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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "#\n# Einfache Pr
\374fpl\344ne (Attribut-Kontrolle), \n# gew\366hnliche, randomisierte \+
und symmetrische Version\n# mit hypergeometrischer Verteilung (ohne Zu
r\374cklegen)\n# " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "#\n# N\344herungsforme
l f\374r notwendigen Stichprobenumfang\n#" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 10 "N := 5000;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 16 "p_alpha := 0.01;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "p
_beta := 0.03;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "alpha := \+
0.9;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "beta := 0.1;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "# Verteilungsfunktion zu N(0
,1)\nPhi := z -> 0.5+0.5*erf(z/sqrt(2.0));" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 81 "# komplement\344re Verteilungsfunktion zu N(0,1)\nP
hic := z -> 0.5*erfc(z/sqrt(2.0));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "z_alpha := fsolve(Phic(z)=1-alpha,z);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "z_1minbeta := fsolve(Phic(z)=beta,z
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "n_Bi := ((z_alpha*sq
rt(p_alpha*(1-p_alpha))+z_1minbeta*sqrt(p_beta*(1-p_beta)))/(p_beta-p_
alpha))^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "# n_Bi runden
 zu ganzer Zahl\nn_Bi := 300.;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 24 "n_Hy := n_Bi*N/(N+n_Bi);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "#\n# Exakte L\366sung\n#" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 100 "# Hypergeometrische Verteilung H(N,M,n)\n# hyp(M,k
) = Pr\{H(N,M,n) = k\}\n# Hyp(M,k) = Pr\{H(N,M,n) <= k\}" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "hyp := (M,k) -> binomial(M,k)*binom
ial(N-M,n-k)/binomial(N,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
37 "Hyp := (M,k) -> sum(hyp(M,j),j=0..k);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 182 "#\n# Randomisierter Pr\374fplan (n,c,delta) mit L(
M_alpha) = alpha und L(M_beta) <= beta\n# c = kleinste ganze Zahl mit \+
 Hyp(M_alpha,c) >= alpha\n# delta so w\344hlen, dass L(M_alpha) = alph
a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "L := M -> Hyp(M,c) - d
elta*hyp(M,c);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "# M_alpha
 = p_alpha*N (als Integerzahl!)\nM_alpha := p_alpha*N;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "M_alpha := convert(%,rational);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "# M_beta = p_beta*N (als In
tegerzahl!)\nM_beta := p_beta*N;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "M_beta := convert(%,rational);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 7 "n:=292;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 5 "c:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "delta := ev
alf((Hyp(M_alpha,c)-alpha)/hyp(M_alpha,c));" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 18 "evalf(L(M_alpha));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "evalf(L(M_beta));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "#\n# Symmetrische L\366sung: 1-L(M_alpha) = L(M_beta)
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "delta := evalf((Hyp(M_a
lpha,c)+Hyp(M_beta,c)-1)/(hyp(M_alpha,c)+hyp(M_beta,c)));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "# Kontrolle" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 13 "L(M_alpha,c);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "L(M_beta,c);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 15 "1-L(M_alpha,c);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "#
\n# Gew\366hnlicher Pr\374fplan (n,c) mit L(M_alpha) >= alpha) und L(M
_beta) <= beta\n# c = kleinste ganze Zahl mit  L(M_alpha) >= alpha" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "# OC-Funktion als Funktion \+
von M\nL := M -> Hyp(M,c);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
7 "n:=292;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "c:=5;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalf(L(M_alpha));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf(L(M_beta));" }}}}
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