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Samenvatting HC5 categoriale uitkomsten 1 steekproef $4.33
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Samenvatting HC5 categoriale uitkomsten 1 steekproef

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HC5 categoriale uitkomsten 1 steekproef STEP statistiek

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  • December 14, 2018
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  • 2017/2018
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Statistiek ien Epideieioiogoeiie Eviegiien Fgoor



Categoriale uitkomsten, 1
steekproef
Kansverdelingen
Bij contnnie nitkoioistien hoort ieien contnnie kanisvierdeiegine zoagis deie norioagie vierdeieginei Catieeoriaag
hondet in deat ier ioaar ieien biepierkt aantag iooeiegijkie nitkoioistien zijn (kgaisisien)i Bij catieeoriagie
nitkoioistien hoort ieien deiiscrietie kanisvierdeiegine, pier kgaisisie wordet aaneieeievien wat deie kanis op iiedeier van
deie iooeiegijkie kgaisisie iisi Voorbieiegdeien hiiervan zijn deie binoioiagie vierdeiegine ien deie poiisison vierdeieginei Die
binoioiagie vierdeiegine koiot voor wannieier ioien tie ioakien hieief ioiet ieien deichotoioie nitkoioist, deit hondet
in: ieien nitkoioist deat ioaar twieie waardeien aan kan nieioieni
- Contnnie kanisvierdeiegine:
o Hiet aantag iooeiegijk nitkoioistien iis onieindeie
o P(X=a) = 0, denis P(Xa) = P(X>a), deie kanis op ieien ispiecifiekie nitkoioist iis 0
o Hiistoeraio bienadeierde deoor ieien cnrvie: kanisvierdeiegine
- Diiscrietie kanisvierdeiegine:
o Uitkoioistien zijn deiiscrietie waardeien (0, 1, 2, …)
o P(X=a)  0, deie kanis op ieien ispiecifiekie nitkoioist iis erotier dean 0

Binomiale verdeling
Bij hiet nitvoierien van n iexpieriioientien hieief iiedeier iexpieriioient twieie iooeiegijkie nitkoioistien A ien Bi Pier
iexpieriioient iis ier deieziegfdeie kanis  op nitkoioist Ai Kanisien wordeien in deie popngatie wieiereieeievien ioiet deie
giettier i Die kanis op r ‘isnccieisisien’ in n iexpieriioientien:


()
P ( r )= n π r ( 1−π )n−r ioiet deie binoioiaagcoëfciënt n =
r ()
n!
r r ! ( n−r ) !
 istaat voor isnccieis ien 1 -  istaat voor ieien ioiisgnkkinei Die binoioiaagcoëfciënt eieief wieier op hoievieieg
vierischiggiendeie ioaniierien ioien n nit r isnccieisisien kan hiebbieni

Binomiale toets
Die binoioiagie toietis eaat nit van 1 istieiekproief ioiet ieien deichotoioie nitkoioisti Hiet deoieg iervan iis p tieistien
tieeien ieien vierondeieristiegdeie kanis in deie popngatie (0)i Die binoioiagie vierdeiegine wordet eiebrnikt oio deie p-
waardeie nit tie riekienieni Die vogeiendeie hypothieisien wordeien opeieistiegde: H 0:  = 0 ioiet H1:   0i
Toietisineiseroothieide: r, voget ieien binoioiagie vierdeiegine ioiet paraioietieris n ien 0i

n = 8, r = 5, p = 0i625
(istieiekproiefproportie 55/8)
H0:   0i14 ioiet H1:  > 0i14
Toietisineiseroothieide: r = 5, voget ieien
binoioiagie vierdeiegine ioiet n = 8 ien 0 =
0i14
p-waardeie: P(r  5)= P(r=5) + P(r=6) +
P(r=7) + P(r=8)




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