Hypotesetest
Moderatorer: Vektormannen, espen180, Aleks855, Solar Plexsus, Gustav, Nebuchadnezzar, Janhaa
a) Hypergeometrisk fordeling?
E(X) = np = 100 x p
Var(X) = np(1-p) x N-n/N-1 = 100 x p x (1-p) x N- 100/N-1
b) [tex]p_{0}= \frac{20}{100}=0,2[/tex]
[tex]H_{0}: p=0,2[/tex] [tex]H_{1}:p<0,2[/tex]
[tex]Z=\frac{\hat{p}-{p_{0}}}{\sqrt{p_{0(1-p_{0})/n}}}[/tex]
[tex]Z\alpha =Z_{0,025}=-1,96[/tex]
Forkast H0 hvis Z<-1,96
c) [tex]P(X=10)=\hat{p}=\frac{10}{100}=0,1[/tex]
ELLER kan det være slik:
a) Binomisk fordeling?
E(X) = np = 100 x p
Var(X) = np(1-p) = 100 x p x (1-p)
b) [tex]p_{0}= \frac{20}{100}=0,2[/tex]
[tex]H_{0}: p=0,2[/tex] [tex]H_{1}:p<0,2[/tex]
[tex]Z=\frac{\hat{p}-{p_{0}}}{\sqrt{p_{0(1-p_{0})/n}}}[/tex]
[tex]Z\alpha =Z_{0,025}=-1,96[/tex]
Forkast H0 hvis Z<-1,96
c) E(X) = 100 x 0,2 = 20
Var(X) = 100 x 0,2 x (1-p) = 16
[tex]\sigma = \sqrt{16}=4[/tex]
[tex]P(X=10)=G(\frac{x-\mu }{\sigma })=G(\frac{10-20}{4})=-2,5 =G =0,0202[/tex]