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(statistic\))f(whic)o(h)g(leads)h(to)g(the)g(decision)f(of)h(the)0
1929 y(acceptance)15 b(or)i(rejection)e(of)h(the)g(n)o(ull)e(h)o(yp)q
(othesis)j Fl(H)1020 1936 y Fu(0)1054 1929 y Fo(:)c Fl(\022)i
Fn(2)f Fo(\002,)h(or)i(alternativ)o(e)d(h)o(yp)q(othesis)i
Fl(H)1816 1936 y Fr(a)1851 1929 y Fo(:)e Fl(\022)h Fn(2)0 1990
y Fo(\002)38 1971 y Fr(c)55 1990 y Fo(.)22 b(Let)16 b Fm(Z)e
Fo(=)g Fm(B)318 1997 y Fr(opt)367 1990 y Fm(Y)f Fo(+)e Fm(N)515
1997 y Fr(a)536 1990 y Fo(,)k(the)h(h)o(yp)q(othesis)h(test)f(of)g(the)g
(feature)g(is)g(as)h(follo)o(ws:)122 2089 y Fl(H)162 2096 y
Fu(0)196 2089 y Fo(:)c Fl(\026)h Fo(=)g Fl(\026)347 2096 y
Fs(z)122 2149 y Fl(H)162 2156 y Fu(1)196 2149 y Fo(:)f Fl(\026)h
Fn(6)p Fo(=)g Fl(\026)347 2156 y Fs(z)122 2209 y Fo(The)i(statistic:)21
b Fl(S)s Fo(\()p Fm(Z)p Fo(\))14 b(=)g(\()p Fm(Z)d Fn(\000)g
Fl(\026)740 2216 y Fs(z)762 2209 y Fo(\))781 2191 y Fs(t)800
2209 y Fm(\006)840 2191 y Fq(\000)p Fs(1)892 2209 y Fo(\()p
Fm(Z)g Fn(\000)g Fl(\026)1035 2216 y Fs(z)1057 2209 y Fo(\))122
2270 y(The)16 b(critical)f(region)h Fl(C)t Fo(\()p Fl(\013)p
Fo(\))e(=)f Fn(f)p Fl(y)j Fo(:)d Fl(S)s Fo(\()p Fm(z)p Fo(\))h
Fl(>)g(c)979 2277 y Fr(\013)1003 2270 y Fn(g)0 2369 y Fo(Since)h
Fm(Z)f Fn(\030)f Fl(N)266 2376 y Fr(n)290 2369 y Fo(\()p Fl(\026)338
2376 y Fs(z)360 2369 y Fl(;)8 b Fm(\006)422 2376 y Fs(z)444
2369 y Fo(\),)15 b(let)g Fl(Z)j Fo(=)c(\()p Fm(Z)d Fn(\000)g
Fl(\026)808 2376 y Fs(z)830 2369 y Fo(\))849 2351 y Fs(t)868
2369 y Fm(\006)908 2351 y Fq(\000)p Fs(1)960 2369 y Fo(\()p
Fm(Z)g Fn(\000)g Fl(\026)1103 2376 y Fs(z)1125 2369 y Fo(\),)16
b(then)f Fl(Z)20 b Fo(is)15 b(a)h(random)f(v)m(ariable)h(with)f
Fl(\037)1927 2351 y Fu(2)1927 2381 y Fr(n)0 2429 y Fo(distribution)h(of)g
Fl(n)h Fo(degree)e(of)i(freedom)760 2411 y Fu(\(15\))824 2429
y Fo(.)73 2550 y(In)i(general,)f(eac)o(h)g(h)o(yp)q(othesis)h(test)g(has)g(a)
g(corresp)q(onding)h(critical)d(region)i Fl(C)t Fo(.)28 b(Giv)o(en)17
b(a)i(sample)0 2610 y(p)q(oin)o(t)14 b Fm(z)p Fo(,)f(if)g Fm(z)h
Fn(2)g Fl(C)t Fo(,)f(the)g Fl(H)492 2617 y Fu(0)526 2610 y
Fo(is)g(rejected.)19 b(If)13 b Fm(z)h Fn(62)g Fl(C)t Fo(,)f
Fl(H)1011 2617 y Fu(0)1045 2610 y Fo(will)f(not)i(b)q(e)g(rejected.)k(The)c
(size)f(of)g(the)h(critical)0 2670 y(region,)h Fl(\013)p Fo(,)g(\(or)g(the)g
(signi\014cance)f(lev)o(el)f(of)i(the)g(test\))f(is)h(de\014ned)g(as)g(the)g
(error)g(probabilit)o(y)f(that)h Fm(x)f Fo(falls)963 2795 y(5)p
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0 1 index
lineto
clip newpath
Mlp
translate
scale
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/Mgmatrix
matrix currentmatrix
def
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3 copy
Mlpfirst
{
Mnodistort
{
Mmin
dup
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4 index
2 index
2 index
Mlprun
11 index
11 -1 roll
10 -4 roll
Mlp1
8 index
9 -5 roll
Mlp1
4 -1 roll
and
{ exit } if
3 -1 roll
pop pop
} loop
exch
3 1 roll
7 -3 roll
pop pop pop
} bind def
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3 -1 roll
dup length
2 copy
-2 add
get
aload
pop pop pop
4 -2 roll
-1 add
get
aload
pop pop pop
6 -1 roll
3 -1 roll
5 -1 roll
sub
div
4 1 roll
exch sub
div
} bind def
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2 copy
4 index
0 get
dup
4 1 roll
Mlprun1
3 copy
8 -2 roll
9 -1 roll
{
3 copy
Mlprun1
3 copy
11 -3 roll
/gt Mlpminmax
8 3 roll
11 -3 roll
/lt Mlpminmax
8 3 roll
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pop pop
aload pop
5 -1 roll
aload pop
exch
6 -1 roll
Mlprun2
8 2 roll
4 -1 roll
Mlprun2
6 2 roll
3 -1 roll
Mlprun2
4 2 roll
exch
Mlprun2
6 2 roll
} bind def
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aload pop
exch
6 -1 roll
5 -1 roll
mul add
4 -2 roll
mul
3 -1 roll
add
} bind def
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2 copy
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3 1 roll
exch sub
} bind def
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cvx
2 index
6 index
2 index
exec
{
7 -3 roll
4 -1 roll
} if
1 index
5 index
3 -1 roll
exec
{
4 1 roll
pop
5 -1 roll
aload
pop pop
4 -1 roll
aload pop
[
8 -2 roll
pop
5 -2 roll
pop
6 -2 roll
pop
5 -1 roll
]
4 1 roll
pop
}
{
pop pop pop
} ifelse
} bind def
/Mlp1 {
5 index
3 index sub
5 index
2 index mul
1 index
le
1 index
0 le
or
dup
not
{
1 index
3 index div
.99999 mul
8 -1 roll
pop
7 1 roll
}
if
8 -1 roll
2 div
7 -2 roll
pop sub
5 index
6 -3 roll
pop pop
mul sub
exch
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