[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8,"_9":-5,"_10":11,"_12":13,"_14":15},"actionData","errors","root",{"_17584":17585,"_17586":17587,"_17588":17589,"_17590":-5,"_17591":40,"_17592":17593,"_17594":40,"_17595":40,"_17596":17597,"_17598":42,"_17599":17600,"_17601":40,"_17602":17603,"_17604":-5,"_17605":-5,"_17606":-5,"_17607":-5,"_17608":-5,"_17609":-5,"_17610":17611,"_17612":17613,"_17614":42,"_17615":-5,"_121":42},"routes/__learning-environment",{"_11099":11516,"_11517":11518,"_11519":11520,"_11521":11522,"_121":42},"routes/__learning-environment/course","routes/__learning-environment/course/$courseSlug",{"_88":11091,"_11092":11093,"_11094":42,"_121":42},"routes/__learning-environment/course/$courseSlug/topic.$topicSlug.$level.$gradeOrExam",{"_88":89,"_90":91,"_92":93,"_94":95,"_96":97,"_98":99,"_100":101,"_102":103,"_104":105,"_106":44,"_107":108,"_109":110,"_111":112,"_113":114,"_115":116,"_117":42,"_118":119,"_120":-5,"_121":42},"routes/__learning-environment/course/$courseSlug/topic.$topicSlug.$level.$gradeOrExam/faq",{"_16":17,"_18":19,"_20":21},"topicTitle","Toetsen van hypothesen 2","questions",[22,23,24,25,26,27],"backButtonHref","/course/wiskunde-a/topic/toetsen-van-hypothesen-2/vwo/4",{"_28":81,"_30":82,"_32":83,"_34":84,"_36":83,"_37":85,"_39":40,"_41":42,"_43":44,"_45":44,"_46":86,"_48":87},{"_28":73,"_30":74,"_32":75,"_34":76,"_36":77,"_37":78,"_39":40,"_41":42,"_43":44,"_45":44,"_46":79,"_48":80},{"_28":65,"_30":66,"_32":67,"_34":68,"_36":69,"_37":70,"_39":40,"_41":42,"_43":44,"_45":44,"_46":71,"_48":72},{"_28":58,"_30":59,"_32":60,"_34":61,"_36":60,"_37":62,"_39":40,"_41":42,"_43":44,"_45":44,"_46":63,"_48":64},{"_28":50,"_30":51,"_32":52,"_34":53,"_36":54,"_37":55,"_39":40,"_41":42,"_43":44,"_45":44,"_46":56,"_48":57},{"_28":29,"_30":31,"_32":33,"_34":35,"_36":33,"_37":38,"_39":40,"_41":42,"_43":44,"_45":44,"_46":47,"_48":49},"uuid","da387d35-87ba-43d6-88fc-53214db4f9ad","slug","welke-geschiedenisonderwerpen-belangrijk-examen","question","Welke geschiedenisonderwerpen zijn belangrijk voor een examen?","cleanedQuestion","Welke geschiedenisonderwerpen belangrijk examen","detailedQuestion","answer","Voor een geschiedenisexamen zijn vaak de grote lijnen en belangrijke gebeurtenissen uit verschillende historische periodes belangrijk. De onderwerpen die je moet kennen, hangen af van je leerjaar en schooltype, maar over het algemeen kun je denken aan:\n\n* **De Eerste Wereldoorlog:** Hierbij zijn de oorzaken (zoals de moord op Franz Ferdinand), het karakter van de oorlog (zoals 'totale oorlog' waarbij de hele samenleving betrokken is), en de gevolgen (zoals het Verdrag van Versailles met herstelbetalingen en gebiedsafstand voor Duitsland) belangrijke onderdelen.\n* **Het Interbellum en de Crisisjaren:** Dit omvat de periode tussen de twee wereldoorlogen, met aandacht voor de economische crisis van de jaren '30 en de maatregelen die regeringen namen om de werkloosheid aan te pakken (zoals overheidssteun met het stempelsysteem).\n* **De Tweede Wereldoorlog:** Belangrijke aspecten zijn de directe aanleiding (de Duitse inval in Polen), de belangrijkste strijdende partijen (zoals de Asmogendheden: Duitsland, Italië en Japan), oorlogstactieken (zoals de Blitzkrieg), de Holocaust (de systematische moord op zes miljoen Europese Joden), en het einde van de oorlog (zoals de inzet van atoombommen op Hiroshima en Nagasaki).\n* **Dekolonisatie:** Dit gaat over het proces waarbij koloniën na de Tweede Wereldoorlog onafhankelijk werden en hun eigen land gingen besturen.\n\nNaast deze specifieke onderwerpen is het ook belangrijk om gebeurtenissen in de juiste chronologische volgorde te kunnen plaatsen en verbanden te kunnen leggen tussen verschillende periodes.","isConcept",false,"isSynced",true,"likeCount",0,"dislikeCount","createdAt",["D",1779146144067],"updatedAt",["D",1779146144302],"bafd7370-76fd-4426-8664-c357e657e030","hoe-herken-je-tweezijdige-hypothesetoets-vraagstelling","Hoe herken je een tweezijdige hypothesetoets aan de vraagstelling?","herken tweezijdige hypothesetoets vraagstelling","Hoe herken je een tweezijdige hypothesetoets aan de vraagstelling, en wat is het verschil met eenzijdige toetsen?","Een tweezijdige hypothesetoets herken je aan de formulering in de vraagstelling die geen specifieke richting aangeeft voor de verwachte verandering. Het gaat erom of iets *anders* is dan een bepaalde waarde, niet per se groter of kleiner.\n\n**Kenmerken van een tweezijdige toets:**\n* **Vraagstelling:** De vraag bevat woorden zoals \"verandert\", \"wijkt af\", \"is anders dan\", of \"is niet gelijk aan\". Deze woorden suggereren dat de waarde zowel hoger als lager kan zijn dan de verwachte waarde.\n* **Alternatieve hypothese ($H_1$):** De alternatieve hypothese gebruikt het \"ongelijk aan\"-teken ($\\neq$). Bijvoorbeeld, $H_1: \\mu_X \\neq 250$. Dit betekent dat de werkelijke gemiddelde waarde ($\\mu_X$) zowel kleiner als groter kan zijn dan de nulhypothese waarde (hier 250).\n\n**Verschil met eenzijdige toetsen:**\nBij een eenzijdige toets wordt wel een specifieke richting verwacht:\n* **Linkszijdige toets:** De vraagstelling bevat woorden als \"minder dan\", \"kleiner dan\", \"daalt\", of \"neemt af\". De alternatieve hypothese is dan $H_1: \\mu_X < \\text{waarde}$.\n * *Voorbeeld:* \"Meneer Spee beweert dat bestuurders onder de 30 jaar door hun rijstijl **minder zuinig rijden**.\" Hier is de richting duidelijk: de actieradius zou *kleiner* zijn.\n* **Rechtszijdige toets:** De vraagstelling bevat woorden als \"meer dan\", \"groter dan\", \"stijgt\", of \"neemt toe\". De alternatieve hypothese is dan $H_1: \\mu_X > \\text{waarde}$.\n * *Voorbeeld:* \"Van bestuurders boven de 50 jaar vermoedt meneer Spee dat deze door hun rijstijl juist **zuiniger rijden**.\" Hier is de richting ook duidelijk: de actieradius zou *groter* zijn.\n\n**Voorbeeld van een tweezijdige toets:**\nStel, de vraag is: \"Men vraagt zich af of de actieradius **verandert** bij gebruik van banden van het merk Peacestone.\"\nHet sleutelwoord \"verandert\" geeft aan dat de actieradius zowel meer als minder kan zijn. Er is geen specifieke richting. Daarom is dit een tweezijdige toets met $H_1: \\mu_X \\neq 250$.",["D",1765929639908],["D",1765929640289],"041bdc8d-93fc-4d25-af8a-89e71163167d","wat-zijn-belangrijkste-kenmerken-gebeurtenissen-wereldoorlogen","Wat zijn de belangrijkste kenmerken en gebeurtenissen van de wereldoorlogen?","belangrijkste kenmerken gebeurtenissen wereldoorlogen","De wereldoorlogen, de Eerste Wereldoorlog (1914-1918) en de Tweede Wereldoorlog (1939-1945), waren wereldwijde conflicten met elk hun eigen belangrijke kenmerken en gebeurtenissen.\n\n**Eerste Wereldoorlog (1914-1918):**\n* **Aanleiding:** De directe aanleiding voor het begin van de Eerste Wereldoorlog was de moord op de Oostenrijkse aartshertog Franz Ferdinand op 28 juni 1914.\n* **Totale oorlog:** Een belangrijk kenmerk van deze oorlog was dat het een 'totale oorlog' was. Dit betekent dat niet alleen soldaten aan het front vochten, maar de hele samenleving betrokken was bij de oorlogsinspanningen. Burgers droegen bij, bijvoorbeeld vrouwen die in fabrieken werkten om wapens te produceren, en de economie draaide op de oorlogsindustrie.\n* **Verdrag van Versailles:** Na de oorlog werd dit verdrag opgesteld. Duitsland kreeg de hoofdschuld van de oorlog, moest herstelbetalingen doen, mocht maar een klein leger hebben (demilitarisatie), en moest koloniën en grondgebied afstaan aan andere landen.\n\n**Tweede Wereldoorlog (1939-1945):**\n* **Aanleiding:** De directe aanleiding voor het begin van de Tweede Wereldoorlog in Europa was de Duitse inval in Polen op 1 september 1939.\n* **Asmogendheden:** De belangrijkste landen die samenwerkten en bekend stonden als de Asmogendheden waren Duitsland, Italië en Japan.\n* **Blitzkrieg:** Een belangrijke Duitse tactiek was de 'Blitzkrieg' (bliksemoorlog). Dit was een snelle en beweeglijke aanvalstactiek met tanks, vliegtuigen en infanterie om snel door vijandelijke linies te breken, zoals succesvol toegepast bij de inval in Polen.\n* **Holocaust:** Een verschrikkelijke gebeurtenis tijdens de Tweede Wereldoorlog was de Holocaust, de systematische moord op zes miljoen Europese Joden, met als doel het Joodse volk in Europa uit te roeien.\n* **Einde van de oorlog:** De oorlog eindigde na de inzet van atoombommen door de Verenigde Staten op de Japanse steden Hiroshima (6 augustus 1945) en Nagasaki (9 augustus 1945) om Japan tot overgave te dwingen.",["D",1779146146043],["D",1779146146294],"5d3b0d7f-17ad-4c7d-9bb1-36528a405c70","visualisatie-tweezijdige-hypothesetoets-normaalkromme","Hoe visualiseer je een tweezijdige hypothesetoets met een normaalkromme?","visualiseer tweezijdige hypothesetoets normaalkromme","Hoe visualiseer je een tweezijdige hypothesetoets met een normaalkromme, en hoe gebruik je daarbij een significantieniveau van $\\alpha = 0,10$ en een berekende overschrijdingskans van $P(\\bar{X} \\leq 244) \\approx 0,065$ bij een nulhypothese van $\\mu_X = 250$?","Bij een tweezijdige hypothesetoets onderzoek je of een parameter (zoals een gemiddelde) *verandert* ten opzichte van een bepaalde waarde, zonder een specifieke richting (groter of kleiner) te verwachten. De alternatieve hypothese ($H_1$) wordt dan geformuleerd als $H_1: \\mu \\neq \\text{waarde}$.\n\n**Visualisatie met een normaalkromme:**\nEen normaalkromme, ook wel klokvormige curve genoemd, is symmetrisch rond het gemiddelde. Bij een tweezijdige toets verdeel je het significantieniveau ($\\alpha$) over twee 'staarten' aan de uiteinden van deze kromme. Dit zijn de kritieke gebieden.\n\n1. **Verdeling van het significantieniveau:** Als je een significantieniveau van $\\alpha = 0,10$ hebt, verdeel je dit over de twee staarten. Elke staart krijgt dan $\\frac{\\alpha}{2} = \\frac{0,10}{2} = 0,05$ van het totale oppervlak onder de kromme.\n2. **Middengebied:** Het gebied tussen de twee kritieke staarten is $1 - \\alpha = 1 - 0,10 = 0,90$, oftewel $90\\%$. Dit is het acceptatiegebied voor de nulhypothese ($H_0$).\n3. **Tekening:** Je tekent een klokvormige curve met:\n * Het gemiddelde van de nulhypothese (in dit voorbeeld $\\mu_X = 250$) precies in het midden.\n * Een linker kritiek gebied aan de linkerkant, dat $5\\%$ van het totale oppervlak beslaat.\n * Een rechter kritiek gebied aan de rechterkant, dat ook $5\\%$ van het totale oppervlak beslaat.\n * Het gebied tussen deze twee kritieke gebieden is $90\\%$.\n\n**Voorbeeld met de gegeven waarden:**\nStel, de nulhypothese is $H_0: \\mu_X = 250$ en de alternatieve hypothese is $H_1: \\mu_X \\neq 250$. Het significantieniveau is $\\alpha = 0,10$.\n* Je verdeelt $\\alpha$ over de twee staarten, dus elke staart heeft een kritiek significantieniveau van $0,05$.\n* Je hebt een steekproefgemiddelde van $\\bar{X} = 244$ gevonden, met een berekende overschrijdingskans van $P(\\bar{X} \\leq 244) \\approx 0,065$. Dit is de kans dat je een steekproefgemiddelde van $244$ of lager vindt, áls de nulhypothese waar zou zijn.\n* Om te bepalen of de nulhypothese verworpen moet worden, vergelijk je de berekende overschrijdingskans ($0,065$) met het kritieke significantieniveau van de betreffende staart ($0,05$).\n* Omdat $0,065 > 0,05$, valt het steekproefgemiddelde van $244$ niet in het kritieke gebied van de linker staart.\n* Daarom wordt de nulhypothese ($H_0$) niet verworpen. Je kunt dus niet concluderen dat het gemiddelde van de actieradius anders is dan $250$.\n\nDe visualisatie helpt je te zien dat de waargenomen waarde van $244$ (met zijn bijbehorende kans van $0,065$) nog binnen het $90\\%$ middengebied valt, en dus niet 'extreem' genoeg is om de nulhypothese te verwerpen.",["D",1765929641402],["D",1765929641702],"d578cd9a-a84c-4923-8eeb-7d8a4ed5a6a3","significantieniveau-tweezijdige-hypothesetoets","Hoe gebruik je het significantieniveau bij een tweezijdige hypothesetoets?","gebruik significantieniveau tweezijdige hypothesetoets","Hoe gebruik je het significantieniveau bij een tweezijdige hypothesetoets, en hoe bepaal je of de nulhypothese wordt verworpen?","Bij een tweezijdige hypothesetoets onderzoek je of een waarde *verandert* ten opzichte van een bepaalde standaard, zonder een specifieke richting (zoals alleen groter of alleen kleiner) te verwachten. Dit zie je vaak aan de alternatieve hypothese ($H_1$), die dan een 'ongelijk aan'-teken ($\\neq$) bevat, bijvoorbeeld $H_1: \\mu \\neq \\text{waarde}$. Ook de vraagstelling kan dit aangeven, bijvoorbeeld door te vragen of iets \"verandert\".\n\nHet significantieniveau, vaak aangeduid met $\\alpha$, is de kans dat je de nulhypothese ($H_0$) onterecht verwerpt. Bij een tweezijdige toets wordt dit totale significantieniveau verdeeld over de twee 'staarten' van de verdeling (bijvoorbeeld de normaalkromme).\n\n**Stappen voor het gebruik van het significantieniveau bij een tweezijdige toets:**\n\n1. **Verdeel het significantieniveau:** Deel het totale significantieniveau ($\\alpha$) door twee. Elke staart van de verdeling krijgt dan $\\frac{\\alpha}{2}$ als kritiek significantieniveau.\n * *Voorbeeld:* Als het significantieniveau $\\alpha = 0,10$ is, dan is het kritieke significantieniveau voor elke staart $\\frac{0,10}{2} = 0,05$.\n\n2. **Visualiseer de normaalkromme:**\n * De normaalkromme is symmetrisch, met het gemiddelde van de nulhypothese precies in het midden.\n * Het middelste gebied, dat $1 - \\alpha$ van het totale oppervlak beslaat, is het acceptatiegebied voor de nulhypothese.\n * Aan de linker- en rechterkant bevinden zich de twee kritieke gebieden (staarten). Elk van deze staarten heeft een oppervlakte van $\\frac{\\alpha}{2}$.\n\n3. **Bereken de overschrijdingskans (p-waarde):** Dit is de kans op het waargenomen steekproefresultaat (of een extremere waarde), aangenomen dat de nulhypothese waar is.\n\n4. **Vergelijk de overschrijdingskans met $\\frac{\\alpha}{2}$:**\n * Als de berekende overschrijdingskans (p-waarde) **kleiner is dan of gelijk aan** $\\frac{\\alpha}{2}$, dan valt het resultaat in een van de kritieke gebieden. In dit geval wordt de nulhypothese ($H_0$) verworpen.\n * Als de berekende overschrijdingskans (p-waarde) **groter is dan** $\\frac{\\alpha}{2}$, dan valt het resultaat niet in een kritiek gebied. In dit geval wordt de nulhypothese ($H_0$) niet verworpen.\n\n**Voorbeeld:**\nStel, je voert een tweezijdige hypothesetoets uit met een significantieniveau van $\\alpha = 0,10$. Je hebt een steekproefgemiddelde gevonden waarvoor de overschrijdingskans aan één kant (bijvoorbeeld de linker staart) $P(\\bar{X} \\leq \\text{waargenomen waarde}) \\approx 0,065$ is.\n\n1. **Verdeel $\\alpha$:** $\\frac{\\alpha}{2} = \\frac{0,10}{2} = 0,05$.\n2. **Vergelijk:** Je vergelijkt de berekende overschrijdingskans van $0,065$ met $0,05$.\n3. **Conclusie:** Omdat $0,065 > 0,05$, is de overschrijdingskans groter dan het kritieke significantieniveau voor die staart. Het steekproefgemiddelde valt dus niet in het kritieke gebied. De nulhypothese ($H_0$) wordt **niet verworpen**. Je kunt dus niet concluderen dat er een significant verschil is.",["D",1765929641771],["D",1765929642592],"089a61f0-22c1-400b-b6d2-b6b90d667826","wanneer-deel-je-standaardafwijking-door-wortel-n","Wanneer deel je de standaardafwijking door de wortel van n?","Wanneer deel standaardafwijking wortel n","Je deelt de standaardafwijking ($\\sigma$) door de wortel van $n$ (de steekproefomvang) wanneer je de *standaardafwijking van het steekproefgemiddelde* wilt berekenen. Dit wordt ook wel de **standaardfout van het gemiddelde** genoemd.\n\nHier is een overzicht van wanneer je dit wel en niet doet:\n\n* **Wanneer je $\\sigma$ deelt door $\\sqrt{n}$:**\n * Dit doe je wanneer je kijkt naar de spreiding van *steekproefgemiddelden* in plaats van individuele waarnemingen.\n * De formule hiervoor is:\n $\\sigma_{\\overline{x}} = \\frac{\\sigma}{\\sqrt{n}}$\n Hierbij is $\\sigma_{\\overline{x}}$ de standaardafwijking van het steekproefgemiddelde, $\\sigma$ de standaardafwijking van de populatie en $n$ de grootte van de steekproef.\n * Deze berekening is essentieel als je op basis van een steekproef een uitspraak wilt doen over het gemiddelde van een grotere populatie. Steekproefgemiddelden variëren namelijk minder dan individuele waarnemingen.\n\n* **Wanneer je $\\sigma$ *niet* deelt door $\\sqrt{n}$:**\n * Dit doe je wanneer je de spreiding van *individuele waarnemingen* binnen een populatie beschrijft.\n * In dit geval gebruik je de 'gewone' standaardafwijking ($\\sigma$) van de populatie direct. 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invnorm 0,90.","e63a3cb6-578c-4ef6-8237-01018c844e70",710000,"Dus dan wil ik ook dat middelste gedeelte uitrekenen.","011feda8-ae46-4bd1-a953-b8527dc78951",706000,"Maar dan moet ik 1 min die alfa gaan nemen.","765303b6-fb1c-4c4c-bdfc-5878f202bb53",701000,"Ik kan ook zeggen dat ik hem als optie center ga gebruiken.","9447ccb6-66d5-4401-94a6-5aaa3d285982",688000,700000,"Dan kan ik dus zeggen dat het kritieke gebied dat ligt links van 1,540 en rechts van 1,560.","852c4a85-4484-41ef-9f67-5fdd96ed937d",685000,"En dan kom ik op 1,5604.","a655364e-c5b9-4f53-b97c-538ea4d68694",683000,"Ook weer met die halve alfa.","f8f702eb-7a38-4564-928e-e2629a079785",680000,"Ik kan hem ook voor de rechtergrens uitrekenen.","c70ea0dd-20cc-4f5c-ab85-aa0603a0ed78",676000,"En die linkergrens die zit op 1,5395.","f4c14be8-282c-4a6d-a6fc-64a631e4b7bc",674000,"En hier die halve alfa.","60d6524e-37d3-4228-8b5d-acb6b02a2c04",671000,"Zodat ik mijn linkergrens ga bekijken.","cca61687-a298-4424-99fc-fdd524b1f8fd",668000,"Gemiddelde, standaarddeviatie en dan left.","a54885f1-2fd3-4658-a27e-f37adbd02178",665000,"Het was 0,10 en nu is het 0,05.","f8c5423f-19cc-4556-8a00-a5b04b55611d",662000,"Ik heb nu mijn alfa gehalveerd.","e3d3bb79-3269-4c50-b2ee-2ea3381b7356",660000,"c908f151-2b7b-4700-9152-816713282bdc",657000,"Ik ga de inform invullen.","faddafe3-5225-4073-bd64-c7e538acc419",653000,"Dus 0,0063 enzovoort.","6e7a0a7e-e7bb-4805-a6e1-26611b54e63d",650000,"Dan krijg ik 0,2 gedeeld door de wortel duizend.","07df1e29-6de3-420b-b3f3-acadb25a02e1",645000,"Standaarddeviatie voor de steekproef van duizend flessen.","86fd8564-a418-4d4c-b2a7-03f84d8053e8",640000,644000,"Dan zit ik in het kritieke gebied.","1ce83043-35a6-4384-a79c-c1b4e7950097",638000,"Of groter dan die rechtergrens.","97dd8839-e2da-4247-a8b6-fdf0a1771092",635000,"En als die kleiner is dan die linkergrens.","718ffa91-ec56-4eb9-b625-f04c5535ccaa",631000,"Dus ik heb een linkergrens en ik heb een rechtergrens.","fd2d2ca8-6374-4528-b6ee-163cd9f2da06",628000,"Kies alfa 0,10.","c4d9be18-99df-47a7-9f8f-1760db8ddeb4",623000,"Bij welke gemiddelde moet de machine nagekeken worden?","3dc4b78e-7908-4af9-9c7b-174c16c5ac57",619000,"Er wordt een controle uitgevoerd op een steekproef van duizend flessen.","3adce2b6-ab9a-49c8-acbe-77cdc4a8cdcf",617000,"Een standaarddeviatie van 0,2.","0b3493b6-0266-4dd4-ba1a-b06d963890d2",613000,"Een vulmachine wordt ingesteld op een gemiddelde van 1,55.","15e65fa2-3ff4-4c94-8f87-51529f781711",610000,"Een voorbeeld van tweezijdig toetsen.","5f18475c-9a9e-4e81-b683-eb174e029d02",608000,"Dan heb ik het centrum.","aa9f9098-b251-4989-b6cb-ad344c7e6a04",603000,"Dan zeg ik van dan ga ik hem voor 95% uitrekenen.","ebef8295-5a2c-46c2-9b52-3e17083850eb",599000,"Dus als ik een significantieniveau van 0,05 heb.","ddeda9e7-252b-45fb-9011-4213774adda1",591000,"Bij die center moet ik dan wel rekening houden met dat ik dan juist het gebied in het centrum wil hebben.","abc90c8e-7e48-42bf-8b31-fea50ba3c4fb",589000,"Kan ik dus center gebruiken.","71c1b999-ff4a-4050-96f7-d908cd3b6489",583000,"Of ik kan, als ik een grafische rekenmachine heb met die keuze van left, right of center.","552d1098-dcf3-488d-a2be-1fc1818a5fd0",579000,"Dus dan moet ik een half alfa gebruiken.","1dad7afd-e56f-43d9-b79c-9ccfbca259ca",574000,"En de ene helft aan de linkerkant en de andere helft aan de rechterkant gaan gebruiken.","acb7e1a4-9205-42c8-9f36-8b9a0c249edd",571000,"Dus dan moet ik mijn alfa in tweeën delen.","c1a6d7e6-ea2b-425d-8944-9b945b52f914",568000,"En dan moet ik mijn significantieniveau opsplitsen.","58e6555c-57b4-466c-8f3d-4184e30b4792",565000,"Of groter dan mijn rechtergrens.","66771918-929b-4c9f-8da0-78d749eeafff",560000,"Dan is het of kleiner dan mijn linkergrens.","36b2f25b-d12b-4894-a7b7-91c80d586470",557000,"En als ik hem tweezijdig ga toetsen.","e43b34c1-cc13-450e-ad4e-ebc4ce4323a4",553000,"Als die overschrijdingskans kleiner is of gelijk aan alfa.","cce668e6-ab28-4e0b-a0b0-156f81efe85b",550000,"Dan moet ik mijn nulhypothese verwerpen.","4998181f-d505-4bfc-83b1-884619a2bb9a",546000,"Want dan komt hij in dat kritieke gebied aan de rechterkant.","47ce039f-083b-4bd9-8c2c-d9f4433fc3f7",541000,"Dan heb ik die overschrijdingskans dat hij groter moet zijn dan die grens.","90781b06-a16f-4484-859e-dcf79662e953",539000,"Bij rechtzijdig toetsen.","aa7e49e5-2a22-4709-947c-a1149d0d2c29",534000,"Als het overschrijdingskans kleiner is of gelijk aan alfa.","ff7b78b1-cf05-43ab-aa81-2bd6d751fb93",531000,"Dus dan moet ik mijn nulhypothese gaan verwerpen.","44d1a0c7-0788-45ba-a2b0-4b01ef039ad6",528000,"Afhankelijk van het significantieniveau alfa.","e93935cd-64fe-4e86-ab0c-beab20184799",526000,"Zit hij in het kritieke gebied.","cbfb2149-a27b-49fb-9e6d-bb7a7a44e9a6",523000,"Dus als hij kleiner is dan die bepaalde grenswaarde.","eca371a8-e06f-4922-a819-a8df2a18bbdb",519000,"Dat mijn gemiddelde dan kleiner is dan die grenswaarde.","687e1e82-fb0e-4333-9d33-fe1c87dfb654",514000,517000,"Dan krijg ik een overschrijdingskans.","ee844330-6c2e-4b2d-bc25-1bac56adc9da",511000,"Als ik het linkzijdig wil toetsen.","0045099f-7943-4b76-9bb1-39017dc8703d",509000,"Dan ga ik eens even kijken.","c6905868-1a80-4761-a4f2-08568e41c49d",505000,"Als het normaal verdeeld is en ik heb een beslissingsvoorschrift.","2d74bf74-e68e-489a-b27e-bf87028f61dc",501000,503000,"Het zit niet in het kritieke gebied.","5bb8aeb2-81d1-4073-9ebf-3158d61aaf80",497000,"Dus conclusie, de nulhypothese die kan ik aannemen.","9c17a79c-7f63-4b03-96d3-8923eff42430",492000,"Het gemiddelde wat ik had gekregen in die toets is kleiner dan die grens.","549a6285-4861-401a-900d-98842e0f6f82",489000,"Dat is kleiner dan die grens.","4a61bb02-5d5f-4b80-9f78-4e409f3608d8",486000,"Dus het gemiddelde wat ik hier heb.","3a6521a1-c5d0-4c38-9582-e85a79773dbc",481000,"En dat is meer dan die 1,57.","d5192c0b-44db-4a0f-92f9-e7e6c96e543f",475000,"Als ik die uitreken dan kom ik op 1,5862.","ad243dc2-0a3d-4a66-871d-36490467f5a7",473000,"En rechts.","30cb2519-c1bc-4464-b036-a8f452d1c98a",468000,"Dus dan krijg ik 0,10, 1,55, 0,028 enzovoort.","be4e1379-7fcb-41d9-823c-dcc3ebbde679",465000,"En nu kies ik voor rechts.","6bc5b2ba-5f6a-4cc8-9c76-715030eb964f",462000,"Met de alfa, het gemiddelde, standaarddeviatie.","932aeca7-eb7e-4e94-99f1-962660623eb9",459000,"En dan ga ik mijn infnorm weer invullen.","3bea9981-bd2f-481c-956b-edcb44730852",455000,458000,"Is 0,02828 enzovoort.","ea8aae83-a7a4-466e-b22a-ae5923b3b761",450000,"Standaarddeviatie uitrekenen krijg ik 0,2 gedeeld door de wortel van 50.","cf5b192d-af24-4ee6-bb76-5e41e1035135",445000,"Of dat het gemiddelde dus groter is dan 1,55.","c7d6f7c3-b98b-4786-9b78-c038ff366ff9",441000,"En mijn alternatieve hypothese is dat de inhoud.","c26096ae-96ec-425c-b8b5-92edef06947e",437000,"Mijn nulhypothese is dat het klopt.","fd1cd4dd-9882-49db-8235-214939def343",432000,"De standaarddeviatie die moet ik weer gaan omzetten met de wortel n.","2eeeee79-ba17-42ea-8418-dbf4a3f53ae8",429000,"Nou het gemiddelde is 1,55.","6d223f14-a584-4b28-af6f-5f37917f98fb",425000,"Of dat in het kritieke gebied ligt of nog niet.","cf7d62a3-0bb1-4ccd-9b0f-471e62731731",421000,"Nou moet ik dus weer gaan kijken of die 1,57.","359eb107-e93a-49dc-8f51-7947c75c1fb2",418000,"80790646-ef4c-419e-92a9-ed546d4b4501",414000,"Kun je nu concluderen dat de machine niet goed werkt.","22e2f77d-5b8e-4f19-906f-5a452d550f88",409000,"Na controle blijkt het gemiddelde van 50 flessen 1,57 liter te zijn.","587b369b-cd95-4ea1-9d8c-b3a6c407bc93",406000,"Met een standaarddeviatie van 0,2 liter.","8a2fd3d3-f042-4e84-9278-8a300e27e4c9",402000,"Een vulmachine wordt ingesteld op een gemiddelde van 1,55 liter.","d0fe836f-3778-45a4-a2fc-3dda002d68ac",399000,"Nu een voorbeeld van rechtzijdig toetsen.","b90c906e-ec64-42fd-8c08-63e03c6c7197",395000,"Of dat de machine niet goed werkt enzovoort.","5beca6ad-7d19-4f85-855d-45c6cf9944f4",390000,"En dan kan ik dus zeggen dat die opnieuw ingesteld moet worden.","eb7e2e78-2b21-4cb6-b965-278e7d112e94",387000,"Ik moet mijn nulhypothese verwerpen.","f0888814-2381-4e97-a786-9532f4ef932c",384000,"Dan kan ik zeggen het zit in het kritieke gebied.","0d1c45ab-5795-4f7c-8e6e-48c0fe2bf8ea",379000,"Dus als ik hem eenzijdig heb getoetst, linkszijdig.","81bf3d4c-6e24-4c4a-90b7-27762943f517",374000,"Dus het gemiddelde is kleiner dan wat ik heb uitgerekend.","da981c00-ed02-4d0e-9326-28a9c978307a",370000,"Nou 1,51 ligt onder deze grens.","0c6b561e-f992-4540-a6ea-5ed5fc7817bc",367000,"Uit die controle kwam 1,51.","ad46fdc3-82d7-4809-a806-45f876bda48f",362000,"En als ik dat ga vergelijken met wat ik had uit die controle.","503d046d-d288-4a55-9c77-6ca53cd3b06e","Als ik dat uitreken dan kom ik op 1,52436.","0d9964f0-3d4e-4668-95b2-37dbf4629631",353000,"Ik kies nu left want ik ga hem nu aan de linkerkant bekijken.","1692afb2-aa2c-4f40-b9a8-2b5b5ee3f72e",349000,"En ik kies left. Ik kan left, right of center kiezen.","f82abda4-33ba-4c24-884e-ef4539d4cb11",344000,"1,55 dat is gemiddelde 0,02 dat is die standaarddeviatie.","3e860e45-4597-4b3c-90fa-3a9869c3a904",338000,"Dus de inf-norm van 0,10 dat is die alfa.","513b8f8d-eb2c-47f3-97f8-7821e8493169",336000,"Want ik ga hem links bekijken.","ba5ac8b3-0425-45f1-b7e9-9905de54e06a",331000,"Nou wat die keuze is, dat zie je hier, dat is dat ik links ga kiezen.","b7a91a9d-8833-472d-93be-5eff337cdd29",326000,"Gemiddelde, standaarddeviatie en een keuze.","6a8846dc-08fe-4c15-8be7-88b10a7ed802",322000,"Nou dan heb ik die alfa, dat is mijn kans die ik ga invoeren.","c1b5f8f5-374f-4ecc-939d-955fe0126b2d",315000,"Dan ga ik de inf-norm invullen om te kijken waar ligt dan die grens.","c2a9b9a1-5086-46c9-813a-135eec21924c",311000,"0,2 gedeeld door 10 is 0,02 liter.","f5726fef-6876-4da9-8955-633c501e7219",306000,"Dus dan krijg ik die standaarddeviatie 0,2 die deel ik dan door wortel 100.","b0a26c03-8d1e-41dd-88a5-0458d6da482e",303000,"Nou we hebben hier dat het om 100 flessen gaat.","3029d6f2-2f6f-4d74-8df7-2135c7fbf06e",298000,"Maar de standaarddeviatie van de steekproef, dan moeten we de wortel N gebruiken.","b2280f60-5915-48a6-98f3-413770742c83",289000,"Het gemiddelde van deze steekproef zal dan ook 1,55 zijn.","692b74db-7c1a-442b-a197-6222cf75e91a",59,283000,"Maar nu gaan we met alfa 0,10 gaan we kijken waar het kritieke gebied zit.","a2222019-4bcf-4a9c-8bc8-48770c9cad40","Het kan natuurlijk een klein beetje minder toevallig zijn.","1fd071cd-f9c6-499b-b671-1152b906998a",276000,"Dat het gemiddelde minder is dan die 1,55.","a5d91ce1-28fc-4390-a27c-1fd19af16095",271000,"En de alternatieve hypothese is dat die dan minder is.","4d4dea81-a712-4110-941a-bee937d3a8fa",268000,"Want zo is die ingesteld, daar gaan we vanuit.","e60f964e-ac32-4bdd-97fa-558d6553e7e7",262000,"De nul hypothese, de H0, is het gemiddelde is 1,55.","15e6cf1e-7986-489f-afce-ab69e1a912e2",260000,"Beslissingsvoorschrift.","972be128-216e-46f5-8715-0f63f5ef6c3f",256000,"Of dat dat er nog buiten zit?","a2604b9e-31b9-441a-bb78-92b8083c88dd",245000,"Dus ik vraag hier, zit het kritieke gebied, zit dat zo dat die 1,51 in het kritieke gebied zit?","e953c45d-c3c3-4f16-ae07-3affabd5efd9",240000,244000,"Kies een alfa 0,10.","bf10ba92-2170-4fe8-b14d-60401e8c3933",237000,"Kun je niet concluderen dat de machine niet goed werkt?","e92c2c90-3a64-405c-a31e-1a804ee495dd",230000,"Na controle blijkt het gemiddelde van 100 flessen 1,51 liter te zijn.","e3a059d3-8ac5-4865-9997-1c2b6600ade9",221000,"Een vulmachine wordt ingesteld met een gemiddelde van 1,55 liter en een standaarddeviatie van 0,03 liter.","fcb05ce3-ef98-486f-9aaf-fb4b36373dca",219000,"Bijvoorbeeld de frisdrankenfabriek.","18a0660e-820c-492b-81f6-5a797e28a28e",213000,"En we krijgen ook nog voorbeelden waarbij het wel logischer is dat je een normale verdeling gebruikt.","62195bc7-3fce-4274-b220-ae594d45e097",203000,"Een normale verdeling is eigenlijk niet voor discrete variabelen, maar hier laat ik zien hoe ik dan die overstap kan maken.","f403d6b2-7f8e-4b9f-926e-79610f464980",198000,"Want ik ga tweezijdig kijken waarbij het dan heel onwaarschijnlijk zal zijn.","096bbf34-c7f1-4b5e-850d-4b009c6716b1",195000,"En dan ben ik tweezijdig aan het toetsen.","d30e1025-1a85-4b28-9308-bb9778ae552f",194000,"Ga ik 2 keer de standaarddeviatie naar links, dan zit ik op 4.","076fff75-9a53-4ad7-b744-5d7db6adc5e5",186000,"Ga ik 2 keer de standaarddeviatie naar rechts, dan kom ik op 16.","d92a62f4-0bb5-4b92-9314-3c7f88c58a7f",183000,"Want ik heb een gemiddelde van 10.","bcafba62-1ad3-4915-9c01-4cda559418b9",173000,"H0 zal ik gaan verwerpen als de x kleiner is dan 4 of als de x groter is dan 16.","0eeec37b-513d-4a4e-8ac4-703ada3afbab",170000,"Een voorbeeld.","c70fa9f3-4b82-4056-83d1-161dd461719e",166000,"En daar buiten hebben we het kritieke gebied.","0265bc5d-f9d2-49b7-b513-cd453c2bea6a",165000,"En dan is het voor die 95% 2 keer de standaarddeviatie naar rechts en 2 keer de standaarddeviatie naar links.","05782c2a-3169-4fc8-b697-95cbc46e6dd3",154000,"Laten we nou gewoon zeggen dat die standaarddeviatie 3 is.","2bae7575-b668-4203-a4f4-07f047bbcb8c",147000,"Het gemiddelde is 10 en de standaarddeviatie is afhankelijk van die n.","f3146a43-1585-49bb-a83e-3b820b497d2b",142000,"We hebben hier een normale verdeling.","7be6d991-b81c-463e-9611-c9df27670642",138000,"Het is afhankelijk van hoe vaak je dat uitvoert.","97a75f13-e79a-46e1-b2d2-26af44d9a18f",135000,"Mijn standaarddeviatie is afhankelijk van de n.","fe04865b-5d65-43ac-88ee-0a7a14b753b9",132000,"Dat is die alfa 0,05.","0eac2542-8c11-4d30-b68b-ceed9e3205e1",127000,"Want die 5% die overblijft, die zit daar buiten in het kritieke gebied.","583c9ea6-e294-42f1-903a-261a263bf900",121000,"Als ik dat heb, dan heb ik dus 95% rond dat gemiddelde.","bef2569e-e1f6-458b-860c-5bcd7953bf7c",112000,"Dus het gemiddelde is 10 en we nemen een significantieniveau alfa van 0,05.","eb935396-4842-4c39-b425-9c56dd39b9d1",109000,"Dat is daar in het midden.","85393ed8-f1ac-4434-89cf-133e33d1b3a2",106000,"Dus dan verwacht ik dat het gemiddelde 10 zal zijn.","0b050a5a-cdaa-4e18-aab4-f127cb50ef79",102000,"Dat is hier 60 keer 1 zesde, de kans op 6.","d7245b63-cec6-47f7-8ba3-96bf054cc1f8",98000,"dan doe ik Ex is n keer p, dus aantal keren.","3e925b40-ea04-48ec-8b9f-e08ab6b90178",91000,"En als ik naar de verwachting kijk, van wat zal ik verwachten hoe vaak ik 6 gooi,","2d537b4a-0090-45d3-95a5-55a5b114445d",86000,"Als ik een normale verdeling heb, dan krijg ik zo'n klokvorm.","2a60e68e-8cf1-4bbf-b075-ced7d93c532d",80000,85000,"Ik ga dan van een binomiaal kans experiment naar een normale verdeling.","5d6562b7-7458-4bd8-92e1-315d19fc275a",74000,"Dus we gaan dus ook weer kijken, hoe vaak zal ik 6 gooien?","55b59698-eaf2-47ae-ac7d-3c6f07f6549a",70000,"kun je ervan uitgaan dat deze stogast normaal verdeeld is.","d5e09a19-a678-4b24-800e-d40d57549050",67000,"en wanneer je dit experiment 10.000 keer herhaalt,","eb293258-944b-4883-bd6a-48d149de2917",62000,"Wanneer je 60 keer met een dobbelsteen gooit, met stogast 6,","acf6e7cd-902e-4362-bd4c-a47169b1f2bb",59000,"Als je het nu bekijkt in de normale verdeling.","ecb08142-4c7f-4ad4-bd34-bdc8e3688bdd",54000,58000,"En dat je dan de alternatieve hypothese, de H1, moet gaan aannemen.","86914c2c-229c-4a8a-b659-5a68d28273ba",49000,"De nulhypothese, of je die kunt aannemen of dat je die kunt verwerpen.","4de61a80-eea5-4585-8188-730fb4793a3e","Wat verwacht je? Wat zijn de uitzonderingen?","df5143cc-34b7-454a-bac8-c3f3aa036a39",41000,"Dan ga je kijken naar wat is de kans om 6 te gooien.","20c0e3a5-9f4c-4dc3-b178-037ae07891c3",37000,"We hebben in les 1 gekeken of een dobbelsteen zuiver is.","86934b79-7954-42c3-9d1d-0ce80250e5c7","Is de dobbelsteen betrouwbaar? Is die zuiver?","a316ba32-6de5-48d5-ab76-ff613806d96f","Hoe toets je hypotheses met een normale verdeling?","toetsen-van-hypothesen-2","metaTitle","Hoe toets je hypotheses met normale verdelingen? | Wiskunde","metaDescription","Leer over beslissingsvoorschriften voor hypothesetoetsen met normaalverdelingen. Ontdek de wortel-n-wet en linkszijdig, rechtzijdig of tweezijdig toetsen.","metaImageUuid","2036f46b-c81c-4884-967a-879397ae9d2b","courseUuid","2c5618d7-8d98-4da3-99e7-f191d7bc4b19","086e8292-fa24-429d-aa20-40a90309b4c5",["D",1777012829957],"createdByUserUuid","8ba75ac8-8763-4d01-b5ed-b64f804b3c28",["D",1706812537063],"improvementsHaveBeenGenerated","metaImage",{"_28":9875,"_811":10206,"_813":10778,"_815":816,"_817":10779,"_819":10780,"_139":10781,"_821":149,"_255":149,"_822":42,"_168":823,"_824":271,"_46":11047,"_826":11048,"_828":11049,"_830":11050},"topicSummaries",[11030,11031,11032],"post",{"_28":9878,"_211":9890},[9891,9892,9893,9894,9895,9896,9897,9898,9899,9900,9901,9902,9903,9904,9905,9906,9907,9908,9909,9910,9911,9912,9913,9914,9915,9916,9917,9918,9919,9920,9921,9922,9923,9924,9925,9926,9927,9928,9929,9930,9931,9932,9933,9934,9935,9936,9937,9938,9939,9940,9941,9942,9943,9944,9945,9946,9947,9948,9949,9950,9951,9952,9953,9954,9955,9956,9957,9958,9959,9960,9961],{"_28":11025,"_215":9878,"_152":44,"_145":10064,"_217":11026,"_219":-5},{"_28":11020,"_215":9878,"_152":703,"_145":216,"_217":11021,"_219":-5},{"_28":11015,"_215":9878,"_152":699,"_145":216,"_217":11016,"_219":-5},{"_28":11010,"_215":9878,"_152":694,"_145":216,"_217":11011,"_219":-5},{"_28":11005,"_215":9878,"_152":99,"_145":216,"_217":11006,"_219":-5},{"_28":11000,"_215":9878,"_152":686,"_145":10064,"_217":11001,"_219":-5},{"_28":10991,"_215":9878,"_152":681,"_145":216,"_217":10992,"_219":-5},{"_28":10955,"_215":9878,"_152":677,"_145":10200,"_217":10956,"_219":10957},{"_28":10917,"_215":9878,"_152":672,"_145":216,"_217":10918,"_219":-5},{"_28":10912,"_215":9878,"_152":667,"_145":10064,"_217":10913,"_219":-5},{"_28":10907,"_215":9878,"_152":105,"_145":216,"_217":10908,"_219":-5},{"_28":10889,"_215":9878,"_152":660,"_145":216,"_217":10890,"_219":-5},{"_28":10869,"_215":9878,"_152":656,"_145":216,"_217":10870,"_219":-5},{"_28":10864,"_215":9878,"_152":652,"_145":10064,"_217":10865,"_219":-5},{"_28":10838,"_215":9878,"_152":648,"_145":216,"_217":10839,"_219":-5},{"_28":10814,"_215":9878,"_152":643,"_145":216,"_217":10815,"_219":-5},{"_28":10774,"_215":9878,"_152":638,"_145":10200,"_217":10775,"_219":10776},{"_28":10769,"_215":9878,"_152":633,"_145":10064,"_217":10770,"_219":-5},{"_28":10751,"_215":9878,"_152":628,"_145":216,"_217":10752,"_219":-5},{"_28":10740,"_215":9878,"_152":623,"_145":216,"_217":10741,"_219":-5},{"_28":10729,"_215":9878,"_152":618,"_145":216,"_217":10730,"_219":-5},{"_28":10712,"_215":9878,"_152":614,"_145":216,"_217":10713,"_219":-5},{"_28":10701,"_215":9878,"_152":609,"_145":216,"_217":10702,"_219":-5},{"_28":10696,"_215":9878,"_152":605,"_145":10064,"_217":10697,"_219":-5},{"_28":10677,"_215":9878,"_152":600,"_145":216,"_217":10678,"_219":-5},{"_28":10672,"_215":9878,"_152":596,"_145":216,"_217":10673,"_219":-5},{"_28":10661,"_215":9878,"_152":592,"_145":216,"_217":10662,"_219":-5},{"_28":10650,"_215":9878,"_152":587,"_145":216,"_217":10651,"_219":-5},{"_28":10639,"_215":9878,"_152":583,"_145":216,"_217":10640,"_219":-5},{"_28":10634,"_215":9878,"_152":579,"_145":216,"_217":10635,"_219":-5},{"_28":10629,"_215":9878,"_152":574,"_145":10064,"_217":10630,"_219":-5},{"_28":10597,"_215":9878,"_152":569,"_145":216,"_217":10598,"_219":-5},{"_28":10560,"_215":9878,"_152":565,"_145":10200,"_217":10561,"_219":10562},{"_28":10556,"_215":9878,"_152":560,"_145":10194,"_217":10557,"_219":-5},{"_28":10546,"_215":9878,"_152":555,"_145":216,"_217":10547,"_219":-5},{"_28":10532,"_215":9878,"_152":550,"_145":216,"_217":10533,"_219":-5},{"_28":10514,"_215":9878,"_152":545,"_145":216,"_217":10515,"_219":-5},{"_28":10502,"_215":9878,"_152":540,"_145":216,"_217":10503,"_219":-5},{"_28":10486,"_215":9878,"_152":535,"_145":216,"_217":10487,"_219":-5},{"_28":10480,"_215":9878,"_152":530,"_145":216,"_217":10481,"_219":-5},{"_28":10469,"_215":9878,"_152":525,"_145":216,"_217":10470,"_219":-5},{"_28":10464,"_215":9878,"_152":521,"_145":10064,"_217":10465,"_219":-5},{"_28":10431,"_215":9878,"_152":517,"_145":216,"_217":10432,"_219":-5},{"_28":10394,"_215":9878,"_152":513,"_145":10200,"_217":10395,"_219":10396},{"_28":10390,"_215":9878,"_152":509,"_145":10194,"_217":10391,"_219":-5},{"_28":10379,"_215":9878,"_152":504,"_145":216,"_217":10380,"_219":-5},{"_28":10364,"_215":9878,"_152":499,"_145":216,"_217":10365,"_219":-5},{"_28":10346,"_215":9878,"_152":494,"_145":216,"_217":10347,"_219":-5},{"_28":10334,"_215":9878,"_152":489,"_145":216,"_217":10335,"_219":-5},{"_28":10323,"_215":9878,"_152":484,"_145":216,"_217":10324,"_219":-5},{"_28":10314,"_215":9878,"_152":479,"_145":216,"_217":10315,"_219":-5},{"_28":10301,"_215":9878,"_152":474,"_145":216,"_217":10302,"_219":-5},{"_28":10296,"_215":9878,"_152":470,"_145":10064,"_217":10297,"_219":-5},{"_28":10239,"_215":9878,"_152":465,"_145":216,"_217":10240,"_219":-5},{"_28":10199,"_215":9878,"_152":460,"_145":10200,"_217":10201,"_219":10202},{"_28":10193,"_215":9878,"_152":455,"_145":10194,"_217":10195,"_219":-5},{"_28":10183,"_215":9878,"_152":451,"_145":216,"_217":1018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in. De rekenmachine geeft dan direct de linker- en rechtergrenzen die het middelste 90% gebied omvatten, wat betekent dat 5% aan elke kant in het kritieke gebied ligt.","invNorm(kans = 0,90, gemiddelde, standaardafwijking, optie = center)",", wil je het middelste 90% gebied vinden. Je voert dan ","7etco","\\alpha=0{,}10",[9980],{"_231":9981},"\\alpha=0{,}10\\alpha=010","-optie gebruiken. Als"," kun je soms ook direct de ","bold","tweezijdig toetsen","Bij ","a0791da4-e4fd-4fef-90a7-810e5a9cea59",{"_220":703,"_221":9989,"_9990":99,"_223":9991},[9992,9993,9994,9995,9996,9997,9998,9999],"listStart","disc",{"_9984":42,"_231":10004},{"_231":10003},{"_257":42,"_231":6229},{"_231":10002},{"_257":42,"_231":4094},{"_231":10001},{"_257":42,"_231":2899},{"_231":10000},") van de verdeling bekijkt.",") of het midden (","), de rechterkant (",": Hier geef je aan of je de linkerkant (","Optie","02e51c70-ec30-4661-9ba4-0dc24825ea1b",{"_220":703,"_221":10007,"_9990":694,"_223":9991},[10008,10009,10010],{"_9984":42,"_231":10016},{"_233":10012,"_235":10013,"_145":237,"_221":10014},{"_231":10011},": De standaardafwijking van de steekproefgemiddelden, berekend met de wortel-n-wet.","tx10m","\\left(\\sigma\\right)",[10015],{"_231":10013},"Standaardafwijking","727025a1-427d-402a-bd4a-c90dc8a612e1",{"_220":703,"_221":10019,"_9990":699,"_223":9991},[10020,10021,10022],{"_9984":42,"_231":3369},{"_233":10024,"_235":10025,"_145":237,"_221":10026},{"_231":10023},": De verwachte waarde volgens de nulhypothese.","xetzl","\\left(\\mu\\right)",[10027],{"_231":10025},"28bb5b6d-7aef-4bcf-953b-3036cea5176c",{"_220":703,"_221":10030,"_223":9991},[10031,10032,10033,10034,10035,10036],{"_9984":42,"_231":10049},{"_231":10048},{"_233":10044,"_235":10045,"_145":237,"_221":10046},{"_231":10043},{"_233":10038,"_235":10039,"_145":237,"_221":10040},{"_231":10037},"om de grens van één van de twee staarten te vinden.","c6kum","\\frac{\\alpha}{2}",[10041],{"_231":10042},"\\frac{\\alpha}{2}\\frac{\\alpha}{\\placeholder{}}",". Voor een tweezijdige toets gebruik je","sqtrj","\\alpha",[10047],{"_231":149},": Dit is de oppervlakte van het kritieke gebied in de staart die je bekijkt. Voor een eenzijdige toets (links- of rechtszijdig) gebruik je het significatieniveau","Kans","4b311a33-e598-4db9-baa5-e113ac819746",{"_221":10052},[10053,10054,10055,10056,10057],{"_231":10062},{"_257":42,"_231":10061},{"_231":10060},{"_257":42,"_231":10059},{"_231":10058},") op je grafische rekenmachine is een handig hulpmiddel bij het bepalen van de grenzen van het kritieke gebied. Je voert meestal de volgende parameters in:","inverseNormal"," (of ","invNorm","De functie ","70263916-ee3d-4fd5-8010-057d6d152509","h2",{"_221":10066},[10067],{"_231":10068},"Werken met je grafische rekenmachine ","ad6dd090-061b-4a13-8410-adaa63b1f086",{"_221":10071},[10072,10073,10074,10075,10076,10077,10078,10079],{"_9984":42,"_231":10095},{"_231":10094},{"_233":10091,"_235":236,"_145":237,"_221":10092},{"_231":3078},{"_233":10086,"_235":10087,"_145":237,"_221":10088},{"_231":463},{"_233":10081,"_235":10082,"_145":237,"_221":10083},{"_231":10080},". Dit is het kritieke gebied.","jteu1","\\bar{X}>1{,}5604",[10084],{"_231":10085},"\\bar{X}>1{,}5604>1{,}5604x>1{,}5604xˉ>1{,}5604xˉ>15604","zulik","\\bar{X}<1{,}5395",[10089],{"_231":10090},"\\bar{X}<1{,}5395\\bar{X}<15395\\bar{X}<1,5395\\bar{X}_{\\bar{X}}xˉ<1,5395_{\\bar{X}}xˉ<1,5395_{\\bar{X}}xˉ<1,5395_{\\bar{X}}xˉ<1,5395_{\\bar{X}}xˉ<1,5395_{\\bar{X}}xˉ<1,5395_{\\bar{X}}xˉ<1,5395_{\\bar{X}}xˉ<1,5395_{\\bar{X}}xˉ<1,5395","bgjyy",[10093],{"_231":149},"\nBeslissingsvoorschrift: Verwerp","Beslissing:","f2546c01-ed06-4892-99f5-f409064f33c1",{"_220":703,"_221":10098,"_9990":699,"_223":9991},[10099,10100,10101,10102],{"_9984":42,"_231":10106},{"_231":10105},{"_257":42,"_231":10104},{"_231":10103},"\nDit geeft een rechtergrens van ongeveer 1,5604 liter.","invNorm(kans = 0,05, gemiddelde = 1,55, standaardafwijking = 0,00632, optie = rechts)","\n","Rechtergrens:","6cc94132-ce53-4724-89bd-6949886690ba",{"_220":703,"_221":10109,"_223":9991},[10110,10111,10112,10113],{"_9984":42,"_231":10116},{"_231":10105},{"_257":42,"_231":10115},{"_231":10114},"\nDit geeft een linkergrens van ongeveer 1,5395 liter.","invNorm(kans = 0,05, gemiddelde = 1,55, standaardafwijking = 0,00632, optie = links)","Linkergrens:","f80bf3ad-b27d-4669-82aa-a7eff68dc008",{"_221":10119},[10120,10121,10122,10123],{"_9984":42,"_231":10131},{"_231":10130},{"_233":10125,"_235":10126,"_145":237,"_221":10127},{"_231":10124},".","ldsgm","\\frac{\\alpha}{2}=\\frac{0{,}10}{2}=0{,}05",[10128],{"_231":10129},"\\frac{\\alpha}{2}=\\frac{0{,}10}{2}=0{,}05\\alpha\\frac{\\alpha}{2}=\\frac{0{,}10}{2}=0{,}05\\alpha:\\frac{\\alpha}{2}=\\frac{0{,}10}{2}=0{,}05\\alpha:\\frac{\\alpha}{2}=\\frac{0{,}10}{2}=005\\alpha:\\frac{\\alpha}{2}=\\frac{0{,}10}{2}=0,05\\alpha:\\frac{\\alpha}{2}=\\frac{0{,}10}{\\placeholder{}}=0,05\\alpha:\\frac{\\alpha}{2}=0{,}10=0,05\\alpha:\\frac{\\alpha}{2}=0{,}10/=0,05\\alpha:\\frac{\\alpha}{2}=0{,}10/2=0,05\\alpha:\\frac{\\alpha}{2}=010/2=0,05\\alpha:\\frac{\\alpha}{2}=0,10/2=0,05\\alpha:\\frac{\\alpha}{\\placeholder{}}=0,10/2=0,05\\alpha:\\alpha=0,10/2=0,05\\alpha:\\alpha/=0,10/2=0,05","\nAangezien het een tweezijdige toets is, verdelen we","Bepalen van de kritieke grenzen:","245ee0bf-31e6-4220-9da9-634573d104e5",{"_221":10134},[10135,10136,10137,10138],{"_9984":42,"_231":10145},{"_231":10105},{"_233":10140,"_235":10141,"_145":237,"_221":10142},{"_231":10139},"liter. (Gebruik voor de berekening op de rekenmachine de onafgeronde waarde van de standaardafwijking voor het meest nauwkeurige antwoord.)","9rzs8","\\sigma_{\\bar{X}}=\\frac{0{,}2}{\\sqrt{1000}}\\approx0{,}00632",[10143],{"_231":10144},"\\sigma_{\\bar{X}}=\\frac{0{,}2}{\\sqrt{1000}}\\approx0{,}00632\\sigma_{\\bar{X}}=\\frac{02}{\\sqrt{1000}}\\approx0{,}00632\\sigma_{\\bar{X}}=\\frac{0,2}{\\sqrt{1000}}\\approx0{,}00632\\sigma_{\\bar{X}}=\\frac{0,2}{\\sqrt{1000}}\\approx000632","Berekening van de standaardafwijking van het steekproefgemiddelde:","4551bc95-8443-4407-be43-fd5211751da2",{"_220":703,"_221":10148,"_9990":699,"_223":9991},[10149,10150,10151,10152,10153],{"_9984":42,"_231":10164},{"_233":10161,"_235":242,"_145":237,"_221":10162},{"_231":10160},{"_233":10155,"_235":10156,"_145":237,"_221":10157},{"_231":10154},". (De machine mag niet significant afwijken, zowel naar boven als naar beneden).","hq0l4","\\left(\\mu\\neq1{,}55\\right)",[10158],{"_231":10159},"\\left(\\mu\\neq1{,}55\\right)\\mu\\neq1{,}55\\mu\\neq155",": Het gemiddelde vulvolume is niet gelijk aan 1,55 liter","9s9k9",[10163],{"_231":242},"Alternatieve hypothese","8d664f9b-9cda-416c-be89-9c62a97ec3c3",{"_220":703,"_221":10167,"_223":9991},[10168,10169,10170,10171,10172],{"_9984":42,"_231":10182},{"_233":10179,"_235":247,"_145":237,"_221":10180},{"_231":10178},{"_233":10173,"_235":10174,"_145":237,"_221":10175},{"_231":10124},"11fvi","\\left(\\mu=1{,}55\\right)",[10176],{"_231":10177},"\\left(\\mu=1{,}55\\right)\\mu=1{,}55\\mu=155",": Het gemiddelde vulvolume is 1,55 liter","ki1xz",[10181],{"_231":247},"Nulhypothese","bb972700-ca95-4553-a799-b480dda89d27",{"_221":10185},[10186,10187,10188],{"_231":10192},{"_233":10189,"_235":9978,"_145":237,"_221":10190},{"_231":10124},"zy2uu",[10191],{"_231":9981},"Een vulmachine wordt ingesteld op een gemiddelde van 1,55 liter en een populatiestandaardafwijking van 0,2 liter. Een controle wordt uitgevoerd op een steekproef van 1000 flessen. Bepaal het kritieke gebied voor het steekproefgemiddelde. Kies","70c3d6e5-0b4e-4a46-90d5-f3a859fa1521","h3",{"_221":10196},[10197],{"_231":10198},"Voorbeeld","e03b8895-1268-45f6-8b43-054a6d2e8715","img",{"_847":7974,"_821":10235,"_221":10236},{"_10203":10199,"_833":10204,"_255":-5,"_847":-5,"_849":-5,"_837":149,"_219":10205},"postComponentUuid","d7405426-d2be-4448-a9db-dbf936a013ac",{"_28":10204,"_811":10206,"_813":10207,"_815":816,"_817":10208,"_819":10209,"_139":10210,"_821":149,"_255":149,"_822":42,"_168":823,"_824":271,"_46":10211,"_826":10212,"_828":10213,"_830":10214,"_10215":-5},"af5ab146-b639-4100-a079-620177e55998","https://jojoschool-cdn.azureedge.net/uploads/d7405426-d2be-4448-a9db-dbf936a013ac.png","Screenshot 2026-04-22 at 17.21.11.png",125151,"Tweezijdig kritiek gebied",["D",1776871288072],["D",1776873695808],["D",1776874565374],{"_28":10216,"_833":10204,"_834":5289,"_836":8390,"_837":10217,"_46":10218,"_839":10219},"audio","e63a5b14-28ca-434e-b9d2-13a924221f17","Een normale verdeling met twee kritieke gebieden",["D",1776871288153],[10220,10221,10222,10223],{"_28":10233,"_845":10216,"_819":5445,"_847":857,"_849":592,"_813":10234},{"_28":10230,"_845":10216,"_819":10231,"_847":853,"_849":530,"_813":10232},{"_28":10227,"_845":10216,"_819":10228,"_847":848,"_849":9153,"_813":10229},{"_28":10224,"_845":10216,"_819":10225,"_847":6967,"_849":8833,"_813":10226},"101610ac-02a8-489e-b11e-a1bde2f3373c",13145,"https://jojoschool.blob.core.windows.net/uploads/d7405426-d2be-4448-a9db-dbf936a013ac-600x156.png","06b52511-bc5b-4c7c-966f-121d882d9e2b",4772,"https://jojoschool.blob.core.windows.net/uploads/d7405426-d2be-4448-a9db-dbf936a013ac-300x78.png","efdb082e-7331-4deb-86d7-8f9784c0e83d",1748,"https://jojoschool.blob.core.windows.net/uploads/d7405426-d2be-4448-a9db-dbf936a013ac-150x39.png","a028381d-8dcc-4878-b187-643a93f0b9bf","https://jojoschool.blob.core.windows.net/uploads/d7405426-d2be-4448-a9db-dbf936a013ac-100x26.png",[10238],[10237],{"_231":149},{"_231":10217},"83849169-d850-464e-8184-81671f0fe5fa",{"_221":10241},[10242,10243,10244,10245,10246,10247,10248,10249,10250,10251,10252,10253,10254,10255,10256,10257,10258,10259,10260],{"_231":10295},{"_9984":42,"_231":10294},{"_231":10293},{"_233":10289,"_235":10290,"_145":237,"_221":10291},{"_231":10288},{"_231":10287,"_10281":42},{"_231":10286},{"_233":10283,"_235":10263,"_145":237,"_221":10284},{"_231":10282},{"_231":10280,"_10281":42},{"_231":10279},{"_233":10276,"_235":10045,"_145":237,"_221":10277},{"_231":10275},{"_233":10272,"_235":10039,"_145":237,"_221":10273},{"_231":10271},{"_233":10267,"_235":10039,"_145":237,"_221":10268},{"_231":10266},{"_233":10262,"_235":10263,"_145":237,"_221":10264},{"_231":10261},"als het steekproefgemiddelde in het kritieke gebied valt, dus als het kleiner is dan de linker kritieke grenswaarde of groter is dan de rechter kritieke grenswaarde.","s4eip","H_{0}",[10265],{"_231":149},"voor de rechterkant. Je verwerpt","u4c78",[10269],{"_231":10270},"\\frac{\\alpha}{2}\\frac{\\alpha}{\\placeholder{}}\\alpha\\alpha/","voor de linkerkant en","cyjr4",[10274],{"_231":10270},"op in twee gelijke delen:","lhckv",[10278],{"_231":149}," uiteinden van de normale verdeling. Je splitst de","beide","italic",", dus het kan zowel kleiner als groter zijn. Het kritieke gebied bevindt zich dan aan ","u58u3",[10285],{"_231":149}," van de waarde in de nulhypothese","verschilt","aangeeft dat het gemiddelde ","7i2ap","H_{1}",[10292],{"_231":149}," gebruik je wanneer de alternatieve hypothese","tweezijdige toets","Een ","e67c55ba-34b5-431c-b9eb-b7e944f7d94a",{"_221":10298},[10299],{"_231":10300},"Tweezijdig toetsen","b73bf3eb-618c-4585-aafe-bfbdeacf7fe4",{"_221":10303},[10304,10305,10306,10307],{"_9984":42,"_231":10313},{"_231":10312},{"_233":10309,"_235":10263,"_145":237,"_221":10310},{"_231":10308},"niet. Op basis van deze steekproef kunnen we niet concluderen dat de machine niet goed werkt.","yp9sk",[10311],{"_231":149}," \nWe verwerpen de nulhypothese","Conclusie:","551ca9e8-5148-49a5-802b-583fe1b52335",{"_221":10316},[10317,10318,10319,10320],{"_9984":42,"_231":10095},{"_231":10322},{"_231":4924,"_10281":42},{"_231":10321}," in het kritieke gebied.","\nHet waargenomen steekproefgemiddelde is 1,57 liter. Dit ligt onder de kritieke grens van 1,5862 liter. Het gemiddelde bevindt zich dus ","aed3a4b9-452b-4582-9174-7d4068ef978e",{"_221":10325},[10326,10327,10328,10329],{"_9984":42,"_231":10333},{"_231":10332},{"_257":42,"_231":10331},{"_231":10330},"\nDit geeft een kritieke grenswaarde van 1,5862 liter.","invNorm(kans = 0,10, gemiddelde = 1,55, standaardafwijking = 0,02828, optie = rechts)","\nMet behulp van een grafische rekenmachine:\n","Bepalen van de kritieke grens:","5d21453e-b0cb-4010-8f03-f0fae3f528a2",{"_221":10336},[10337,10338,10339,10340],{"_9984":42,"_231":10145},{"_231":10105},{"_233":10341,"_235":10342,"_145":237,"_221":10343},{"_231":5697},"a3pqw","\\sigma_{\\bar{X}}=\\frac{0{,}2}{\\sqrt{50}}\\approx0{,}02828",[10344],{"_231":10345},"\\sigma_{\\bar{X}}=\\frac{0{,}2}{\\sqrt{50}}\\approx0{,}02828\\sigma_{\\bar{X}}=\\frac{02}{\\sqrt{50}}\\approx0{,}02828\\sigma_{\\bar{X}}=\\frac{0,2}{\\sqrt{50}}\\approx0{,}02828\\sigma_{\\bar{X}}=\\frac{0,2}{\\sqrt{50}}\\approx002828","da0400b7-9251-4bf1-9889-f9da5303b958",{"_220":703,"_221":10348,"_9990":699,"_223":9991},[10349,10350,10351,10352,10353],{"_9984":42,"_231":10164},{"_233":10360,"_235":242,"_145":237,"_221":10361},{"_231":10359},{"_233":10355,"_235":10356,"_145":237,"_221":10357},{"_231":10354},". (De fabriek is bang voor te veel inhoud, verspilling, dus rechtszijdig).","8hwbw","\\left(\\mu>1,55\\right)",[10358],{"_231":10356},": Het gemiddelde vulvolume is groter dan 1,55 liter","oj2jb",[10362],{"_231":10363},"\\left(H_1\\right)\\left(qH_1\\right)\\left(H_1\\right)","6c74e2f3-434c-4d68-ace6-8e49f2d50f41",{"_220":703,"_221":10366,"_223":9991},[10367,10368,10369,10370,10371],{"_9984":42,"_231":10182},{"_233":10376,"_235":247,"_145":237,"_221":10377},{"_231":10178},{"_233":10372,"_235":10373,"_145":237,"_221":10374},{"_231":10124},"7stvl","\\left(\\mu=1,55\\right)",[10375],{"_231":10373},"16zj5",[10378],{"_231":247},"8bfea3ed-038c-47d5-8888-7da2601bda03",{"_221":10381},[10382,10383,10384],{"_231":10389},{"_233":10385,"_235":10386,"_145":237,"_221":10387},{"_231":10124},"7l84x","\\alpha = 0,10",[10388],{"_231":149},"Een vulmachine wordt ingesteld op een gemiddelde van 1,55 liter met een populatiestandaardafwijking van 0,2 liter. Na controle van 50 flessen blijkt het gemiddelde 1,57 liter te zijn. Kun je concluderen dat de machine niet goed werkt? Kies","828b4bde-7cd4-4c3d-8944-0717924adc54",{"_221":10392},[10393],{"_231":10198},"366db3e6-7338-42ee-a78b-d8c1d4097366",{"_847":7950,"_821":10426,"_221":10427},{"_10203":10394,"_833":10397,"_255":-5,"_847":-5,"_849":-5,"_837":149,"_219":10398},"3d05267e-1d01-4470-a94e-9e3fd214d6e5",{"_28":10397,"_811":10206,"_813":10399,"_815":816,"_817":10400,"_819":10401,"_139":10402,"_821":149,"_255":149,"_822":42,"_168":823,"_824":271,"_46":10403,"_826":10404,"_828":10405,"_830":10406,"_10215":-5},"https://jojoschool-cdn.azureedge.net/uploads/3d05267e-1d01-4470-a94e-9e3fd214d6e5.png","Screenshot 2026-04-22 at 17.14.12.png",170933,"Kritiek gebied rechts",["D",1776870868942],["D",1776873687465],["D",1776874565401],{"_28":10407,"_833":10397,"_834":5338,"_836":8158,"_837":10408,"_46":10409,"_839":10410},"aa2da6dd-03c0-4494-b146-6a9752e4a6f0","Voorbeeld van een normale verdeling met een kritiek gebied aan de rechterkant ",["D",1776870869021],[10411,10412,10413,10414],{"_28":10424,"_845":10407,"_819":3256,"_847":857,"_849":565,"_813":10425},{"_28":10421,"_845":10407,"_819":10422,"_847":853,"_849":489,"_813":10423},{"_28":10418,"_845":10407,"_819":10419,"_847":848,"_849":9077,"_813":10420},{"_28":10415,"_845":10407,"_819":10416,"_847":6967,"_849":8679,"_813":10417},"89d13e60-9ca6-4811-b61c-8fe25faece98",19664,"https://jojoschool.blob.core.windows.net/uploads/3d05267e-1d01-4470-a94e-9e3fd214d6e5-600x192.png","8e6e3d97-772e-4df3-88d1-883d14213b70",6905,"https://jojoschool.blob.core.windows.net/uploads/3d05267e-1d01-4470-a94e-9e3fd214d6e5-300x96.png","74539e05-35d0-4271-8832-17460a019d5f",2580,"https://jojoschool.blob.core.windows.net/uploads/3d05267e-1d01-4470-a94e-9e3fd214d6e5-150x48.png","f034e64b-7013-48e3-8f97-0568cb964785","https://jojoschool.blob.core.windows.net/uploads/3d05267e-1d01-4470-a94e-9e3fd214d6e5-100x32.png",[10429],[10428],{"_231":149},{"_231":10430},"Voorbeeld van een normale verdeling met het kritieke gebied aan de rechterkant ","2cdf1862-e649-4c17-8c11-71996c11f8a7",{"_221":10433},[10434,10435,10436,10437,10438,10439,10440,10441,10442,10443,10444,10445,10446],{"_231":10295},{"_9984":42,"_231":10463},{"_231":10293},{"_233":10460,"_235":242,"_145":237,"_221":10461},{"_231":10288},{"_231":3601,"_10281":42},{"_231":10459},{"_233":10456,"_235":10263,"_145":237,"_221":10457},{"_231":10455},{"_233":10452,"_235":10263,"_145":237,"_221":10453},{"_231":10451},{"_233":10448,"_235":10045,"_145":237,"_221":10449},{"_231":10447},"hoort.","67uq3",[10450],{"_231":149},"als het steekproefgemiddelde in het kritieke gebied valt, dus als het groter is dan de kritieke grenswaarde die bij significantieniveau","2kswt",[10454],{"_231":149},"wordt gesteld. Het kritieke gebied bevindt zich dan volledig aan de rechterkant van de normale verdeling. Je verwerpt","nenyk",[10458],{"_231":149}," is dan de waarde die in de nulhypothese","4ytii",[10462],{"_231":242},"rechtszijdige toets","b3cb26b8-3884-4653-bd79-2d41b7ee8d28",{"_221":10466},[10467],{"_231":10468},"Rechtszijdig toetsen","6c0eb226-f2bc-42ac-90d0-63ddfbbe57e9",{"_221":10471},[10472,10473,10474,10475],{"_9984":42,"_231":10313},{"_231":10312},{"_233":10477,"_235":247,"_145":237,"_221":10478},{"_231":10476},". We kunnen concluderen dat de machine niet goed werkt en waarschijnlijk opnieuw ingesteld moet worden.","mai5j",[10479],{"_231":247},"861ba4ed-b591-4c99-a36a-79a21e351d7b",{"_221":10482},[10483,10484],{"_9984":42,"_231":10095},{"_231":10485},"\nHet waargenomen steekproefgemiddelde is 1,51 liter. Dit ligt onder de kritieke grens van 1,52436 liter. Het gemiddelde bevindt zich dus in het kritieke gebied.","f882a113-d90f-4e22-aac9-b9c34823fb1b",{"_221":10488},[10489,10490,10491,10492,10493,10494,10495,10496],{"_9984":42,"_231":10333},{"_231":10501},{"_257":42,"_231":10061},{"_231":10500},{"_257":42,"_231":10059},{"_231":10499},{"_257":42,"_231":10498},{"_231":10497},"\nDit geeft een kritieke grenswaarde van 1,52436 liter.","invNorm(kans = 0,10, gemiddelde = 1,55, standaardafwijking = 0,02, optie = links)","):\n"," of ","\nMet behulp van een grafische rekenmachine (functie ","03c2d30b-b95e-4182-98f1-80e4529a3994",{"_221":10504},[10505,10506,10507,10508],{"_9984":42,"_231":10145},{"_231":10105},{"_233":10509,"_235":10510,"_145":237,"_221":10511},{"_231":5697},"261gt","\\sigma_{\\bar{X}}=\\frac{0{,}2}{\\sqrt{100}}=\\frac{0{,}2}{10}=0{,}02",[10512],{"_231":10513},"\\sigma_{\\bar{X}}=\\frac{0{,}2}{\\sqrt{100}}=\\frac{0{,}2}{10}=0{,}02\\sigma_{\\bar{X}}=\\frac{0{,}2}{\\sqrt{100}}=\\frac{0{,}2}{10}=002\\sigma_{\\bar{X}}=\\frac{0{,}2}{\\sqrt{100}}=\\frac{0{,}2}{10}=0,02\\sigma_{\\bar{X}}=\\frac{0{,}2}{\\sqrt{100}}=\\frac{02}{10}=0,02\\sigma_{\\bar{X}}=\\frac{0{,}2}{\\sqrt{100}}=\\frac{0,2}{10}=0,02\\sigma_{\\bar{X}}=\\frac{02}{\\sqrt{100}}=\\frac{0,2}{10}=0,02","4a1efa37-00b2-4d13-ac71-1ea51a81184f",{"_220":703,"_221":10516,"_9990":699,"_223":9991},[10517,10518,10519,10520,10521],{"_9984":42,"_231":10164},{"_233":10529,"_235":242,"_145":237,"_221":10530},{"_231":10528},{"_233":10523,"_235":10524,"_145":237,"_221":10525},{"_231":10522},". (De fabriek is bang voor te weinig inhoud, dus linkszijdig).","qaz55","\\left(\\mu<1{,}55\\right)",[10526],{"_231":10527},"\\left(\\mu<1{,}55\\right)\\left(\\mu1{,}55\\right)\\left(\\mu=1{,}55\\right)",": Het gemiddelde vulvolume is kleiner dan 1,55 liter","5d26t",[10531],{"_231":242},"5be6e5d0-3ff2-4d66-8013-63864a78cb5e",{"_220":703,"_221":10534,"_223":9991},[10535,10536,10537,10538,10539],{"_9984":42,"_231":10182},{"_233":10543,"_235":247,"_145":237,"_221":10544},{"_231":10178},{"_233":10540,"_235":10174,"_145":237,"_221":10541},{"_231":10124},"f45rf",[10542],{"_231":10177},"ej5av",[10545],{"_231":247},"90727093-4f80-4d2c-b18b-195d074d36f9",{"_221":10548},[10549,10550,10551],{"_231":10555},{"_233":10552,"_235":10386,"_145":237,"_221":10553},{"_231":10124},"hrqb1",[10554],{"_231":149},"Een vulmachine hoort flessen af te vullen met gemiddeld 1,55 liter en een populatiestandaardafwijking van 0,2 liter. Na controle van 100 flessen blijkt het gemiddelde 1,51 liter te zijn. Kun je concluderen dat de machine niet goed werkt? Kies","83776294-b733-47c5-b1af-f626795ea810",{"_221":10558},[10559],{"_231":10198},"164a64c6-ca6e-46a5-bd7c-897c42349866",{"_847":7958,"_821":10592,"_221":10593},{"_10203":10560,"_833":10563,"_255":-5,"_847":-5,"_849":-5,"_837":149,"_219":10564},"8f7826bf-a153-418c-8a3c-41a97b8a9ec0",{"_28":10563,"_811":10206,"_813":10565,"_815":816,"_817":10566,"_819":10567,"_139":10568,"_821":149,"_255":149,"_822":42,"_168":823,"_824":271,"_46":10569,"_826":10570,"_828":10571,"_830":10572,"_10215":-5},"https://jojoschool-cdn.azureedge.net/uploads/8f7826bf-a153-418c-8a3c-41a97b8a9ec0.png","Screenshot 2026-04-22 at 17.10.09.png",173312,"Kritiek gebied links",["D",1776870654642],["D",1776873711005],["D",1776874565340],{"_28":10573,"_833":10563,"_834":5412,"_836":8076,"_837":10574,"_46":10575,"_839":10576},"20ef07c0-53d8-4f56-a262-4442dcce20c2","Voorbeeld van een normale verdeling met een kritiek gebied aan de linkerkant ",["D",1776870654718],[10577,10578,10579,10580],{"_28":10590,"_845":10573,"_819":2562,"_847":857,"_849":550,"_813":10591},{"_28":10587,"_845":10573,"_819":10588,"_847":853,"_849":470,"_813":10589},{"_28":10584,"_845":10573,"_819":10585,"_847":848,"_849":9046,"_813":10586},{"_28":10581,"_845":10573,"_819":10582,"_847":6967,"_849":8613,"_813":10583},"df2f328d-53c0-4f69-bbcc-46f03c825cb4",20770,"https://jojoschool.blob.core.windows.net/uploads/8f7826bf-a153-418c-8a3c-41a97b8a9ec0-600x208.png","c1050422-4454-452b-b762-903a3894eda5",7412,"https://jojoschool.blob.core.windows.net/uploads/8f7826bf-a153-418c-8a3c-41a97b8a9ec0-300x104.png","b28413a3-d26d-4097-9c27-1784361ca100",2712,"https://jojoschool.blob.core.windows.net/uploads/8f7826bf-a153-418c-8a3c-41a97b8a9ec0-150x52.png","ffbae386-1e1b-4219-a122-4ac785a769c3","https://jojoschool.blob.core.windows.net/uploads/8f7826bf-a153-418c-8a3c-41a97b8a9ec0-100x35.png",[10595],[10594],{"_231":149},{"_231":10596},"Voorbeeld van een normale verdeling met het kritieke gebied aan de linkerkant ","ec9e8dfe-b624-40e8-bc1d-2d413e527b5e",{"_221":10599},[10600,10601,10602,10603,10604,10605,10606,10607,10608,10609,10610,10611,10612],{"_231":10295},{"_9984":42,"_231":10628},{"_231":10293},{"_233":10624,"_235":10625,"_145":237,"_221":10626},{"_231":10288},{"_231":3625,"_10281":42},{"_231":10459},{"_233":10621,"_235":236,"_145":237,"_221":10622},{"_231":10620},{"_233":10617,"_235":10263,"_145":237,"_221":10618},{"_231":10616},{"_233":10613,"_235":10045,"_145":237,"_221":10614},{"_231":10447},"qmmkm",[10615],{"_231":149},"als het steekproefgemiddelde in het kritieke gebied valt, dus als het kleiner is dan de kritieke grenswaarde die bij significantieniveau","6mor7",[10619],{"_231":149},"wordt gesteld. Dit is bijvoorbeeld relevant als je wilt onderzoeken of een machine te weinig van een product afvult. Het kritieke gebied bevindt zich dan volledig aan de linkerkant van de normale verdeling. Je verwerpt","6fuz3",[10623],{"_231":149},"sakrr","H_1",[10627],{"_231":149},"linkszijdige toets","44fa7e8e-0372-4417-bed1-5bcf39c7d4be",{"_221":10631},[10632],{"_231":10633},"Linkszijdig toetsen","953f301a-1f46-442a-8f07-2ada26b92259",{"_221":10636},[10637],{"_231":10638},"Deze wet is cruciaal voor het toetsen van hypothesen met steekproefgemiddelden, omdat het de spreiding van onze waarnemingen correct weergeeft.","976e6993-361d-4672-981a-6608a8333499",{"_220":703,"_221":10641,"_9990":694,"_223":9991},[10642,10643,10644],{"_231":149},{"_233":10646,"_235":10647,"_145":237,"_221":10648},{"_231":10645},"de grootte van de steekproef.","pegs7","n",[10649],{"_231":149},"0dba01d3-1399-4009-b88d-2455848b3005",{"_220":703,"_221":10652,"_9990":699,"_223":9991},[10653,10654,10655],{"_231":149},{"_233":10657,"_235":10658,"_145":237,"_221":10659},{"_231":10656},"de standaardafwijking van de populatie;","ocm6m","\\sigma",[10660],{"_231":149},"7faad740-885e-490f-bdd2-f9a286da9f83",{"_220":703,"_221":10663,"_223":9991},[10664,10665,10666],{"_231":149},{"_233":10668,"_235":10669,"_145":237,"_221":10670},{"_231":10667},"de standaardafwijking van het steekproefgemiddelde;","v4zkd","\\sigma_{\\bar{X}}",[10671],{"_231":149},"9f7356eb-26d3-4d6c-b460-11cc26d64372",{"_221":10674},[10675],{"_231":10676},"Hierbij is:","237cd9f1-4f9b-49b8-832d-bfd76382f77f",{"_221":10679},[10680,10681,10682,10683,10684,10685,10686],{"_231":10695},{"_9984":42,"_231":10694},{"_231":10693},{"_9984":42,"_231":10692},{"_231":10691},{"_233":10687,"_235":10688,"_145":237,"_221":10689},{"_231":10124},"oyc27","\\sigma_{\\bar{X}} = \\frac{\\sigma}{\\sqrt{n}}",[10690],{"_231":149}," beschrijft dit verband:","wortel-n-wet"," kleiner is dan de standaardafwijking van de individuele metingen in de populatie. Dit komt omdat extreme waarden elkaar in een steekproef vaak opheffen. De ","steekproefgemiddelden","Wanneer we werken met steekproeven, moeten we rekening houden met het feit dat de standaardafwijking van de ","deeef668-ba4b-4405-a6c6-3d0f2d6559bb",{"_221":10698},[10699],{"_231":10700},"De wortel-n-wet","4d8093d1-c9b4-439f-a266-194a21ad0107",{"_221":10703},[10704,10705,10706],{"_231":10711},{"_233":10708,"_235":10647,"_145":237,"_221":10709},{"_231":10707},"ook gebruiken als benadering voor discrete variabelen (zoals het aantal keer zes gooien). Voor continue variabelen, zoals de inhoud van flessen, is de normale verdeling echter veel logischer om te gebruiken.","xql1l",[10710],{"_231":149},"Hoewel de normale verdeling in principe voor continue variabelen is, kunnen we deze bij een voldoende grote","cb3e0f7f-f135-4976-8256-8ea30d6bd003",{"_221":10714},[10715,10716,10717,10718,10719],{"_231":10728},{"_233":10725,"_235":236,"_145":237,"_221":10726},{"_231":10724},{"_233":10721,"_235":236,"_145":237,"_221":10722},{"_231":10720},"aan.","xmgp0",[10723],{"_231":149},"als de waargenomen frequentie van zes kleiner is dan 4 of groter is dan 16. Als de uitkomst binnen het bereik van 4 tot en met 16 ligt, nemen we","orat8",[10727],{"_231":149},"Het beslissingsvoorschrift is dan: verwerp","3545191e-2dd6-4c24-a5ee-bb8a03270b50",{"_220":703,"_221":10731,"_9990":699,"_223":9991},[10732,10733,10734],{"_231":10116},{"_233":10735,"_235":10736,"_145":237,"_221":10737},{"_231":149},"ua5z0","\\text{gemiddelde }-\\text{ }2\\text{ }\\cdot\\text{ standaardafwijking}=10-2\\cdot3=4",[10738],{"_231":10739},"\\text{gemiddelde }-\\text{ }2\\text{ }\\cdot\\text{ standaardafwijking}=10-2\\cdot3=4\\text{gemiddelde }-\\text{ }2\\text{ }\\cdot\\text{ standaardafwijking}=10-2\\cdot3=4\\text{gemiddelde }-\\text{ }2\\text{ }\\cdot\\text{standaardafwijking}=10-2\\cdot3=4\\text{gemiddelde }-\\text{ }2\\text{ }\\cdot\\text{standaardafwijking}=10-2\\cdot3=4\\text{gemiddelde }-\\text{ }2\\cdot\\text{standaardafwijking}=10-2\\cdot3=4\\text{gemiddelde }-\\text{ }2\\cdot\\text{standaardafwijking}=10-2\\cdot3=4\\text{gemiddelde }-2\\cdot\\text{standaardafwijking}=10-2\\cdot3=4","f806468e-59f0-4325-93ed-9571cd5dbb2a",{"_220":703,"_221":10742,"_223":9991},[10743,10744,10745],{"_231":10106},{"_233":10746,"_235":10747,"_145":237,"_221":10748},{"_231":149},"b3uex","\\text{gemiddelde }+\\text{ }2\\text{ }\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16",[10749],{"_231":10750},"\\text{gemiddelde }+\\text{ }2\\text{ }\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde }+\\text{ }2\\text{ }\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde }+\\text{ }2\\text{ }\\cdot\\text{standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde }+\\text{ }2\\text{ }\\cdot\\text{standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde }+\\text{ }2\\cdot\\text{standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde }+\\text{ }2\\cdot\\text{standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde }+2\\cdot\\text{standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{ standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{standaardafwijking}=10+2\\cdot3=16\\text{gemiddelde}+2\\cdot\\text{standaardafwijking }=10+2\\cdot3=16","89280d21-9c9d-4fc6-9af5-a26af01627c0",{"_221":10753},[10754,10755,10756,10757,10758,10759,10760],{"_231":10295},{"_9984":42,"_231":918},{"_231":10768},{"_9984":42,"_231":9985},{"_231":10767},{"_233":10762,"_235":10763,"_145":237,"_221":10764},{"_231":10761},"), kunnen we de grenzen bepalen:","vknp9","\\alpha\\approx0{,}05",[10765],{"_231":10766},"\\alpha\\approx0{,}05\\alpha\\approx005"," en als we de vuistregel hanteren dat 95% van de waarnemingen binnen twee standaardafwijkingen van het gemiddelde valt (wat overeenkomt met"," geeft aan wanneer je de nulhypothese moet verwerpen. Laten we teruggaan naar het dobbelsteenvoorbeeld met een gemiddelde van 10. De standaardafwijking van 3 is hier een aangenomen waarde om het voorbeeld te illustreren. Als we voor dit voorbeeld ","2fc2bbaa-651f-4364-9197-8ca5974a3915",{"_221":10771},[10772],{"_231":10773},"Het beslissingsvoorschrift opstellen","3f82e42b-b0da-4b3d-b4ac-7ba9f36e6bff",{"_847":7183,"_821":10809,"_221":10810},{"_10203":10774,"_833":9875,"_255":-5,"_847":-5,"_849":-5,"_837":149,"_219":10777},{"_28":9875,"_811":10206,"_813":10778,"_815":816,"_817":10779,"_819":10780,"_139":10781,"_821":149,"_255":149,"_822":42,"_168":823,"_824":271,"_46":10782,"_826":10783,"_828":10784,"_830":10785,"_10215":-5},"https://jojoschool-cdn.azureedge.net/uploads/2036f46b-c81c-4884-967a-879397ae9d2b.png","Screenshot 2026-04-22 at 17.01.30.png",329839,"Een normale verdeling met kritieke gebieden",["D",1776870101839],["D",1776870187758],["D",1776871903331],{"_28":10786,"_833":9875,"_834":3295,"_836":7516,"_837":10787,"_46":10788,"_839":10789},"a929d2ab-2007-4005-ad83-d6af64ce062f","Een normale verdeling met het gemiddelde, het 95%-gebied rond het gemiddelde en de twee kritieke gebieden (elk 2,5%) aan de uiteinden, gemarkeerd met alfa gedeeld door 2.",["D",1776870101924],[10790,10791,10792,10793,10794],{"_28":10807,"_845":10786,"_819":3043,"_847":857,"_849":565,"_813":10808},{"_28":10804,"_845":10786,"_819":10805,"_847":853,"_849":489,"_813":10806},{"_28":10801,"_845":10786,"_819":10802,"_847":848,"_849":9077,"_813":10803},{"_28":10798,"_845":10786,"_819":10799,"_847":6967,"_849":8679,"_813":10800},{"_28":10795,"_845":10786,"_819":10796,"_847":4460,"_849":7875,"_813":10797},"8fccdd24-648f-4ed4-8b74-26a46e2fcdb1",55561,"https://jojoschool.blob.core.windows.net/uploads/2036f46b-c81c-4884-967a-879397ae9d2b-1200x384.png","5dd43614-1590-4a6f-9b22-c0d38fb84228",19704,"https://jojoschool.blob.core.windows.net/uploads/2036f46b-c81c-4884-967a-879397ae9d2b-600x192.png","c76ed217-92f5-4291-b860-dbb0caacee1e",6970,"https://jojoschool.blob.core.windows.net/uploads/2036f46b-c81c-4884-967a-879397ae9d2b-300x96.png","d662a56a-8b39-4c54-8ab9-795fcee44ac0",2592,"https://jojoschool.blob.core.windows.net/uploads/2036f46b-c81c-4884-967a-879397ae9d2b-150x48.png","dfeab90f-34e5-4028-b11b-4ff7de7611be","https://jojoschool.blob.core.windows.net/uploads/2036f46b-c81c-4884-967a-879397ae9d2b-100x32.png",[10812],[10811],{"_231":149},{"_231":10813},"Een normale verdeling met het gemiddelde, het 95%-gebied rond het gemiddelde en de twee kritieke gebieden (elk 2,5%) aan de uiteinden, gemarkeerd met alpha gedeeld door 2.","d752401b-da56-41db-b3b7-c976c46571a2",{"_221":10816},[10817,10818,10819,10820,10821,10822,10823],{"_231":10837},{"_9984":42,"_231":10836},{"_231":10835},{"_233":10831,"_235":10045,"_145":237,"_221":10832},{"_231":10830},{"_233":10825,"_235":10826,"_145":237,"_221":10827},{"_231":10824},", betekent dit dat 95% van de waarnemingen rond het gemiddelde ligt en 5% daarbuiten, in het kritieke gebied.","g735k","0{,}05",[10828],{"_231":10829},"0{,}05\\left(0{,}05\\right.\\left(0{,}05\\right)","gelijk is aan","3eycf",[10833],{"_231":10834},"\\alpha\\alpha\\,\\alpha\\,\\left(0{,}05\\right)",". Dit is het gebied in de normale verdeling waar de waarnemingen zo extreem zijn dat ze hoogstwaarschijnlijk niet afkomstig zijn van de verdeling zoals beschreven in de nulhypothese. Als het significantieniveau","kritieke gebied","Het significatieniveau bepaalt het ","4d221b15-36a7-44de-b01f-48255b55401f",{"_221":10840},[10841,10842,10843,10844,10845,10846,10847,10848],{"_231":10863},{"_9984":42,"_231":10862},{"_233":10857,"_235":10858,"_145":237,"_221":10859},{"_231":10856},{"_233":10853,"_235":10045,"_145":237,"_221":10854},{"_231":641},{"_233":10850,"_235":10826,"_145":237,"_221":10851},{"_231":10849},"(of 5%) gebruikt.","zm81w",[10852],{"_231":149},"l800z",[10855],{"_231":149},". Dit is de kans dat je de nulhypothese ten onrechte verwerpt (ook wel een type I-fout genoemd). Vaak wordt een","r6xvt","\\left(\\alpha\\right)",[10860],{"_231":10861},"\\left(\\alpha\\right)\\alpha","significatieniveau","Om te bepalen of we de nulhypothese verwerpen of aannemen, gebruiken we een ","1d56a9c4-f813-4e0f-8924-c4c2d3a50aa0",{"_221":10866},[10867],{"_231":10868},"Het significatieniveau en kritieke gebied","9a666db5-fd34-4e37-9a86-0302d8bcc644",{"_220":703,"_221":10871,"_9990":699,"_223":9991},[10872,10873,10874,10875,10876,10877],{"_231":10888},{"_9984":42,"_231":198},{"_233":10885,"_235":10290,"_145":237,"_221":10886},{"_231":10884},{"_233":10879,"_235":10880,"_145":237,"_221":10881},{"_231":10878},". Dit is de bewering die je aanneemt als de nulhypothese wordt verworpen. Bij de dobbelsteen zou de alternatieve hypothese kunnen zijn: \"De dobbelsteen is niet zuiver (de kans op een zes is niet 1/6).\"","k68vn","p\\neq\\frac16",[10882],{"_231":10883},"p\\neq\\frac16p\\neq\\frac{1}{\\placeholder{}}",":","kquer",[10887],{"_231":149},"De ","1bbe4fac-63b7-46a9-86df-f5cfe1eceda4",{"_220":703,"_221":10891,"_223":9991},[10892,10893,10894,10895,10896,10897],{"_231":10888},{"_9984":42,"_231":204},{"_233":10904,"_235":10263,"_145":237,"_221":10905},{"_231":10884},{"_233":10899,"_235":10900,"_145":237,"_221":10901},{"_231":10898},". Dit is de bewering die je wilt toetsen en waarvan je in principe uitgaat dat deze waar is, tenzij het tegendeel wordt bewezen. Bij de dobbelsteen is de nulhypothese bijvoorbeeld: \"De dobbelsteen is zuiver (de kans op een zes is 1/6).\"","l6sjv","p=\\frac16",[10902],{"_231":10903},"p=\\frac16p=\\frac{1}{\\placeholder{}}p=1p=","9ysbw",[10906],{"_231":149},"c98bbfd5-0555-4eaa-bccf-5008b2a4d697",{"_221":10909},[10910],{"_231":10911},"Bij het toetsen van een hypothese stel je altijd twee hypothesen op:","ce34b1d1-6859-43d2-89c8-8174b0fcd230",{"_221":10914},[10915],{"_231":10916},"Nulhypothese en alternatieve hypothese","8e241f6b-54f1-4fbb-b32d-fc92135a6f89",{"_221":10919},[10920,10921,10922,10923,10924,10925,10926,10927,10928,10929,10930,10931,10932],{"_231":10888},{"_9984":42,"_231":895},{"_231":10954},{"_9984":42,"_231":3719},{"_231":10953},{"_233":10948,"_235":10949,"_145":237,"_221":10950},{"_231":10947},{"_233":10944,"_235":10647,"_145":237,"_221":10945},{"_231":10943},{"_233":10940,"_235":216,"_145":237,"_221":10941},{"_231":10939},{"_233":10934,"_235":10935,"_145":237,"_221":10936},{"_231":10933},". Je verwacht dus gemiddeld tien keer een zes te gooien. Dit gemiddelde bevindt zich in het midden van de klokvormige grafiek.","ga9hq","E(x)=60\\cdot\\frac16=10",[10937],{"_231":10938},"E(x)=60\\cdot\\frac16=10E(x)=60\\cdot\\frac{1}{\\placeholder{}}=10E(x)=60\\cdot1=10E(x)=60\\cdot=10E(x)=60\\cdot(=10E(x)=60\\cdot(1=10E(x)=60\\cdot(1/=10E(x)=60\\cdot(1/6=10","de kans op succes is. 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Veelgestelde vragen over Toetsen van hypothesen 2

Alle vragen