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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "#\n# Randomisierter
 zweistufiger Pr\374fplan:\n# Bestimmung der Randomisierungsgewichte d
elta1,delta2,delta3 so,\n# dass L(p_alpha)=alpha und L(p_beta)=beta\n#
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "# hyp(k) = Pr\{X1 = k\} = P\{H(N,M,
n1) = k\}" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "hyp := k ->1.0*binomia
l(M,k)*binomial(N-M,n1-k)/binomial(N,n1);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 50 "# hyp2(j,k) = Pr\{X2|j = k\} = P\{H(N-n1,M-j,n2) = \+
k\}" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "hyp2 := (j,k) -> 1.0*binomia
l(M-j,k)*binomial(N-n1-M+j,n2-k)/binomial(N-n1,n2);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 8 "N:=5000;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "n1:=100;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "
n2:=200;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "c1:=0;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "d1:=3;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 5 "c:=6;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 27 "# Berechnung von L(p_alpha)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "M:=50; # p_alpha = 0.01" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 92 "# Annahmewahrscheinlichkeit bei 1. Stichprobe\nL_alph
a := sum(hyp(i),i=0..c1)-delta1*hyp(c1);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 113 "# Annahmewahrscheinlichkeit bei 2. Stichprobe\n# sum
(P\{X1 = j\}*(P\{X2|j <= c-j\}-delta3*P\{X2|j = c-j\}, j=c1+1..d1-1)" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "A:=0;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 5 "B:=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 100 "for j from c1+1 to d1-1 do\n  A:=A+hyp(j)*sum(hyp2(j,i),i=0..
c-j);\n  B:=B+hyp(j)*hyp2(j,c-j);\nend do:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 28 "L_alpha:=L_alpha+A-delta3*B;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 18 "# Randpunkte c1,d1" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 362 "if (c1<d1) then\n  # Randpunkt c1\n  L_alpha := L_
alpha + delta1*hyp(c1)*(sum(hyp2(c1,i),i=0..c-c1)-delta3*hyp2(c1,c-c1)
);\n  # Randpunkt d1\n  L_alpha := L_alpha + delta2*hyp(d1)*(sum(hyp2(
d1,i),i=0..c-d1)-delta3*hyp2(d1,c-d1));\nelif (c1=d1) then\n  L_alpha \+
:= L_alpha\n             +(delta1+delta2-1)*hyp(c1)*(sum(hyp2(c1,i),i=
0..c-c1)-delta3*hyp2(c1,c-c1));\nend if;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "L_alpha := simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 2 "# " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "# Ber
echnung von L(p_beta)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "M \+
:= 150;  # p_beta = 0.03" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 
"L_beta := sum(hyp(i),i=0..c1)-delta1*hyp(c1);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 5 "A:=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 5 "B:=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "for j from c
1+1 to d1-1 do\n  A:=A+hyp(j)*sum(hyp2(j,i),i=0..c-j);\n  B:=B+hyp(j)*
hyp2(j,c-j);\nend do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "L_
beta:=L_beta+A-delta3*B;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
322 "if (c1<d1) then\n  L_beta := L_beta + delta1*hyp(c1)*(sum(hyp2(c1
,i),i=0..c-c1)-delta3*hyp2(c1,c-c1));\n  L_beta := L_beta + delta2*hyp
(d1)*(sum(hyp2(d1,i),i=0..c-d1)-delta3*hyp2(d1,c-d1));\nelif (c1=d1) t
hen\n  L_beta := L_beta \n            +(delta1+delta2-1)*hyp(c1)*(sum(
hyp2(c1,i),i=0..c-c1)-delta3*hyp2(c1,c-c1));\nend if;" }{TEXT -1 1 "
\000" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "L_beta := simplify(
%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "delta1:=1;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "unassign('delta2','delta3');
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "fsolve(\{L_alpha-0.9,L_
beta-0.1\},\{delta2,delta3\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 10 "assign(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "#\n# \+
Maximum der ASN-Funktion\n#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "unassign('M','j');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "#
 hyper(M,k) = Pr\{X1 = k\} = P\{H(N,M,n1) = k\}" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 69 "hyper := (M,k) ->1.0*binomial(M,k)*binomial(N-M,n1-k)
/binomial(N,n1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 222 "# ASN-
Funktion als Funktion von M\nif (c1<d1) then \n  ASN := M -> n1 + n2*(
sum(hyper(M,j),j=c1+1..d1-1)+delta1*hyper(M,c1)+delta2*hyper(M,d1));\n
elif (c1=d1) then\n  ASN := M -> n1 + n2*(delta1+delta2-1)*hyper(M,c1)
;\nend if ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "print ('M','
p','ASN(p)');\nfor M from 0 by 10 to 100 do\n  print(M,evalf(M/N),ASN(
M))\nend do;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK 
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