862},[2125,2126],[573,3864,3866],{"className":3865},[1984],[573,3867,3869,3934],{"className":3868},[700,701],[573,3870,3872,3931],{"className":3871},[705],[573,3873,3875,3886,3894],{"className":3874,"style":3768},[709],[573,3876,3877,3880],{"style":2821},[573,3878],{"className":3879,"style":2146},[717],[573,3881,3883],{"className":3882},[616],[573,3884,3487],{"className":3885},[616],[573,3887,3888,3891],{"style":2204},[573,3889],{"className":3890,"style":2146},[717],[573,3892],{"className":3893,"style":2212},[2211],[573,3895,3896,3899],{"style":2841},[573,3897],{"className":3898,"style":2146},[717],[573,3900,3902],{"className":3901},[616],[573,3903,3905,3908],{"className":3904},[616],[573,3906,672],{"className":3907},[616],[573,3909,3911],{"className":3910},[696],[573,3912,3914],{"className":3913},[700],[573,3915,3917],{"className":3916},[705],[573,3918,3920],{"className":3919,"style":979},[709],[573,3921,3922,3925],{"style":982},[573,3923],{"className":3924,"style":718},[717],[573,3926,3928],{"className":3927},[722,723,724,725],[573,3929,947],{"className":3930},[616,725],[573,3932,733],{"className":3933},[732],[573,3935,3937],{"className":3936},[705],[573,3938,3940],{"className":3939,"style":2920},[709],[573,3941],{},[573,3943],{"className":3944},[2296,2126],[573,3946],{"className":3947,"style":1084},[1083],[573,3949,2704],{"className":3950},[1088],[573,3952],{"className":3953,"style":1084},[1083],[573,3955,3957,3960,4051,4054,4057],{"className":3956},[607],[573,3958],{"className":3959,"style":3749},[611],[573,3961,3963,3966,4048],{"className":3962},[616],[573,3964],{"className":3965},[2125,2126],[573,3967,3969],{"className":3968},[1984],[573,3970,3972,4040],{"className":3971},[700,701],[573,3973,3975,4037],{"className":3974},[705],[573,3976,3978,3989,3997],{"className":3977,"style":3768},[709],[573,3979,3980,3983],{"style":2821},[573,3981],{"className":3982,"style":2146},[717],[573,3984,3986],{"className":3985},[616],[573,3987,3516],{"className":3988},[616],[573,3990,3991,3994],{"style":2204},[573,3992],{"className":3993,"style":2146},[717],[573,3995],{"className":3996,"style":2212},[2211],[573,3998,3999,4002],{"style":2841},[573,4000],{"className":4001,"style":2146},[717],[573,4003,4005,4008],{"className":4004},[616],[573,4006,1051],{"className":4007},[616],[573,4009,4011,4014],{"className":4010},[616],[573,4012,3030],{"className":4013},[616],[573,4015,4017],{"className":4016},[696],[573,4018,4020],{"className":4019},[700],[573,4021,4023],{"className":4022},[705],[573,4024,4026],{"className":4025,"style":979},[709],[573,4027,4028,4031],{"style":982},[573,4029],{"className":4030,"style":718},[717],[573,4032,4034],{"className":4033},[722,723,724,725],[573,4035,947],{"className":4036},[616,725],[573,4038,733],{"className":4039},[732],[573,4041,4043],{"className":4042},[705],[573,4044,4046],{"className":4045,"style":2920},[709],[573,4047],{},[573,4049],{"className":4050},[2296,2126],[573,4052],{"className":4053,"style":1276},[1083],[573,4055,1255],{"className":4056},[1280],[573,4058],{"className":4059,"style":1276},[1083],[573,4061,4063,4066,4069,4075,4079,4082,4085],{"className":4062},[607],[573,4064],{"className":4065,"style":1738},[611],[573,4067,1742],{"className":4068},[616],[573,4070,4072],{"className":4071},[616],[573,4073,1063],{"className":4074},[1136],[573,4076,4078],{"className":4077},[616],"24",[573,4080],{"className":4081,"style":1084},[1083],[573,4083,2704],{"className":4084},[1088],[573,4086],{"className":4087,"style":1084},[1083],[573,4089,4091,4094,4097,4100,4103],{"className":4090},[607],[573,4092],{"className":4093,"style":1098},[611],[573,4095,672],{"className":4096},[616],[573,4098],{"className":4099,"style":1084},[1083],[573,4101,2704],{"className":4102},[1088],[573,4104],{"className":4105,"style":1084},[1083],[573,4107,4109,4112,4115,4121,4124,4127,4130],{"className":4108},[607],[573,4110],{"className":4111,"style":1738},[611],[573,4113,3030],{"className":4114},[616],[573,4116,4118],{"className":4117},[616],[573,4119,1063],{"className":4120},[1136],[573,4122,1051],{"className":4123},[616],[573,4125],{"className":4126,"style":1276},[1083],[573,4128,1255],{"className":4129},[1280],[573,4131],{"className":4132,"style":1276},[1083],[573,4134,4136,4139,4142,4148],{"className":4135},[607],[573,4137],{"className":4138,"style":1738},[611],[573,4140,1909],{"className":4141},[616],[573,4143,4145],{"className":4144},[616],[573,4146,1063],{"className":4147},[1136],[573,4149,4151],{"className":4150},[616],"34",[565,4153,3033,4154,3107,4182,4219,4220,4259],{},[573,4155,4157,4170],{"className":4156},[576],[573,4158,4160],{"className":4159},[580],[582,4161,4162],{"xmlns":584},[586,4163,4164,4168],{},[589,4165,4166],{},[670,4167,947],{},[596,4169,947],{"encoding":598},[573,4171,4173],{"className":4172,"ariaHidden":603},[602],[573,4174,4176,4179],{"className":4175},[607],[573,4177],{"className":4178,"style":1290},[611],[573,4180,947],{"className":4181},[616],[573,4183,4185,4198],{"className":4184},[576],[573,4186,4188],{"className":4187},[580],[582,4189,4190],{"xmlns":584},[586,4191,4192,4196],{},[589,4193,4194],{},[670,4195,1768],{},[596,4197,1771],{"encoding":598},[573,4199,4201],{"className":4200,"ariaHidden":603},[602],[573,4202,4204,4207,4210,4216],{"className":4203},[607],[573,4205],{"className":4206,"style":1738},[611],[573,4208,1662],{"className":4209},[616],[573,4211,4213],{"className":4212},[616],[573,4214,1063],{"className":4215},[1136],[573,4217,1793],{"className":4218},[616],". Das Modell wird auf dem ",[573,4221,4223,4241],{"className":4222},[576],[573,4224,4226],{"className":4225},[580],[582,4227,4228],{"xmlns":584},[586,4229,4230,4238],{},[589,4231,4232,4234,4236],{},[670,4233,1662],{},[1058,4235,1458],{},[592,4237,1668],{"mathvariant":1667},[596,4239,4240],{"encoding":598},"5\\,\\%",[573,4242,4244],{"className":4243,"ariaHidden":603},[602],[573,4245,4247,4250,4253,4256],{"className":4246},[607],[573,4248],{"className":4249,"style":1699},[611],[573,4251,1662],{"className":4252},[616],[573,4254],{"className":4255,"style":1706},[1083],[573,4257,1668],{"className":4258},[616],"-Niveau verworfen.",[560,4261,4263],{"id":4262},"typische-fehler","Typische Fehler",[4265,4266,4267,4271,4303,4387],"ul",{},[4268,4269,4270],"li",{},"Durch die beobachtete statt durch die erwartete Häufigkeit teilen.",[4268,4272,4273,4274,4302],{},"Mit relativen Häufigkeiten statt mit absoluten Anzahlen rechnen. Die Testgröße hängt von ",[573,4275,4277,4290],{"className":4276},[576],[573,4278,4280],{"className":4279},[580],[582,4281,4282],{"xmlns":584},[586,4283,4284,4288],{},[589,4285,4286],{},[592,4287,594],{},[596,4289,594],{"encoding":598},[573,4291,4293],{"className":4292,"ariaHidden":603},[602],[573,4294,4296,4299],{"className":4295},[607],[573,4297],{"className":4298,"style":612},[611],[573,4300,594],{"className":4301},[616,617]," ab.",[4268,4304,4305,4306,4357,4358,4386],{},"Die Freiheitsgrade falsch zählen: Es sind ",[573,4307,4309,4327],{"className":4308},[576],[573,4310,4312],{"className":4311},[580],[582,4313,4314],{"xmlns":584},[586,4315,4316,4324],{},[589,4317,4318,4320,4322],{},[592,4319,633],{},[1046,4321,1048],{},[670,4323,1051],{},[596,4325,4326],{"encoding":598},"k - 1",[573,4328,4330,4348],{"className":4329,"ariaHidden":603},[602],[573,4331,4333,4336,4339,4342,4345],{"className":4332},[607],[573,4334],{"className":4335,"style":1076},[611],[573,4337,633],{"className":4338,"style":649},[616,617],[573,4340],{"className":4341,"style":1084},[1083],[573,4343,1048],{"className":4344},[1088],[573,4346],{"className":4347,"style":1084},[1083],[573,4349,4351,4354],{"className":4350},[607],[573,4352],{"className":4353,"style":1290},[611],[573,4355,1051],{"className":4356},[616],", nicht ",[573,4359,4361,4374],{"className":4360},[576],[573,4362,4364],{"className":4363},[580],[582,4365,4366],{"xmlns":584},[586,4367,4368,4372],{},[589,4369,4370],{},[592,4371,633],{},[596,4373,633],{"encoding":598},[573,4375,4377],{"className":4376,"ariaHidden":603},[602],[573,4378,4380,4383],{"className":4379},[607],[573,4381],{"className":4382,"style":645},[611],[573,4384,633],{"className":4385,"style":649},[616,617],", und für jeden geschätzten Parameter einer weniger.",[4268,4388,4389,4390,4418],{},"Den Test trotz erwarteter Häufigkeiten unter ",[573,4391,4393,4406],{"className":4392},[576],[573,4394,4396],{"className":4395},[580],[582,4397,4398],{"xmlns":584},[586,4399,4400,4404],{},[589,4401,4402],{},[670,4403,1662],{},[596,4405,1662],{"encoding":598},[573,4407,4409],{"className":4408,"ariaHidden":603},[602],[573,4410,4412,4415],{"className":4411},[607],[573,4413],{"className":4414,"style":1290},[611],[573,4416,1662],{"className":4417},[616]," anwenden, ohne Klassen zusammenzufassen.",{"title":4420,"searchDepth":4421,"depth":4421,"links":4422},"",2,[4423,4424,4425],{"id":562,"depth":4421,"text":563},{"id":2317,"depth":4421,"text":2318},{"id":4262,"depth":4421,"text":4263},[4427,4429,4431,4434,4437,4439,4444,4446,4448,4451,4454],{"lhs":4428,"rhs":2336},"15 + 22 + 18 + 25 + 17 + 23",{"lhs":4430,"rhs":2450},"120 \u002F 6",{"lhs":4432,"rhs":4433},"((15-20)^2 + (22-20)^2 + (18-20)^2 + (25-20)^2 + (17-20)^2 + (23-20)^2) \u002F 20","3.8",{"lhs":4435,"rhs":4436},"round(1 - sum(map(0:999, f(k) = ((k + 0.5)\u002F1000*11.07)^1.5 * exp(-(k + 0.5)\u002F1000*11.07\u002F2) \u002F (2^2.5*gamma(2.5)))) * 11.07\u002F1000, 3)","0.05",{"lhs":4438,"rhs":4433},"(15^2 + 22^2 + 18^2 + 25^2 + 17^2 + 23^2) \u002F 20 - 120",{"lhs":4440,"rhs":4441,"where":4442},"((x - n*p)^2 \u002F (n*p) + (n - x - n*(1-p))^2 \u002F (n*(1-p)))","(x^2 \u002F (n*p) + (n - x)^2 \u002F (n*(1-p))) - n",{"p":4443},0.3,{"lhs":4445,"rhs":3458},"200 * 0.5",{"lhs":4447,"rhs":3428},"118 + 60 + 22",{"lhs":4449,"rhs":4450},"18^2 \u002F 100","3.24",{"lhs":4452,"rhs":4453},"18^2 \u002F 40","8.1",{"lhs":4455,"rhs":4456},"(118 - 100)^2 \u002F 100 + (60 - 60)^2 \u002F 60 + (22 - 40)^2 \u002F 40","11.34","n p_i \\geq 5 \\text{ für alle } i \\text{ (Faustregel)},\\ p_1 + \\ldots + p_k = 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>5\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n p_i \\geq 5\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:0.8304em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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:0.3117em;\">\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 mathnormal mtight\">i\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=\"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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">5\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">für alle\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">i\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:0.6595em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">(Faustregel)\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>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_1 + \\ldots + p_k = 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:0.7778em;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>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\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:0.3361em;\">\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 mathnormal mtight\" style=\"margin-right:0.0315em;\">k\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=\"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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","chi-square-test","\\chi^2 = \\sum_{i=1}^{k} \\frac{(N_i - n p_i)^2}{n p_i}","\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>χ\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmfrac>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>N\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\chi^2 = \\sum_{i=1}^{k} \\frac{(N_i - n p_i)^2}{n p_i}\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:1.0585em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">χ\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\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=\"mord mtight\">2\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:3.1138em;vertical-align:-1.2777em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.8361em;\">\u003Cspan style=\"top:-1.8723em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\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:1.2777em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4911em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\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:0.3117em;\">\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 mathnormal mtight\">i\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>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\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=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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:0.3117em;\">\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 mathnormal mtight\">i\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=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\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=\"mord mtight\">2\u003C\u002Fspan>\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:0.8804em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fchi-quadrat-anpassungstest",[],[4470,4471,4472],"hypothesis-test","relative-frequency","chi-square-independence",{"title":548,"description":4420},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fchi-quadrat-anpassungstest","Der Chi-Quadrat-Anpassungstest prüft, ob beobachtete Häufigkeiten zu einer vermuteten Verteilung passen.",[4477,4478,4479,4480,4481],"hypothesentest","chi-quadrat-verteilung","anpassungstest","häufigkeiten","freiheitsgrade",[4483,4486,4489,4493,4496,4499],{"symbol":950,"meaning":4484,"symbolHtml":4485},"Wert der Testgröße","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>χ\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\chi^2\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:1.0085em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">χ\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\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=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":633,"meaning":4487,"symbolHtml":4488},"Anzahl der Klassen (Kategorien)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4490,"meaning":4491,"symbolHtml":4492},"N_i","beobachtete Häufigkeit in Klasse i","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>N\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">N_i\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:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\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":594,"meaning":4494,"symbolHtml":4495},"Stichprobenumfang, Summe aller N_i","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1189,"meaning":4497,"symbolHtml":4498},"Wahrscheinlichkeit der Klasse i 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>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_i\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:0.3117em;\">\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 mathnormal mtight\">i\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":797,"meaning":4500,"symbolHtml":4501},"erwartete Häufigkeit in Klasse i unter H₀","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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