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Die Forderung",[569,876,879],{"className":877},[878],"katex-display",[569,880,882,928],{"className":881},[572],[569,883,885],{"className":884},[576],[578,886,888],{"xmlns":580,"display":887},"block",[582,889,890,925],{},[585,891,892,894,896,920,923],{},[588,893,637],{},[639,895,641],{},[643,897,898],{},[646,899,900,918],{},[585,901,902,904,908,910,912,914,916],{},[588,903,565],{},[905,906,907],"mtext",{}," ",[639,909,655],{"stretchy":654},[657,911,659],{},[639,913,662],{},[588,915,565],{},[639,917,667],{"stretchy":654},[588,919,670],{},[639,921,922],{},"≤",[588,924,590],{},[592,926,927],{"encoding":594},"z \\cdot \\sqrt{\\frac{p\\,(1-p)}{n}} \\leq d",[569,929,931,949,1111],{"className":930,"ariaHidden":599},[598],[569,932,934,937,940,943,946],{"className":933},[603],[569,935],{"className":936,"style":683},[607],[569,938,637],{"className":939,"style":687},[612,613],[569,941],{"className":942,"style":692},[691],[569,944,641],{"className":945},[696],[569,947],{"className":948,"style":692},[691],[569,950,952,956,1100,1104,1108],{"className":951},[603],[569,953],{"className":954,"style":955},[607],"height:2.44em;vertical-align:-0.7356em;",[569,957,959],{"className":958},[612,710],[569,960,962,1091],{"className":961},[714,715],[569,963,965,1088],{"className":964},[719],[569,966,969,1071],{"className":967,"style":968},[723],"height:1.7044em;",[569,970,973,977],{"className":971,"style":972},[728],"top:-4.4em;",[569,974],{"className":975,"style":976},[733],"height:4.4em;",[569,978,980],{"className":979,"style":738},[612],[569,981,983,986,1068],{"className":982},[612],[569,984],{"className":985},[745,746],[569,987,989],{"className":988},[646],[569,990,992,1059],{"className":991},[714,715],[569,993,995,1056],{"className":994},[719],[569,996,999,1011,1019],{"className":997,"style":998},[723],"height:1.427em;",[569,1000,1002,1005],{"style":1001},"top:-2.314em;",[569,1003],{"className":1004,"style":766},[733],[569,1006,1008],{"className":1007},[612],[569,1009,670],{"className":1010},[612,613],[569,1012,1013,1016],{"style":782},[569,1014],{"className":1015,"style":766},[733],[569,1017],{"className":1018,"style":790},[789],[569,1020,1022,1025],{"style":1021},"top:-3.677em;",[569,1023],{"className":1024,"style":766},[733],[569,1026,1028,1031,1035,1038,1041,1044,1047,1050,1053],{"className":1027},[612],[569,1029,565],{"className":1030},[612,613],[569,1032],{"className":1033,"style":1034},[691],"margin-right:0.1667em;",[569,1036,655],{"className":1037},[745],[569,1039,659],{"className":1040},[612],[569,1042],{"className":1043,"style":692},[691],[569,1045,662],{"className":1046},[696],[569,1048],{"className":1049,"style":692},[691],[569,1051,565],{"className":1052},[612,613],[569,1054,667],{"className":1055},[821],[569,1057,826],{"className":1058},[825],[569,1060,1062],{"className":1061},[719],[569,1063,1066],{"className":1064,"style":1065},[723],"height:0.686em;",[569,1067],{},[569,1069],{"className":1070},[821,746],[569,1072,1074,1077],{"style":1073},"top:-3.6644em;",[569,1075],{"className":1076,"style":976},[733],[569,1078,1081],{"className":1079,"style":1080},[848],"min-width:1.02em;height:2.48em;",[851,1082,1085],{"xmlns":853,"width":854,"height":1083,"viewBox":1084,"preserveAspectRatio":857},"2.48em","0 0 400000 2592",[859,1086],{"d":1087},"M424,2478\nc-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514\nc0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20\ns-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121\ns209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081\nl0 -0c4,-6.7,10,-10,18,-10 H400000\nv40H1014.6\ns-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185\nc-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2z M1001 80\nh400000v40h-400000z",[569,1089,826],{"className":1090},[825],[569,1092,1094],{"className":1093},[719],[569,1095,1098],{"className":1096,"style":1097},[723],"height:0.7356em;",[569,1099],{},[569,1101],{"className":1102,"style":1103},[691],"margin-right:0.2778em;",[569,1105,922],{"className":1106},[1107],"mrel",[569,1109],{"className":1110,"style":1103},[691],[569,1112,1114,1117],{"className":1113},[603],[569,1115],{"className":1116,"style":608},[607],[569,1118,590],{"className":1119},[612,613],[565,1121,1122,1123,1152,1153,1156,1157,1192,1193,1260,1261,1291],{},"löst man nach ",[569,1124,1126,1139],{"className":1125},[572],[569,1127,1129],{"className":1128},[576],[578,1130,1131],{"xmlns":580},[582,1132,1133,1137],{},[585,1134,1135],{},[588,1136,670],{},[592,1138,670],{"encoding":594},[569,1140,1142],{"className":1141,"ariaHidden":599},[598],[569,1143,1145,1149],{"className":1144},[603],[569,1146],{"className":1147,"style":1148},[607],"height:0.4306em;",[569,1150,670],{"className":1151},[612,613]," auf und erhält die Formel. Das Ergebnis wird immer ",[616,1154,1155],{},"aufgerundet",". Die Formel nutzt die Normalverteilungsnäherung und setzt voraus, dass ",[569,1158,1160,1176],{"className":1159},[572],[569,1161,1163],{"className":1162},[576],[578,1164,1165],{"xmlns":580},[582,1166,1167,1173],{},[585,1168,1169,1171],{},[588,1170,670],{},[588,1172,565],{},[592,1174,1175],{"encoding":594},"n p",[569,1177,1179],{"className":1178,"ariaHidden":599},[598],[569,1180,1182,1186,1189],{"className":1181},[603],[569,1183],{"className":1184,"style":1185},[607],"height:0.625em;vertical-align:-0.1944em;",[569,1187,670],{"className":1188},[612,613],[569,1190,565],{"className":1191},[612,613]," und ",[569,1194,1196,1220],{"className":1195},[572],[569,1197,1199],{"className":1198},[576],[578,1200,1201],{"xmlns":580},[582,1202,1203,1217],{},[585,1204,1205,1207,1209,1211,1213,1215],{},[588,1206,670],{},[639,1208,655],{"stretchy":654},[657,1210,659],{},[639,1212,662],{},[588,1214,565],{},[639,1216,667],{"stretchy":654},[592,1218,1219],{"encoding":594},"n(1-p)",[569,1221,1223,1248],{"className":1222,"ariaHidden":599},[598],[569,1224,1226,1230,1233,1236,1239,1242,1245],{"className":1225},[603],[569,1227],{"className":1228,"style":1229},[607],"height:1em;vertical-align:-0.25em;",[569,1231,670],{"className":1232},[612,613],[569,1234,655],{"className":1235},[745],[569,1237,659],{"className":1238},[612],[569,1240],{"className":1241,"style":692},[691],[569,1243,662],{"className":1244},[696],[569,1246],{"className":1247,"style":692},[691],[569,1249,1251,1254,1257],{"className":1250},[603],[569,1252],{"className":1253,"style":1229},[607],[569,1255,565],{"className":1256},[612,613],[569,1258,667],{"className":1259},[821]," nicht zu klein sind (Faustregel: beide mindestens ",[569,1262,1264,1278],{"className":1263},[572],[569,1265,1267],{"className":1266},[576],[578,1268,1269],{"xmlns":580},[582,1270,1271,1276],{},[585,1272,1273],{},[657,1274,1275],{},"10",[592,1277,1275],{"encoding":594},[569,1279,1281],{"className":1280,"ariaHidden":599},[598],[569,1282,1284,1288],{"className":1283},[603],[569,1285],{"className":1286,"style":1287},[607],"height:0.6444em;",[569,1289,1275],{"className":1290},[612],").",[565,1293,1294,1295,1323,1324,1391,1392,1458,1459,1561,1562,1755],{},"Der Anteil ",[569,1296,1298,1311],{"className":1297},[572],[569,1299,1301],{"className":1300},[576],[578,1302,1303],{"xmlns":580},[582,1304,1305,1309],{},[585,1306,1307],{},[588,1308,565],{},[592,1310,565],{"encoding":594},[569,1312,1314],{"className":1313,"ariaHidden":599},[598],[569,1315,1317,1320],{"className":1316},[603],[569,1318],{"className":1319,"style":1185},[607],[569,1321,565],{"className":1322},[612,613]," ist vor der Umfrage unbekannt. Hat man eine Vorabschätzung (z.B. aus einer früheren Umfrage), setzt man sie ein. Sonst nimmt man den ungünstigsten Fall ",[569,1325,1327,1347],{"className":1326},[572],[569,1328,1330],{"className":1329},[576],[578,1331,1332],{"xmlns":580},[582,1333,1334,1344],{},[585,1335,1336,1338,1341],{},[588,1337,565],{},[639,1339,1340],{},"=",[657,1342,1343],{},"0,5",[592,1345,1346],{"encoding":594},"p = 0{,}5",[569,1348,1350,1368],{"className":1349,"ariaHidden":599},[598],[569,1351,1353,1356,1359,1362,1365],{"className":1352},[603],[569,1354],{"className":1355,"style":1185},[607],[569,1357,565],{"className":1358},[612,613],[569,1360],{"className":1361,"style":1103},[691],[569,1363,1340],{"className":1364},[1107],[569,1366],{"className":1367,"style":1103},[691],[569,1369,1371,1375,1379,1387],{"className":1370},[603],[569,1372],{"className":1373,"style":1374},[607],"height:0.8389em;vertical-align:-0.1944em;",[569,1376,1378],{"className":1377},[612],"0",[569,1380,1382],{"className":1381},[612],[569,1383,1386],{"className":1384},[1385],"mpunct",",",[569,1388,1390],{"className":1389},[612],"5",", denn ",[569,1393,1395,1419],{"className":1394},[572],[569,1396,1398],{"className":1397},[576],[578,1399,1400],{"xmlns":580},[582,1401,1402,1416],{},[585,1403,1404,1406,1408,1410,1412,1414],{},[588,1405,565],{},[639,1407,655],{"stretchy":654},[657,1409,659],{},[639,1411,662],{},[588,1413,565],{},[639,1415,667],{"stretchy":654},[592,1417,1418],{"encoding":594},"p(1-p)",[569,1420,1422,1446],{"className":1421,"ariaHidden":599},[598],[569,1423,1425,1428,1431,1434,1437,1440,1443],{"className":1424},[603],[569,1426],{"className":1427,"style":1229},[607],[569,1429,565],{"className":1430},[612,613],[569,1432,655],{"className":1433},[745],[569,1435,659],{"className":1436},[612],[569,1438],{"className":1439,"style":692},[691],[569,1441,662],{"className":1442},[696],[569,1444],{"className":1445,"style":692},[691],[569,1447,1449,1452,1455],{"className":1448},[603],[569,1450],{"className":1451,"style":1229},[607],[569,1453,565],{"className":1454},[612,613],[569,1456,667],{"className":1457},[821]," ist dort am größten (",[569,1460,1462,1481],{"className":1461},[572],[569,1463,1465],{"className":1464},[576],[578,1466,1467],{"xmlns":580},[582,1468,1469,1478],{},[585,1470,1471],{},[646,1472,1473,1475],{},[657,1474,659],{},[657,1476,1477],{},"4",[592,1479,1480],{"encoding":594},"\\frac{1}{4}",[569,1482,1484],{"className":1483,"ariaHidden":599},[598],[569,1485,1487,1491],{"className":1486},[603],[569,1488],{"className":1489,"style":1490},[607],"height:1.1901em;vertical-align:-0.345em;",[569,1492,1494,1497,1558],{"className":1493},[612],[569,1495],{"className":1496},[745,746],[569,1498,1500],{"className":1499},[646],[569,1501,1503,1550],{"className":1502},[714,715],[569,1504,1506,1547],{"className":1505},[719],[569,1507,1510,1524,1532],{"className":1508,"style":1509},[723],"height:0.8451em;",[569,1511,1512,1515],{"style":762},[569,1513],{"className":1514,"style":766},[733],[569,1516,1518],{"className":1517},[770,771,772,773],[569,1519,1521],{"className":1520},[612,773],[569,1522,1477],{"className":1523},[612,773],[569,1525,1526,1529],{"style":782},[569,1527],{"className":1528,"style":766},[733],[569,1530],{"className":1531,"style":790},[789],[569,1533,1535,1538],{"style":1534},"top:-3.394em;",[569,1536],{"className":1537,"style":766},[733],[569,1539,1541],{"className":1540},[770,771,772,773],[569,1542,1544],{"className":1543},[612,773],[569,1545,659],{"className":1546},[612,773],[569,1548,826],{"className":1549},[825],[569,1551,1553],{"className":1552},[719],[569,1554,1556],{"className":1555,"style":833},[723],[569,1557],{},[569,1559],{"className":1560},[821,746],"). Dann gilt einfach ",[569,1563,1565,1604],{"className":1564},[572],[569,1566,1568],{"className":1567},[576],[578,1569,1570],{"xmlns":580},[582,1571,1572,1601],{},[585,1573,1574,1576,1579],{},[588,1575,670],{},[639,1577,1578],{},"≥",[1580,1581,1582,1599],"msup",{},[585,1583,1584,1586,1597],{},[639,1585,655],{"fence":599},[646,1587,1588,1590],{},[588,1589,637],{},[585,1591,1592,1595],{},[657,1593,1594],{},"2",[588,1596,590],{},[639,1598,667],{"fence":599},[657,1600,1594],{},[592,1602,1603],{"encoding":594},"n \\geq \\left(\\frac{z}{2d}\\right)^2",[569,1605,1607,1626],{"className":1606,"ariaHidden":599},[598],[569,1608,1610,1614,1617,1620,1623],{"className":1609},[603],[569,1611],{"className":1612,"style":1613},[607],"height:0.7719em;vertical-align:-0.136em;",[569,1615,670],{"className":1616},[612,613],[569,1618],{"className":1619,"style":1103},[691],[569,1621,1578],{"className":1622},[1107],[569,1624],{"className":1625,"style":1103},[691],[569,1627,1629,1633],{"className":1628},[603],[569,1630],{"className":1631,"style":1632},[607],"height:1.404em;vertical-align:-0.35em;",[569,1634,1637,1728],{"className":1635},[1636],"minner",[569,1638,1640,1650,1722],{"className":1639},[1636],[569,1641,1645],{"className":1642,"style":1644},[745,1643],"delimcenter","top:0em;",[569,1646,655],{"className":1647},[1648,1649],"delimsizing","size1",[569,1651,1653,1656,1719],{"className":1652},[612],[569,1654],{"className":1655},[745,746],[569,1657,1659],{"className":1658},[646],[569,1660,1662,1711],{"className":1661},[714,715],[569,1663,1665,1708],{"className":1664},[719],[569,1666,1669,1686,1694],{"className":1667,"style":1668},[723],"height:0.6954em;",[569,1670,1671,1674],{"style":762},[569,1672],{"className":1673,"style":766},[733],[569,1675,1677],{"className":1676},[770,771,772,773],[569,1678,1680,1683],{"className":1679},[612,773],[569,1681,1594],{"className":1682},[612,773],[569,1684,590],{"className":1685},[612,613,773],[569,1687,1688,1691],{"style":782},[569,1689],{"className":1690,"style":766},[733],[569,1692],{"className":1693,"style":790},[789],[569,1695,1696,1699],{"style":1534},[569,1697],{"className":1698,"style":766},[733],[569,1700,1702],{"className":1701},[770,771,772,773],[569,1703,1705],{"className":1704},[612,773],[569,1706,637],{"className":1707,"style":687},[612,613,773],[569,1709,826],{"className":1710},[825],[569,1712,1714],{"className":1713},[719],[569,1715,1717],{"className":1716,"style":833},[723],[569,1718],{},[569,1720],{"className":1721},[821,746],[569,1723,1725],{"className":1724,"style":1644},[821,1643],[569,1726,667],{"className":1727},[1648,1649],[569,1729,1732],{"className":1730},[1731],"msupsub",[569,1733,1735],{"className":1734},[714],[569,1736,1738],{"className":1737},[719],[569,1739,1742],{"className":1740,"style":1741},[723],"height:1.054em;",[569,1743,1745,1749],{"style":1744},"top:-3.3029em;margin-right:0.05em;",[569,1746],{"className":1747,"style":1748},[733],"height:2.7em;",[569,1750,1752],{"className":1751},[770,771,772,773],[569,1753,1594],{"className":1754},[612,773],".",[565,1757,1758,1759,1762,1763,1794],{},"Für einen ",[616,1760,1761],{},"Mittelwert"," mit bekannter (oder geschätzter) Standardabweichung ",[569,1764,1766,1781],{"className":1765},[572],[569,1767,1769],{"className":1768},[576],[578,1770,1771],{"xmlns":580},[582,1772,1773,1778],{},[585,1774,1775],{},[588,1776,1777],{},"σ",[592,1779,1780],{"encoding":594},"\\sigma",[569,1782,1784],{"className":1783,"ariaHidden":599},[598],[569,1785,1787,1790],{"className":1786},[603],[569,1788],{"className":1789,"style":1148},[607],[569,1791,1777],{"className":1792,"style":1793},[612,613],"margin-right:0.0359em;"," lautet die entsprechende Formel",[569,1796,1798],{"className":1797},[878],[569,1799,1801,1839],{"className":1800},[572],[569,1802,1804],{"className":1803},[576],[578,1805,1806],{"xmlns":580,"display":887},[582,1807,1808,1836],{},[585,1809,1810,1812,1814],{},[588,1811,670],{},[639,1813,1578],{},[1580,1815,1816,1834],{},[585,1817,1818,1820,1832],{},[639,1819,655],{"fence":599},[646,1821,1822,1830],{},[585,1823,1824,1826,1828],{},[588,1825,637],{},[639,1827,641],{},[588,1829,1777],{},[588,1831,590],{},[639,1833,667],{"fence":599},[657,1835,1594],{},[592,1837,1838],{"encoding":594},"n \\geq \\left(\\frac{z \\cdot \\sigma}{d}\\right)^2",[569,1840,1842,1860],{"className":1841,"ariaHidden":599},[598],[569,1843,1845,1848,1851,1854,1857],{"className":1844},[603],[569,1846],{"className":1847,"style":1613},[607],[569,1849,670],{"className":1850},[612,613],[569,1852],{"className":1853,"style":1103},[691],[569,1855,1578],{"className":1856},[1107],[569,1858],{"className":1859,"style":1103},[691],[569,1861,1863,1867],{"className":1862},[603],[569,1864],{"className":1865,"style":1866},[607],"height:2.04em;vertical-align:-0.686em;",[569,1868,1870,1961],{"className":1869},[1636],[569,1871,1873,1880,1955],{"className":1872},[1636],[569,1874,1876],{"className":1875,"style":1644},[745,1643],[569,1877,655],{"className":1878},[1648,1879],"size2",[569,1881,1883,1886,1952],{"className":1882},[612],[569,1884],{"className":1885},[745,746],[569,1887,1889],{"className":1888},[646],[569,1890,1892,1944],{"className":1891},[714,715],[569,1893,1895,1941],{"className":1894},[719],[569,1896,1899,1910,1918],{"className":1897,"style":1898},[723],"height:1.1215em;",[569,1900,1901,1904],{"style":1001},[569,1902],{"className":1903,"style":766},[733],[569,1905,1907],{"className":1906},[612],[569,1908,590],{"className":1909},[612,613],[569,1911,1912,1915],{"style":782},[569,1913],{"className":1914,"style":766},[733],[569,1916],{"className":1917,"style":790},[789],[569,1919,1920,1923],{"style":1021},[569,1921],{"className":1922,"style":766},[733],[569,1924,1926,1929,1932,1935,1938],{"className":1925},[612],[569,1927,637],{"className":1928,"style":687},[612,613],[569,1930],{"className":1931,"style":692},[691],[569,1933,641],{"className":1934},[696],[569,1936],{"className":1937,"style":692},[691],[569,1939,1777],{"className":1940,"style":1793},[612,613],[569,1942,826],{"className":1943},[825],[569,1945,1947],{"className":1946},[719],[569,1948,1950],{"className":1949,"style":1065},[723],[569,1951],{},[569,1953],{"className":1954},[821,746],[569,1956,1958],{"className":1957,"style":1644},[821,1643],[569,1959,667],{"className":1960},[1648,1879],[569,1962,1964],{"className":1963},[1731],[569,1965,1967],{"className":1966},[714],[569,1968,1970],{"className":1969},[719],[569,1971,1974],{"className":1972,"style":1973},[723],"height:1.354em;",[569,1975,1977,1980],{"style":1976},"top:-3.6029em;margin-right:0.05em;",[569,1978],{"className":1979,"style":1748},[733],[569,1981,1983],{"className":1982},[770,771,772,773],[569,1984,1594],{"className":1985},[612,773],[565,1987,1988],{},"Die nötige Stichprobe wächst mit dem Quadrat der Genauigkeit: Halbe Fehlerspanne bedeutet vierfachen Umfang.",[560,1990,1992],{"id":1991},"beispiele","Beispiele",[565,1994,1995,1996,2039,2040,2077,2078,2137],{},"Ein Meinungsforschungsinstitut möchte einen Stimmenanteil mit ",[569,1997,1999,2020],{"className":1998},[572],[569,2000,2002],{"className":2001},[576],[578,2003,2004],{"xmlns":580},[582,2005,2006,2017],{},[585,2007,2008,2011,2013],{},[657,2009,2010],{},"95",[905,2012,907],{},[588,2014,2016],{"mathvariant":2015},"normal","%",[592,2018,2019],{"encoding":594},"95\\,\\%",[569,2021,2023],{"className":2022,"ariaHidden":599},[598],[569,2024,2026,2030,2033,2036],{"className":2025},[603],[569,2027],{"className":2028,"style":2029},[607],"height:0.8056em;vertical-align:-0.0556em;",[569,2031,2010],{"className":2032},[612],[569,2034],{"className":2035,"style":1034},[691],[569,2037,2016],{"className":2038},[612]," Sicherheit auf ",[569,2041,2043,2061],{"className":2042},[572],[569,2044,2046],{"className":2045},[576],[578,2047,2048],{"xmlns":580},[582,2049,2050,2058],{},[585,2051,2052,2055],{},[639,2053,2054],{},"±",[657,2056,2057],{},"3",[592,2059,2060],{"encoding":594},"\\pm 3",[569,2062,2064],{"className":2063,"ariaHidden":599},[598],[569,2065,2067,2071,2074],{"className":2066},[603],[569,2068],{"className":2069,"style":2070},[607],"height:0.7278em;vertical-align:-0.0833em;",[569,2072,2054],{"className":2073},[612],[569,2075,2057],{"className":2076},[612]," Prozentpunkte genau bestimmen. Ohne Vorwissen (",[569,2079,2081,2098],{"className":2080},[572],[569,2082,2084],{"className":2083},[576],[578,2085,2086],{"xmlns":580},[582,2087,2088,2096],{},[585,2089,2090,2092,2094],{},[588,2091,565],{},[639,2093,1340],{},[657,2095,1343],{},[592,2097,1346],{"encoding":594},[569,2099,2101,2119],{"className":2100,"ariaHidden":599},[598],[569,2102,2104,2107,2110,2113,2116],{"className":2103},[603],[569,2105],{"className":2106,"style":1185},[607],[569,2108,565],{"className":2109},[612,613],[569,2111],{"className":2112,"style":1103},[691],[569,2114,1340],{"className":2115},[1107],[569,2117],{"className":2118,"style":1103},[691],[569,2120,2122,2125,2128,2134],{"className":2121},[603],[569,2123],{"className":2124,"style":1374},[607],[569,2126,1378],{"className":2127},[612],[569,2129,2131],{"className":2130},[612],[569,2132,1386],{"className":2133},[1385],[569,2135,1390],{"className":2136},[612],"):",[569,2139,2141],{"className":2140},[878],[569,2142,2144,2204],{"className":2143},[572],[569,2145,2147],{"className":2146},[576],[578,2148,2149],{"xmlns":580,"display":887},[582,2150,2151,2201],{},[585,2152,2153,2155,2157,2180,2183,2186,2189,2192,2194,2196,2198],{},[588,2154,670],{},[639,2156,1578],{},[646,2158,2159,2173],{},[585,2160,2161,2168,2170],{},[1580,2162,2163,2166],{},[657,2164,2165],{},"1,96",[657,2167,1594],{},[639,2169,641],{},[657,2171,2172],{},"0,25",[1580,2174,2175,2178],{},[657,2176,2177],{},"0,03",[657,2179,1594],{},[639,2181,2182],{},"≈",[657,2184,2185],{},"1067,1",[691,2187],{"width":2188},"1em",[639,2190,2191],{},"⇒",[691,2193],{"width":2188},[588,2195,670],{},[639,2197,1340],{},[657,2199,2200],{},"1068",[592,2202,2203],{"encoding":594},"n \\geq \\frac{1{,}96^2 \\cdot 0{,}25}{0{,}03^2} \\approx 1067{,}1 \\quad \\Rightarrow \\quad n = 1068",[569,2205,2207,2225,2409,2444,2462],{"className":2206,"ariaHidden":599},[598],[569,2208,2210,2213,2216,2219,2222],{"className":2209},[603],[569,2211],{"className":2212,"style":1613},[607],[569,2214,670],{"className":2215},[612,613],[569,2217],{"className":2218,"style":1103},[691],[569,2220,1578],{"className":2221},[1107],[569,2223],{"className":2224,"style":1103},[691],[569,2226,2228,2232,2400,2403,2406],{"className":2227},[603],[569,2229],{"className":2230,"style":2231},[607],"height:2.3715em;vertical-align:-0.8804em;",[569,2233,2235,2238,2397],{"className":2234},[612],[569,2236],{"className":2237},[745,746],[569,2239,2241],{"className":2240},[646],[569,2242,2244,2388],{"className":2243},[714,715],[569,2245,2247,2385],{"className":2246},[719],[569,2248,2251,2302,2310],{"className":2249,"style":2250},[723],"height:1.4911em;",[569,2252,2253,2256],{"style":1001},[569,2254],{"className":2255,"style":766},[733],[569,2257,2259,2262,2268,2271],{"className":2258},[612],[569,2260,1378],{"className":2261},[612],[569,2263,2265],{"className":2264},[612],[569,2266,1386],{"className":2267},[1385],[569,2269,1378],{"className":2270},[612],[569,2272,2274,2277],{"className":2273},[612],[569,2275,2057],{"className":2276},[612],[569,2278,2280],{"className":2279},[1731],[569,2281,2283],{"className":2282},[714],[569,2284,2286],{"className":2285},[719],[569,2287,2290],{"className":2288,"style":2289},[723],"height:0.7401em;",[569,2291,2293,2296],{"style":2292},"top:-2.989em;margin-right:0.05em;",[569,2294],{"className":2295,"style":1748},[733],[569,2297,2299],{"className":2298},[770,771,772,773],[569,2300,1594],{"className":2301},[612,773],[569,2303,2304,2307],{"style":782},[569,2305],{"className":2306,"style":766},[733],[569,2308],{"className":2309,"style":790},[789],[569,2311,2312,2315],{"style":1021},[569,2313],{"className":2314,"style":766},[733],[569,2316,2318,2321,2327,2331,2363,2366,2369,2372,2375,2381],{"className":2317},[612],[569,2319,659],{"className":2320},[612],[569,2322,2324],{"className":2323},[612],[569,2325,1386],{"className":2326},[1385],[569,2328,2330],{"className":2329},[612],"9",[569,2332,2334,2338],{"className":2333},[612],[569,2335,2337],{"className":2336},[612],"6",[569,2339,2341],{"className":2340},[1731],[569,2342,2344],{"className":2343},[714],[569,2345,2347],{"className":2346},[719],[569,2348,2351],{"className":2349,"style":2350},[723],"height:0.8141em;",[569,2352,2354,2357],{"style":2353},"top:-3.063em;margin-right:0.05em;",[569,2355],{"className":2356,"style":1748},[733],[569,2358,2360],{"className":2359},[770,771,772,773],[569,2361,1594],{"className":2362},[612,773],[569,2364],{"className":2365,"style":692},[691],[569,2367,641],{"className":2368},[696],[569,2370],{"className":2371,"style":692},[691],[569,2373,1378],{"className":2374},[612],[569,2376,2378],{"className":2377},[612],[569,2379,1386],{"className":2380},[1385],[569,2382,2384],{"className":2383},[612],"25",[569,2386,826],{"className":2387},[825],[569,2389,2391],{"className":2390},[719],[569,2392,2395],{"className":2393,"style":2394},[723],"height:0.8804em;",[569,2396],{},[569,2398],{"className":2399},[821,746],[569,2401],{"className":2402,"style":1103},[691],[569,2404,2182],{"className":2405},[1107],[569,2407],{"className":2408,"style":1103},[691],[569,2410,2412,2415,2419,2425,2428,2432,2435,2438,2441],{"className":2411},[603],[569,2413],{"className":2414,"style":1374},[607],[569,2416,2418],{"className":2417},[612],"1067",[569,2420,2422],{"className":2421},[612],[569,2423,1386],{"className":2424},[1385],[569,2426,659],{"className":2427},[612],[569,2429],{"className":2430,"style":2431},[691],"margin-right:1em;",[569,2433],{"className":2434,"style":1103},[691],[569,2436,2191],{"className":2437},[1107],[569,2439],{"className":2440,"style":2431},[691],[569,2442],{"className":2443,"style":1103},[691],[569,2445,2447,2450,2453,2456,2459],{"className":2446},[603],[569,2448],{"className":2449,"style":1148},[607],[569,2451,670],{"className":2452},[612,613],[569,2454],{"className":2455,"style":1103},[691],[569,2457,1340],{"className":2458},[1107],[569,2460],{"className":2461,"style":1103},[691],[569,2463,2465,2468],{"className":2464},[603],[569,2466],{"className":2467,"style":1287},[607],[569,2469,2200],{"className":2470},[612],[565,2472,2473,2474,2514],{},"Ist aus früheren Umfragen bekannt, dass der Anteil bei etwa ",[569,2475,2477,2496],{"className":2476},[572],[569,2478,2480],{"className":2479},[576],[578,2481,2482],{"xmlns":580},[582,2483,2484,2493],{},[585,2485,2486,2489,2491],{},[657,2487,2488],{},"20",[905,2490,907],{},[588,2492,2016],{"mathvariant":2015},[592,2494,2495],{"encoding":594},"20\\,\\%",[569,2497,2499],{"className":2498,"ariaHidden":599},[598],[569,2500,2502,2505,2508,2511],{"className":2501},[603],[569,2503],{"className":2504,"style":2029},[607],[569,2506,2488],{"className":2507},[612],[569,2509],{"className":2510,"style":1034},[691],[569,2512,2016],{"className":2513},[612]," liegt:",[569,2516,2518],{"className":2517},[878],[569,2519,2521,2581],{"className":2520},[572],[569,2522,2524],{"className":2523},[576],[578,2525,2526],{"xmlns":580,"display":887},[582,2527,2528,2578],{},[585,2529,2530,2532,2534,2560,2562,2565,2567,2569,2571,2573,2575],{},[588,2531,670],{},[639,2533,1578],{},[646,2535,2536,2554],{},[585,2537,2538,2544,2546,2549,2551],{},[1580,2539,2540,2542],{},[657,2541,2165],{},[657,2543,1594],{},[639,2545,641],{},[657,2547,2548],{},"0,2",[639,2550,641],{},[657,2552,2553],{},"0,8",[1580,2555,2556,2558],{},[657,2557,2177],{},[657,2559,1594],{},[639,2561,2182],{},[657,2563,2564],{},"682,95",[691,2566],{"width":2188},[639,2568,2191],{},[691,2570],{"width":2188},[588,2572,670],{},[639,2574,1340],{},[657,2576,2577],{},"683",[592,2579,2580],{"encoding":594},"n \\geq \\frac{1{,}96^2 \\cdot 0{,}2 \\cdot 0{,}8}{0{,}03^2} \\approx 682{,}95 \\quad \\Rightarrow \\quad n = 683",[569,2582,2584,2602,2798,2832,2850],{"className":2583,"ariaHidden":599},[598],[569,2585,2587,2590,2593,2596,2599],{"className":2586},[603],[569,2588],{"className":2589,"style":1613},[607],[569,2591,670],{"className":2592},[612,613],[569,2594],{"className":2595,"style":1103},[691],[569,2597,1578],{"className":2598},[1107],[569,2600],{"className":2601,"style":1103},[691],[569,2603,2605,2608,2789,2792,2795],{"className":2604},[603],[569,2606],{"className":2607,"style":2231},[607],[569,2609,2611,2614,2786],{"className":2610},[612],[569,2612],{"className":2613},[745,746],[569,2615,2617],{"className":2616},[646],[569,2618,2620,2778],{"className":2619},[714,715],[569,2621,2623,2775],{"className":2622},[719],[569,2624,2626,2675,2683],{"className":2625,"style":2250},[723],[569,2627,2628,2631],{"style":1001},[569,2629],{"className":2630,"style":766},[733],[569,2632,2634,2637,2643,2646],{"className":2633},[612],[569,2635,1378],{"className":2636},[612],[569,2638,2640],{"className":2639},[612],[569,2641,1386],{"className":2642},[1385],[569,2644,1378],{"className":2645},[612],[569,2647,2649,2652],{"className":2648},[612],[569,2650,2057],{"className":2651},[612],[569,2653,2655],{"className":2654},[1731],[569,2656,2658],{"className":2657},[714],[569,2659,2661],{"className":2660},[719],[569,2662,2664],{"className":2663,"style":2289},[723],[569,2665,2666,2669],{"style":2292},[569,2667],{"className":2668,"style":1748},[733],[569,2670,2672],{"className":2671},[770,771,772,773],[569,2673,1594],{"className":2674},[612,773],[569,2676,2677,2680],{"style":782},[569,2678],{"className":2679,"style":766},[733],[569,2681],{"className":2682,"style":790},[789],[569,2684,2685,2688],{"style":1021},[569,2686],{"className":2687,"style":766},[733],[569,2689,2691,2694,2700,2703,2732,2735,2738,2741,2744,2750,2753,2756,2759,2762,2765,2771],{"className":2690},[612],[569,2692,659],{"className":2693},[612],[569,2695,2697],{"className":2696},[612],[569,2698,1386],{"className":2699},[1385],[569,2701,2330],{"className":2702},[612],[569,2704,2706,2709],{"className":2705},[612],[569,2707,2337],{"className":2708},[612],[569,2710,2712],{"className":2711},[1731],[569,2713,2715],{"className":2714},[714],[569,2716,2718],{"className":2717},[719],[569,2719,2721],{"className":2720,"style":2350},[723],[569,2722,2723,2726],{"style":2353},[569,2724],{"className":2725,"style":1748},[733],[569,2727,2729],{"className":2728},[770,771,772,773],[569,2730,1594],{"className":2731},[612,773],[569,2733],{"className":2734,"style":692},[691],[569,2736,641],{"className":2737},[696],[569,2739],{"className":2740,"style":692},[691],[569,2742,1378],{"className":2743},[612],[569,2745,2747],{"className":2746},[612],[569,2748,1386],{"className":2749},[1385],[569,2751,1594],{"className":2752},[612],[569,2754],{"className":2755,"style":692},[691],[569,2757,641],{"className":2758},[696],[569,2760],{"className":2761,"style":692},[691],[569,2763,1378],{"className":2764},[612],[569,2766,2768],{"className":2767},[612],[569,2769,1386],{"className":2770},[1385],[569,2772,2774],{"className":2773},[612],"8",[569,2776,826],{"className":2777},[825],[569,2779,2781],{"className":2780},[719],[569,2782,2784],{"className":2783,"style":2394},[723],[569,2785],{},[569,2787],{"className":2788},[821,746],[569,2790],{"className":2791,"style":1103},[691],[569,2793,2182],{"className":2794},[1107],[569,2796],{"className":2797,"style":1103},[691],[569,2799,2801,2804,2808,2814,2817,2820,2823,2826,2829],{"className":2800},[603],[569,2802],{"className":2803,"style":1374},[607],[569,2805,2807],{"className":2806},[612],"682",[569,2809,2811],{"className":2810},[612],[569,2812,1386],{"className":2813},[1385],[569,2815,2010],{"className":2816},[612],[569,2818],{"className":2819,"style":2431},[691],[569,2821],{"className":2822,"style":1103},[691],[569,2824,2191],{"className":2825},[1107],[569,2827],{"className":2828,"style":2431},[691],[569,2830],{"className":2831,"style":1103},[691],[569,2833,2835,2838,2841,2844,2847],{"className":2834},[603],[569,2836],{"className":2837,"style":1148},[607],[569,2839,670],{"className":2840},[612,613],[569,2842],{"className":2843,"style":1103},[691],[569,2845,1340],{"className":2846},[1107],[569,2848],{"className":2849,"style":1103},[691],[569,2851,2853,2856],{"className":2852},[603],[569,2854],{"className":2855,"style":1287},[607],[569,2857,2577],{"className":2858},[612],[565,2860,2861,2862,2906,2907,2940],{},"Für ",[569,2863,2865,2882],{"className":2864},[572],[569,2866,2868],{"className":2867},[576],[578,2869,2870],{"xmlns":580},[582,2871,2872,2879],{},[585,2873,2874,2876],{},[639,2875,2054],{},[657,2877,2878],{},"1,5",[592,2880,2881],{"encoding":594},"\\pm 1{,}5",[569,2883,2885],{"className":2884,"ariaHidden":599},[598],[569,2886,2888,2891,2894,2897,2903],{"className":2887},[603],[569,2889],{"className":2890,"style":1374},[607],[569,2892,2054],{"className":2893},[612],[569,2895,659],{"className":2896},[612],[569,2898,2900],{"className":2899},[612],[569,2901,1386],{"className":2902},[1385],[569,2904,1390],{"className":2905},[612]," Prozentpunkte statt ",[569,2908,2910,2925],{"className":2909},[572],[569,2911,2913],{"className":2912},[576],[578,2914,2915],{"xmlns":580},[582,2916,2917,2923],{},[585,2918,2919,2921],{},[639,2920,2054],{},[657,2922,2057],{},[592,2924,2060],{"encoding":594},[569,2926,2928],{"className":2927,"ariaHidden":599},[598],[569,2929,2931,2934,2937],{"className":2930},[603],[569,2932],{"className":2933,"style":2070},[607],[569,2935,2054],{"className":2936},[612],[569,2938,2057],{"className":2939},[612]," bräuchte man den vierfachen Umfang.",[565,2942,2943,2944,2996,2997,2039,3035,3069],{},"Mittelwert: Ein IQ-Test hat ",[569,2945,2947,2966],{"className":2946},[572],[569,2948,2950],{"className":2949},[576],[578,2951,2952],{"xmlns":580},[582,2953,2954,2963],{},[585,2955,2956,2958,2960],{},[588,2957,1777],{},[639,2959,1340],{},[657,2961,2962],{},"15",[592,2964,2965],{"encoding":594},"\\sigma = 15",[569,2967,2969,2987],{"className":2968,"ariaHidden":599},[598],[569,2970,2972,2975,2978,2981,2984],{"className":2971},[603],[569,2973],{"className":2974,"style":1148},[607],[569,2976,1777],{"className":2977,"style":1793},[612,613],[569,2979],{"className":2980,"style":1103},[691],[569,2982,1340],{"className":2983},[1107],[569,2985],{"className":2986,"style":1103},[691],[569,2988,2990,2993],{"className":2989},[603],[569,2991],{"className":2992,"style":1287},[607],[569,2994,2962],{"className":2995},[612],". Um den mittleren IQ einer Gruppe mit ",[569,2998,3000,3017],{"className":2999},[572],[569,3001,3003],{"className":3002},[576],[578,3004,3005],{"xmlns":580},[582,3006,3007,3015],{},[585,3008,3009,3011,3013],{},[657,3010,2010],{},[905,3012,907],{},[588,3014,2016],{"mathvariant":2015},[592,3016,2019],{"encoding":594},[569,3018,3020],{"className":3019,"ariaHidden":599},[598],[569,3021,3023,3026,3029,3032],{"className":3022},[603],[569,3024],{"className":3025,"style":2029},[607],[569,3027,2010],{"className":3028},[612],[569,3030],{"className":3031,"style":1034},[691],[569,3033,2016],{"className":3034},[612],[569,3036,3038,3054],{"className":3037},[572],[569,3039,3041],{"className":3040},[576],[578,3042,3043],{"xmlns":580},[582,3044,3045,3051],{},[585,3046,3047,3049],{},[639,3048,2054],{},[657,3050,1594],{},[592,3052,3053],{"encoding":594},"\\pm 2",[569,3055,3057],{"className":3056,"ariaHidden":599},[598],[569,3058,3060,3063,3066],{"className":3059},[603],[569,3061],{"className":3062,"style":2070},[607],[569,3064,2054],{"className":3065},[612],[569,3067,1594],{"className":3068},[612]," Punkte genau zu schätzen:",[569,3071,3073],{"className":3072},[878],[569,3074,3076,3132],{"className":3075},[572],[569,3077,3079],{"className":3078},[576],[578,3080,3081],{"xmlns":580,"display":887},[582,3082,3083,3129],{},[585,3084,3085,3087,3089,3111,3113,3116,3118,3120,3122,3124,3126],{},[588,3086,670],{},[639,3088,1578],{},[1580,3090,3091,3109],{},[585,3092,3093,3095,3107],{},[639,3094,655],{"fence":599},[646,3096,3097,3105],{},[585,3098,3099,3101,3103],{},[657,3100,2165],{},[639,3102,641],{},[657,3104,2962],{},[657,3106,1594],{},[639,3108,667],{"fence":599},[657,3110,1594],{},[639,3112,1340],{},[657,3114,3115],{},"216,09",[691,3117],{"width":2188},[639,3119,2191],{},[691,3121],{"width":2188},[588,3123,670],{},[639,3125,1340],{},[657,3127,3128],{},"217",[592,3130,3131],{"encoding":594},"n \\geq \\left(\\frac{1{,}96 \\cdot 15}{2}\\right)^2 = 216{,}09 \\quad \\Rightarrow \\quad n = 217",[569,3133,3135,3153,3297,3332,3350],{"className":3134,"ariaHidden":599},[598],[569,3136,3138,3141,3144,3147,3150],{"className":3137},[603],[569,3139],{"className":3140,"style":1613},[607],[569,3142,670],{"className":3143},[612,613],[569,3145],{"className":3146,"style":1103},[691],[569,3148,1578],{"className":3149},[1107],[569,3151],{"className":3152,"style":1103},[691],[569,3154,3156,3160,3288,3291,3294],{"className":3155},[603],[569,3157],{"className":3158,"style":3159},[607],"height:2.604em;vertical-align:-0.95em;",[569,3161,3163,3263],{"className":3162},[1636],[569,3164,3166,3172,3257],{"className":3165},[1636],[569,3167,3169],{"className":3168,"style":1644},[745,1643],[569,3170,655],{"className":3171},[1648,772],[569,3173,3175,3178,3254],{"className":3174},[612],[569,3176],{"className":3177},[745,746],[569,3179,3181],{"className":3180},[646],[569,3182,3184,3246],{"className":3183},[714,715],[569,3185,3187,3243],{"className":3186},[719],[569,3188,3191,3202,3210],{"className":3189,"style":3190},[723],"height:1.3214em;",[569,3192,3193,3196],{"style":1001},[569,3194],{"className":3195,"style":766},[733],[569,3197,3199],{"className":3198},[612],[569,3200,1594],{"className":3201},[612],[569,3203,3204,3207],{"style":782},[569,3205],{"className":3206,"style":766},[733],[569,3208],{"className":3209,"style":790},[789],[569,3211,3212,3215],{"style":1021},[569,3213],{"className":3214,"style":766},[733],[569,3216,3218,3221,3227,3231,3234,3237,3240],{"className":3217},[612],[569,3219,659],{"className":3220},[612],[569,3222,3224],{"className":3223},[612],[569,3225,1386],{"className":3226},[1385],[569,3228,3230],{"className":3229},[612],"96",[569,3232],{"className":3233,"style":692},[691],[569,3235,641],{"className":3236},[696],[569,3238],{"className":3239,"style":692},[691],[569,3241,2962],{"className":3242},[612],[569,3244,826],{"className":3245},[825],[569,3247,3249],{"className":3248},[719],[569,3250,3252],{"className":3251,"style":1065},[723],[569,3253],{},[569,3255],{"className":3256},[821,746],[569,3258,3260],{"className":3259,"style":1644},[821,1643],[569,3261,667],{"className":3262},[1648,772],[569,3264,3266],{"className":3265},[1731],[569,3267,3269],{"className":3268},[714],[569,3270,3272],{"className":3271},[719],[569,3273,3276],{"className":3274,"style":3275},[723],"height:1.654em;",[569,3277,3279,3282],{"style":3278},"top:-3.9029em;margin-right:0.05em;",[569,3280],{"className":3281,"style":1748},[733],[569,3283,3285],{"className":3284},[770,771,772,773],[569,3286,1594],{"className":3287},[612,773],[569,3289],{"className":3290,"style":1103},[691],[569,3292,1340],{"className":3293},[1107],[569,3295],{"className":3296,"style":1103},[691],[569,3298,3300,3303,3307,3313,3317,3320,3323,3326,3329],{"className":3299},[603],[569,3301],{"className":3302,"style":1374},[607],[569,3304,3306],{"className":3305},[612],"216",[569,3308,3310],{"className":3309},[612],[569,3311,1386],{"className":3312},[1385],[569,3314,3316],{"className":3315},[612],"09",[569,3318],{"className":3319,"style":2431},[691],[569,3321],{"className":3322,"style":1103},[691],[569,3324,2191],{"className":3325},[1107],[569,3327],{"className":3328,"style":2431},[691],[569,3330],{"className":3331,"style":1103},[691],[569,3333,3335,3338,3341,3344,3347],{"className":3334},[603],[569,3336],{"className":3337,"style":1148},[607],[569,3339,670],{"className":3340},[612,613],[569,3342],{"className":3343,"style":1103},[691],[569,3345,1340],{"className":3346},[1107],[569,3348],{"className":3349,"style":1103},[691],[569,3351,3353,3356],{"className":3352},[603],[569,3354],{"className":3355,"style":1287},[607],[569,3357,3128],{"className":3358},[612],[560,3360,3362],{"id":3361},"typische-fehler","Typische Fehler",[3364,3365,3366,3399,3460,3610],"ul",{},[3367,3368,3369,3370,3398],"li",{},"Abrunden statt aufrunden. Mit ",[569,3371,3373,3386],{"className":3372},[572],[569,3374,3376],{"className":3375},[576],[578,3377,3378],{"xmlns":580},[582,3379,3380,3384],{},[585,3381,3382],{},[657,3383,2418],{},[592,3385,2418],{"encoding":594},[569,3387,3389],{"className":3388,"ariaHidden":599},[598],[569,3390,3392,3395],{"className":3391},[603],[569,3393],{"className":3394,"style":1287},[607],[569,3396,2418],{"className":3397},[612]," Befragten wird die Genauigkeit knapp verfehlt.",[3367,3400,3401,3402,3430,3431,3459],{},"Die volle Breite des Intervalls für ",[569,3403,3405,3418],{"className":3404},[572],[569,3406,3408],{"className":3407},[576],[578,3409,3410],{"xmlns":580},[582,3411,3412,3416],{},[585,3413,3414],{},[588,3415,590],{},[592,3417,590],{"encoding":594},[569,3419,3421],{"className":3420,"ariaHidden":599},[598],[569,3422,3424,3427],{"className":3423},[603],[569,3425],{"className":3426,"style":608},[607],[569,3428,590],{"className":3429},[612,613]," einsetzen. ",[569,3432,3434,3447],{"className":3433},[572],[569,3435,3437],{"className":3436},[576],[578,3438,3439],{"xmlns":580},[582,3440,3441,3445],{},[585,3442,3443],{},[588,3444,590],{},[592,3446,590],{"encoding":594},[569,3448,3450],{"className":3449,"ariaHidden":599},[598],[569,3451,3453,3456],{"className":3452},[603],[569,3454],{"className":3455,"style":608},[607],[569,3457,590],{"className":3458},[612,613]," ist die halbe Breite, also der Abstand vom Schätzwert zur Grenze.",[3367,3461,3462,3463,3496,3497,3558,3559,1755],{},"Prozentpunkte als Prozent einsetzen: ",[569,3464,3466,3481],{"className":3465},[572],[569,3467,3469],{"className":3468},[576],[578,3470,3471],{"xmlns":580},[582,3472,3473,3479],{},[585,3474,3475,3477],{},[639,3476,2054],{},[657,3478,2057],{},[592,3480,2060],{"encoding":594},[569,3482,3484],{"className":3483,"ariaHidden":599},[598],[569,3485,3487,3490,3493],{"className":3486},[603],[569,3488],{"className":3489,"style":2070},[607],[569,3491,2054],{"className":3492},[612],[569,3494,2057],{"className":3495},[612]," Prozentpunkte bedeutet ",[569,3498,3500,3518],{"className":3499},[572],[569,3501,3503],{"className":3502},[576],[578,3504,3505],{"xmlns":580},[582,3506,3507,3515],{},[585,3508,3509,3511,3513],{},[588,3510,590],{},[639,3512,1340],{},[657,3514,2177],{},[592,3516,3517],{"encoding":594},"d = 0{,}03",[569,3519,3521,3539],{"className":3520,"ariaHidden":599},[598],[569,3522,3524,3527,3530,3533,3536],{"className":3523},[603],[569,3525],{"className":3526,"style":608},[607],[569,3528,590],{"className":3529},[612,613],[569,3531],{"className":3532,"style":1103},[691],[569,3534,1340],{"className":3535},[1107],[569,3537],{"className":3538,"style":1103},[691],[569,3540,3542,3545,3548,3554],{"className":3541},[603],[569,3543],{"className":3544,"style":1374},[607],[569,3546,1378],{"className":3547},[612],[569,3549,3551],{"className":3550},[612],[569,3552,1386],{"className":3553},[1385],[569,3555,3557],{"className":3556},[612],"03",", nicht ",[569,3560,3562,3580],{"className":3561},[572],[569,3563,3565],{"className":3564},[576],[578,3566,3567],{"xmlns":580},[582,3568,3569,3577],{},[585,3570,3571,3573,3575],{},[588,3572,590],{},[639,3574,1340],{},[657,3576,2057],{},[592,3578,3579],{"encoding":594},"d = 3",[569,3581,3583,3601],{"className":3582,"ariaHidden":599},[598],[569,3584,3586,3589,3592,3595,3598],{"className":3585},[603],[569,3587],{"className":3588,"style":608},[607],[569,3590,590],{"className":3591},[612,613],[569,3593],{"className":3594,"style":1103},[691],[569,3596,1340],{"className":3597},[1107],[569,3599],{"className":3600,"style":1103},[691],[569,3602,3604,3607],{"className":3603},[603],[569,3605],{"className":3606,"style":1287},[607],[569,3608,2057],{"className":3609},[612],[3367,3611,3612],{},"Denken, eine doppelte Stichprobe halbiere den Fehler. Dafür braucht man die vierfache Stichprobe.",{"title":3614,"searchDepth":3615,"depth":3615,"links":3616},"",2,[3617,3618,3619],{"id":562,"depth":3615,"text":563},{"id":1991,"depth":3615,"text":1992},{"id":3361,"depth":3615,"text":3362},[3621,3625,3628,3631,3633,3636,3638,3641,3644],{"lhs":3622,"rhs":590,"where":3623},"z * sqrt(p*(1-p) \u002F (z^2 * p*(1-p) \u002F d^2))",{"p":3624},0.4,{"lhs":3626,"rhs":3627},"0.25 - p*(1-p)","(p - 0.5)^2",{"lhs":3629,"rhs":3630},"round(1.96^2 * 0.25 \u002F 0.03^2, 1)","1067.1",{"lhs":3632,"rhs":2200},"ceil(1.96^2 * 0.25 \u002F 0.03^2)",{"lhs":3634,"rhs":3635},"round(1.96^2 * 0.2 * 0.8 \u002F 0.03^2, 2)","682.95",{"lhs":3637,"rhs":2577},"ceil(1.96^2 * 0.2 * 0.8 \u002F 0.03^2)",{"lhs":3639,"rhs":3640},"1.96^2 * 0.25 \u002F 0.015^2","4 * 1.96^2 * 0.25 \u002F 0.03^2",{"lhs":3642,"rhs":3643},"(1.96 * 15 \u002F 2)^2","216.09",{"lhs":3645,"rhs":3128},"ceil((1.96 * 15 \u002F 2)^2)","d > 0,\\ 0 \\leq p \\leq 1;\\ \\text{ohne Vorwissen über } p \\text{ setzt man } p = 0{,}5","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>d\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">d > 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:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\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:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\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>\u003Cmn>0\u003C\u002Fmn>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">;\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0 \\leq p \\leq 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:0.7804em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\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:0.8304em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\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:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">;\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">ohne Vorwissen über\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p\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 mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">setzt man\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0,5\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p = 0{,}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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\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:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">5\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","sample-size","n \\geq \\frac{z^2 \\cdot p\\,(1 - p)}{d^2}","\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>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsup>\u003Cmi>z\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmsup>\u003Cmi>d\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq \\frac{z^2 \\cdot p\\,(1 - p)}{d^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:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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:2.1771em;vertical-align:-0.686em;\">\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\">\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7401em;\">\u003Cspan style=\"top:-2.989em;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>\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=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.044em;\">z\u003C\u002Fspan>\u003Cspan 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