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Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 7-1 Chapter 7 Sampling and Sampling Distributions Business Statistics: A First Course 5 th Edition
Transcript of Business Statistics: A First Course - الصفحات الشخصية |...
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
all,
In
c.
Chap 7
-1
Ch
ap
ter
7
Sam
plin
g a
nd S
am
plin
g D
istr
ibutions
Busin
ess S
tatistics:
A F
irst C
ou
rse
5th
Ed
itio
n
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
all,
In
c..
Chap 7
-2
Lea
rnin
g O
bje
ctives
In t
his
ch
ap
ter,
yo
u learn
:
�T
o d
istin
gu
ish
be
twe
en
diffe
ren
t sa
mp
ling
me
tho
ds
�T
he
co
nce
pt
of
the s
am
plin
g d
istr
ibu
tio
n
�T
o c
om
pu
te p
rob
ab
ilitie
s r
ela
ted
to
the
sa
mp
le
me
an
an
d t
he
sam
ple
pro
po
rtio
n
�T
he
im
po
rta
nce
of th
e C
en
tra
l L
imit T
he
ore
m
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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c..
Chap 7
-3
Why S
am
ple
?
�S
ele
ctin
g a
sa
mp
le is le
ss t
ime
-co
nsu
min
g t
ha
n
se
lectin
g e
ve
ry ite
m in
th
e p
op
ula
tio
n (
ce
nsu
s).
�S
ele
ctin
g a
sa
mp
le is le
ss c
ostly th
an
se
lectin
g
eve
ry ite
m in
th
e p
op
ula
tio
n.
�A
n a
na
lysis
of a
sa
mp
le is le
ss c
um
be
rso
me
a
nd
mo
re p
ractica
l th
an
an
an
aly
sis
of th
e e
ntire
p
op
ula
tio
n.
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-4
A S
am
plin
g P
roce
ss B
eg
ins W
ith
A
Sa
mp
ling
Fra
me
�T
he
sa
mp
ling
fra
me
is a
lis
tin
g o
f ite
ms t
ha
t
ma
ke
up
th
e p
op
ula
tio
n
�F
ram
es a
re d
ata
so
urc
es s
uch
as p
op
ula
tio
n
lists
, d
ire
cto
rie
s,
or
ma
ps
�In
accu
rate
or
bia
se
d r
esu
lts c
an
re
su
lt if a
fr
am
e e
xclu
de
s c
ert
ain
po
rtio
ns o
f th
e
po
pu
latio
n
�U
sin
g d
iffe
ren
t fr
am
es t
o g
en
era
te d
ata
ca
n
lea
d t
o d
issim
ilar
co
nclu
sio
ns
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-5
Types o
f S
am
ple
s
Sa
mp
les
No
n-P
rob
ab
ilit
y
Sa
mp
les
Ju
dg
men
t
Pro
ba
bil
ity
Sam
ple
s
Sim
ple
Ra
nd
om Sy
stem
ati
cStr
ati
fied C
lust
er
Co
nv
enie
nce
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-6
Typ
es o
f S
am
ple
s:
No
np
rob
ab
ility
Sa
mp
le
�In
a n
on
pro
ba
bili
ty s
am
ple
, ite
ms in
clu
de
d a
re
ch
ose
n w
ith
ou
t re
ga
rd t
o t
heir
pro
ba
bili
ty o
f o
ccu
rre
nce
.
�In
co
nv
en
ien
ce
sa
mp
lin
g, item
s a
re s
ele
cte
d b
ased
on
ly o
n the
fa
ct th
at th
ey a
re e
asy, in
exp
en
siv
e, o
r con
ve
nie
nt to
sam
ple
.
�In
a ju
dg
me
nt
sa
mp
le, yo
u g
et th
e o
pin
ion
s o
f pre
-
se
lecte
d e
xpe
rts in
the
sub
ject m
atte
r.
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-7
Typ
es o
f S
am
ple
s:
Pro
ba
bili
ty S
am
ple
�In
a p
rob
ab
ilit
y s
am
ple
, ite
ms in
th
e
sa
mp
le a
re c
ho
se
n o
n t
he
ba
sis
of kn
ow
n
pro
ba
bili
tie
s. P
rob
ab
ilit
y S
am
ple
s
Sim
ple
Ra
nd
om
Sy
stem
ati
cS
trati
fied
Clu
ster
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-8
Pro
ba
bili
ty S
am
ple
:
Sim
ple
Ra
ndom
Sa
mp
le
�E
ve
ry in
div
idu
al o
r ite
m f
rom
th
e f
ram
e h
as a
n
eq
ua
l ch
an
ce
of
be
ing
se
lecte
d
�S
ele
ctio
n m
ay b
e w
ith
re
pla
ce
me
nt
(se
lecte
d
ind
ivid
ua
l is
re
turn
ed
to
fra
me
fo
r p
ossib
le
rese
lectio
n)
or
with
ou
t re
pla
ce
me
nt
(se
lecte
d
ind
ivid
ua
l is
n’t r
etu
rne
d t
o t
he
fra
me
).
�S
am
ple
s o
bta
ine
d f
rom
ta
ble
of
ran
do
m
nu
mb
ers
or
co
mp
ute
r ra
nd
om
nu
mb
er
ge
ne
rato
rs.
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-9
Sele
cting a
Sim
ple
Random
Sam
ple
U
sin
g A
Random
Num
ber
Table
Sa
mp
ling
Fra
me
Fo
r
Po
pu
latio
n W
ith
850
It
em
s
Ite
m N
am
e
Ite
m #
Be
v R
.0
01
Ula
n X
.0
02
..
..
..
..
Jo
an
n P
.8
49
Pa
ul F
.8
50
Po
rtio
n O
f A
Ran
do
m N
um
ber
Tab
le
49280 88924 35779 00283 81163 07275
11100 02340 12860 74697 96644 89439
09893 23997 20048 49420 88872 08401
Th
e F
irst
5 I
tem
s i
n a
sim
ple
ran
do
m s
am
ple
Item
# 4
92
Item
# 8
08
Item
# 8
92 --
does n
ot exis
t so ignore
Item
# 4
35
Item
# 7
79
Item
# 0
02
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-10
�D
ecid
e o
n s
am
ple
siz
e:
n
�D
ivid
e f
ram
e o
f N
ind
ivid
ua
ls in
to g
rou
ps o
f k
ind
ivid
ua
ls: k
=N
/n
�R
an
do
mly
se
lect on
e in
div
idu
al fr
om
th
e 1
st
gro
up
�S
ele
ct
eve
ry k
thin
div
idu
al th
ere
aft
er
Pro
ba
bili
ty S
am
ple
:
Syste
ma
tic S
am
ple
N =
40
n =
4
k =
10
Fir
st
Gro
up
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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Chap 7
-11
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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Chap 7
-12
Pro
ba
bili
ty S
am
ple
:
Str
atifie
d S
am
ple
�D
ivid
e p
op
ula
tio
n in
to tw
o o
r m
ore
sub
gro
up
s (
ca
lled
str
ata
) a
ccord
ing
to s
om
e c
om
mo
n c
hara
cte
ristic
�A
sim
ple
ra
ndo
m s
am
ple
is s
ele
cte
d fro
m e
ach
sub
gro
up
, w
ith s
am
ple
siz
es p
rop
ort
ion
al to
str
ata
siz
es
�S
am
ple
s fro
m s
ub
gro
ups a
re c
om
bin
ed in
to o
ne
�T
his
is a
com
mo
n te
ch
niq
ue
wh
en
sa
mplin
g p
op
ula
tion
of vo
ters
, str
atify
ing
acro
ss r
acia
l o
r socio
-econ
om
ic lin
es.
Po
pu
lati
on
Div
ide
d
into
4
str
ata
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-13
Pro
ba
bili
ty S
am
ple
Clu
ste
r S
am
ple
�P
op
ula
tio
n is d
ivid
ed
in
to s
eve
ral “c
luste
rs,”
each
rep
resen
tative
of
the
po
pu
lation
�A
sim
ple
ra
ndo
m s
am
ple
of clu
ste
rs is s
ele
cte
d
�A
ll ite
ms in
the
se
lecte
d c
luste
rs c
an
be
used
, or
item
s c
an
be
ch
osen
fro
m a
clu
ste
r usin
g a
noth
er
pro
ba
bili
ty s
am
plin
g te
ch
niq
ue
�A
co
mm
on
ap
plic
atio
n o
f clu
ste
r sa
mp
ling
in
vo
lve
s e
lectio
n e
xit p
olls
,
wh
ere
cert
ain
ele
ctio
n d
istr
icts
are
se
lecte
d a
nd
sa
mp
led
.
Po
pu
lati
on
d
ivid
ed
in
to
16 c
luste
rs.
Ra
nd
om
ly s
ele
cte
d
clu
ste
rs f
or
sa
mp
le
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-14
Pro
ba
bili
ty S
am
ple
:
Co
mp
ari
ng
Sam
plin
g M
eth
ods
�S
imp
le r
an
do
m s
am
ple
an
d S
yste
ma
tic s
am
ple
�S
imple
to u
se
�M
ay n
ot
be a
good r
epre
senta
tion o
f th
e p
opula
tion’s
underlyin
g c
hara
cte
ristics
�S
tra
tifie
d s
am
ple
�E
nsure
s r
epre
senta
tion o
f in
div
iduals
acro
ss the e
ntire
popula
tion
�C
luste
r sa
mp
le
�M
ore
cost
effective
�Less e
ffic
ient (n
eed larg
er
sam
ple
to a
cquire t
he s
am
e
level of
pre
cis
ion)
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-15
Evalu
ating S
urv
ey W
ort
hin
ess
�W
ha
t is
th
e p
urp
ose
of th
e s
urv
ey?
�Is
th
e s
urv
ey b
ased
on
a p
rob
ab
ility
sa
mp
le?
�C
ove
rag
e e
rro
r –
ap
pro
pri
ate
fra
me
?
�N
on
resp
on
se
err
or
–fo
llow
up
�M
ea
su
rem
en
t e
rro
r –
go
od
qu
estio
ns e
licit g
ood
re
sp
on
se
s
�S
am
plin
g e
rro
r –
alw
ays e
xis
ts
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-16
Types o
f S
urv
ey E
rrors
�C
ove
rag
e e
rro
r o
r se
lectio
n b
ias
�E
xis
ts if som
e g
rou
ps a
re e
xclu
de
d fro
m th
e fra
me
an
d h
ave
no
ch
ance
of b
ein
g s
ele
cte
d
�N
on
re
sp
on
se
err
or
or
bia
s�
Pe
op
le w
ho
do
no
t re
spo
nd m
ay b
e d
iffe
ren
t fr
om
tho
se
wh
o
do
resp
ond
�S
am
plin
g e
rro
r�
Va
ria
tio
n fro
m s
am
ple
to
sa
mp
le w
ill a
lwa
ys e
xis
t
�M
ea
su
rem
en
t e
rro
r�
Du
e to w
eakne
sses in
que
stio
n d
esig
n, re
spo
nd
en
t err
or,
an
d
inte
rvie
wer’
s e
ffects
on
th
e r
espo
nd
en
t (“
Ha
wth
orn
e e
ffe
ct”
)
Basic
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ess S
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rentice-H
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Chap 7
-17
Types o
f S
urv
ey E
rrors
�C
ove
rag
e e
rro
r
�N
on
re
sp
on
se
err
or
�S
am
plin
g e
rro
r
�M
ea
su
rem
en
t e
rro
r
Exclu
ded
fro
m
fram
e
Fo
llo
w u
p o
n
no
nre
sp
on
ses
Ran
do
m
dif
fere
nce
s f
rom
sam
ple
to
sam
ple
Bad
or
lead
ing
q
uesti
on
(co
ntin
ue
d)
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-18
Sam
plin
g D
istr
ibutio
ns
�A
sa
mp
ling
dis
trib
ution
is a
dis
trib
ution
of a
ll o
f th
e
po
ssib
le v
alu
es o
f a
sam
ple
sta
tistic fo
r a
giv
en
siz
e
sam
ple
se
lecte
d fro
m a
po
pu
lation
.
�F
or
exam
ple
, suppo
se
you
sam
ple
50
stu
de
nts
fro
m y
our
co
llege
rega
rdin
g the
ir m
ean
GP
A. If yo
u o
bta
ined
man
y
diffe
ren
t sam
ple
s o
f 5
0, yo
u w
ill c
om
pu
te a
diffe
ren
t
mean
for
each
sa
mp
le. W
e a
re in
tere
ste
d in
the
dis
trib
ution
of all
po
ten
tia
l m
ean
GP
A w
e m
ight ca
lcu
late
for
any g
ive
n s
am
ple
of 5
0 s
tude
nts
.
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-19
Develo
pin
g a
S
am
plin
g D
istr
ibutio
n
�A
ss
um
e t
he
re i
s a
po
pu
lati
on
…
�P
op
ula
tio
n s
ize
N=
4
�R
an
do
m v
ari
ab
le,
X,
is a
ge
of
ind
ivid
ua
ls
�V
alu
es o
f X
: 1
8,
20,
22
, 2
4(y
ea
rs)
AB
CD
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-20
.3 .2 .1 018
2
0
22
24
A B
C
D
Un
iform
Dis
trib
ution
P(x
)
x
(co
ntin
ue
d)
Sum
mary
Measure
s f
or
the P
opula
tio
n D
istr
ibution:
Develo
pin
g a
S
am
plin
g D
istr
ibutio
n
21
4
24
22
20
18N
Xµ
i
=+
++
==∑
2.2
36
N
µ)
(Xσ
2
i=
−
=∑
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-21
16
possib
le s
am
ple
s
(sa
mp
ling
with
re
pla
cem
en
t)
Now
con
sid
er
all
po
ssib
le s
am
ple
s o
f siz
e n
=2
1st
2n
d O
bserv
ati
on
Ob
s
18
20
22
24
18
18
19
20
21
20
19
20
21
22
22
20
21
22
23
24
21
22
23
24
(co
ntin
ue
d)
Develo
pin
g a
S
am
plin
g D
istr
ibutio
n 16 S
am
ple
M
eans
1st
Ob
s2
nd
Ob
se
rva
tio
n
18
20
22
24
18
18
,18
18
,20
18
,22
18
,24
20
20
,18
20
,20
20
,22
20
,24
22
22
,18
22
,20
22
,22
22
,24
24
24
,18
24
,20
24
,22
24
,24
Basic
Busin
ess S
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rentice-H
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Chap 7
-22
1st
2n
d O
bserv
ati
on
Ob
s
18
20
22
24
18
18
19
20
21
20
19
20
21
22
22
20
21
22
23
24
21
22
23
24
Sam
plin
g D
istr
ibution o
f A
ll S
am
ple
Means
18
19
20
21
22
23
24
0
.1
.2
.3
P(X
)
X
Sa
mp
le M
ea
ns
Dis
trib
utio
n1
6 S
am
ple
Me
an
s
_
Develo
pin
g a
S
am
plin
g D
istr
ibution
(co
ntin
ue
d)
(no lo
ng
er
un
ifo
rm)
_
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-23
Su
mm
ary
Mea
sure
s o
f th
is S
am
plin
g D
istr
ibu
tion
:
Develo
pin
g a
Sam
plin
g D
istr
ibution
(co
ntin
ue
d)
21
16
24
19
19
18
N
Xµ
i
X=
++
++
==∑
L
1.5
816
21)
-(2
421)
-(1
921)
-(1
8
N
)µ
X(σ
22
2
2
Xi
X
=+
++
=
−
=∑
L
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
all,
In
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Chap 7
-24
Com
paring the P
opula
tion D
istr
ibution
to the S
am
ple
Means D
istr
ibution
18
19
20
21
22
23
24
0
.1
.2
.3
P(X
)
X18
20
22
24
A B
C
D
0
.1
.2
.3
Po
pu
latio
n
N =
4
P(X
)
X_
1.5
8σ
2
1µ
XX
==
2.2
36
σ
21
µ=
=
Sa
mp
le M
ea
ns D
istr
ibu
tio
nn
= 2
_
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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Chap 7
-25
Sam
ple
Mean S
am
plin
g D
istr
ibution:
Sta
ndard
Err
or
of th
e M
ean
�D
iffe
rent sam
ple
s o
f th
e s
am
e s
ize f
rom
the s
am
e
pop
ula
tion w
ill y
ield
diffe
rent
sam
ple
means
�A
measure
of th
e v
aria
bili
ty in t
he m
ean f
rom
sam
ple
to
sam
ple
is g
ive
n b
y t
he S
tandard
Err
or
of th
e M
ean:
(Th
is a
ssum
es tha
t sa
mp
ling
is w
ith
rep
lacem
en
t or
sa
mp
ling
is w
ith
ou
t re
pla
cem
en
t fr
om
an in
fin
ite
po
pu
latio
n)
�N
ote
that th
e s
tandard
err
or
of th
e m
ean d
ecre
ases a
s
the s
am
ple
siz
e incre
ases
nσσ
X=
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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In
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Chap 7
-26
Sam
ple
Mean S
am
plin
g D
istr
ibution:
If the P
opula
tion is N
orm
al
�If
a p
op
ula
tio
n is n
orm
ally
dis
trib
ute
dw
ith
me
an
µa
nd
sta
nd
ard
de
via
tio
n σ
, th
e s
am
plin
g
dis
trib
utio
n o
f is a
lso
no
rma
lly d
istr
ibu
ted
with
an
d
X
µµ
X=
nσσ
X=
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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Chap 7
-27
Z-v
alu
e f
or
Sa
mplin
g D
istr
ibution
of
the M
ean
�Z
-va
lue
fo
r th
e s
am
plin
g d
istr
ibu
tio
n o
f :
where
:=
sam
ple
mean
= p
opula
tion m
ean
= p
opula
tion s
tandard
devia
tion
n =
sam
ple
siz
e
X µ σ
nσ
µ)
X(
σ
)µ
X(Z
X
X−
=−
=
X
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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Chap 7
-28
No
rma
l P
op
ula
tio
n
Dis
trib
utio
n
No
rma
l S
am
plin
g
Dis
trib
utio
n
(has th
e s
am
e m
ea
n)
Sam
plin
g D
istr
ibutio
n P
rop
ert
ies
�
(i.e
.
is u
nb
iase
d)
xx x
µµ
x=
µ xµ
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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Chap 7
-29
Sam
plin
g D
istr
ibutio
n P
rop
ert
ies
As n
in
cre
ases,
decre
ases
La
rge
r s
am
ple
siz
e
Sm
alle
r s
am
ple
siz
e
x
(co
ntin
ue
d)
xσ
µ
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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Chap 7
-30
Dete
rmin
ing A
n Inte
rval In
clu
din
g A
F
ixed P
roport
ion o
f th
e S
am
ple
Means
Fin
d a
sym
me
tric
ally
dis
trib
ute
d in
terv
al a
rou
nd
µ
tha
t w
ill in
clu
de
95
% o
f th
e s
am
ple
me
an
s w
he
n µ
= 3
68
, σ
= 1
5,
an
d n
= 2
5.
�S
ince t
he inte
rval con
tain
s 9
5%
of th
e s
am
ple
means
5%
of th
e s
am
ple
mea
ns w
ill b
e o
uts
ide t
he inte
rval
�S
ince t
he inte
rval is
sym
metr
ic 2
.5%
will
be a
bove
the u
pper
limit a
nd 2
.5%
will
be b
elo
w t
he lo
wer
limit.
�F
rom
the s
tand
ard
ize
d n
orm
al ta
ble
, th
e Z
score
with
2.5
% (
0.0
250)
belo
w it is
-1.9
6 a
nd t
he Z
score
with
2.5
% (
0.0
250)
above it is
1.9
6.
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-31
Dete
rmin
ing A
n Inte
rval In
clu
din
g A
F
ixed P
roport
ion o
f th
e S
am
ple
Means
�C
alc
ula
tin
g t
he
lo
we
r lim
it o
f th
e in
terv
al
�C
alc
ula
tin
g t
he
up
pe
r lim
it o
f th
e in
terv
al
�9
5%
of
all
sa
mp
le m
ea
ns o
f sa
mp
le s
ize
25
are
b
etw
ee
n 3
62
.12
an
d 3
73
.88
12
.3
62
25
15
)9
6.
1(
36
8=
−+
=+
=
nZ
XL
σµ
(co
ntin
ue
d)
88
.3
73
25
15
)9
6.
1(3
68
=+
=+
=
nZ
XU
σµ
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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Chap 7
-32
Sa
mp
le M
ea
n S
am
plin
g D
istr
ibu
tion:
If th
e P
op
ula
tio
n is n
ot
No
rma
l
�W
e c
an
ap
ply
th
e C
en
tra
l L
imit T
he
ore
m:
�E
ven if
the p
op
ula
tion is n
ot
norm
al,
�…
sam
ple
means f
rom
the p
opu
lation w
ill b
eappro
xim
ate
ly n
orm
alas lon
g a
s the s
am
ple
siz
e is
larg
e e
no
ugh.
Pro
pert
ies o
f th
e s
am
plin
g d
istr
ibution:
and
µµ
x=
nσσ
x=
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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Chap 7
-33
n↑
Centr
al Lim
it T
heo
rem
As t
he
sa
mp
le
siz
e g
ets
la
rge
e
no
ug
h…
the
sa
mp
ling
dis
trib
utio
n
be
co
me
s
alm
ost
no
rma
l re
ga
rdle
ss o
f sh
ap
e o
f
po
pu
latio
n
x
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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In
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Chap 7
-34
Po
pu
latio
n D
istr
ibu
tio
n
Sa
mp
ling
Dis
trib
utio
n
(becom
es n
orm
al a
s n
in
cre
ase
s)
Ce
ntr
al T
en
de
ncy
Va
ria
tio
n
x x
La
rge
r s
am
ple
s
ize
Sm
alle
r s
am
ple
siz
e
Sa
mp
le M
ea
n S
am
plin
g D
istr
ibu
tion:
If th
e P
op
ula
tio
n is n
ot
No
rma
l(c
on
tin
ue
d)
Sam
plin
g d
istr
ibution
pro
pert
ies:
µµ
x=
nσσ
x=
xµµ
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
all,
In
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Chap 7
-35
Ho
w L
arg
e is L
arg
e E
nou
gh?
�F
or
mo
st d
istr
ibu
tio
ns,
n >
30
will
giv
e a
sa
mp
ling
dis
trib
utio
n t
ha
t is
ne
arl
y n
orm
al
�F
or
fair
ly s
ym
me
tric
dis
trib
utio
ns,
n >
15
will
u
su
ally
giv
e a
sa
mp
ling
dis
trib
utio
n is a
lmo
st
no
rma
l
�F
or
no
rma
l p
op
ula
tio
n d
istr
ibu
tio
ns,
the
sa
mp
ling
dis
trib
utio
n o
f th
e m
ea
n is a
lwa
ys
no
rma
lly d
istr
ibu
ted
Basic
Busin
ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-36
Exam
ple
�S
up
po
se
a p
op
ula
tio
n h
as m
ea
n µ
= 8
an
d
sta
nd
ard
de
via
tio
n σ
= 3
. S
up
po
se
a r
an
do
m
sa
mp
le o
f siz
e n
= 3
6is
se
lecte
d.
�W
ha
t is
th
e p
rob
ab
ility
th
at th
e s
am
ple
me
an
is
be
twe
en
7.8
an
d 8
.2?
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
all,
In
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Chap 7
-37
Exam
ple
So
lutio
n:
�E
ve
n if
the
po
pu
latio
n is n
ot n
orm
ally
d
istr
ibu
ted
, th
e c
en
tra
l lim
it t
he
ore
m c
an
be
use
d (
n >
30
)
�…
so
th
e s
am
plin
g d
istr
ibu
tio
n o
f is
ap
pro
xim
ate
ly n
orm
al
�…
with
me
an
=
8
�…
an
d s
tan
da
rd d
evia
tio
n
(co
ntin
ue
d)
x
xµ
0.5
36
3
nσσ
x=
==
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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In
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Chap 7
-38
Exam
ple
So
lution
(co
ntin
ue
d):
(co
ntin
ue
d)
0.3
108
0.4
)Z
P(-
0.4
36
3
8-8.2
nσ
µ- X
36
3
8-7.8
P
8.2
)
X
P
(7.8
=<
<=
<<
=<
<
Z7
.8
8
.2-0
.4
0
.4
Sam
plin
g
Dis
trib
ution
Sta
ndard
Norm
al
Dis
trib
ution
.1554
+.1
554
Popula
tion
Dis
trib
ution
??
??
??
??
??
??
Sam
ple
Sta
ndard
ize
8µ
=8
µX
=0
µz
=x
X
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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Chap 7
-39
Popula
tion P
rop
ort
ions
π=
th
e p
rop
ort
ion
of
the
po
pu
latio
n h
avin
g
so
me
ch
ara
cte
ristic
�S
am
ple
pro
port
ion
( p
)pro
vid
es a
n e
stim
ate
of π
:
�0 ≤
p ≤
1
�p is a
ppro
xim
ate
ly d
istr
ibute
d a
s a
norm
al d
istr
ibution
wh
en n
is larg
e
(assu
min
g s
am
plin
g w
ith
re
pla
cem
ent fr
om
a fin
ite
pop
ula
tio
n o
r w
ith
ou
t re
pla
ce
me
nt fr
om
an
in
fin
ite
pop
ula
tio
n)
siz
e
sa
mp
le
in
tere
st
o
fstic
ch
ara
cte
ri
the
h
avin
g
sa
mp
le
the
in
ite
ms
of
nu
mb
er
nXp
==
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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Chap 7
-40
Sam
plin
g D
istr
ibutio
n o
f p
�A
pp
roxim
ate
d b
y a
no
rma
l d
istr
ibu
tio
n if:
� wh
ere
an
d
(whe
re π
= p
op
ula
tio
n p
ropo
rtio
n)
Sa
mp
ling
Dis
trib
utio
nP
(ps)
.3 .2 .1 00
.
2
.4
.
6
8
1
p
π=
pµ
n
)(1
σp
ππ
−=
5)
n(1
5n an
d
≥−≥
π
π
Basic
Busin
ess S
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rentice-H
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Chap 7
-41
Z-V
alu
e f
or
Pro
port
ions
n
)(1p
σ
pZ
pπ
π
ππ
−
−=
−=
Sta
nd
ard
ize
p t
o a
Z v
alu
e w
ith
th
e f
orm
ula
:
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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In
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Chap 7
-42
Exam
ple
�If
th
e t
rue p
rop
ort
ion
of
vo
ters
wh
o s
up
po
rt
Pro
po
sitio
n A
is
π
= 0
.4, w
ha
t is
the
pro
ba
bili
ty
tha
t a
sam
ple
of
siz
e 2
00
yie
lds a
sam
ple
pro
po
rtio
n b
etw
ee
n 0
.40
an
d 0
.45
?
�i.e
.: if
π=
0.4
a
nd
n
= 2
00
, w
ha
t is
P(0
.40 ≤
p ≤
0.4
5)
?
Basic
Busin
ess S
tatistics, 11e ©
2009 P
rentice-H
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In
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Chap 7
-43
Exam
ple
�if
π
= 0
.4
an
d
n =
20
0,
wh
at
is
P(0
.40 ≤
p ≤
0.4
5)
?
(co
ntin
ue
d)
0.0
3464
2000
.4)
0.4
(1
n
)(1
σp
=−
=−
=π
π
1.4
4)
ZP
(0
0.0
3464
0.4
00.4
5Z
0.0
34
64
0.4
00
.40
P0.4
5)
pP
(0.4
0
≤≤
=
−≤
≤−
=≤
≤
Fin
d :
Co
nvert
to
sta
ndard
ized
norm
al:
pσ
Basic
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ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-44
Exam
ple
Z0
.45
1.4
4
0.4
251
Sta
ndard
ize
Sa
mp
ling
Dis
trib
utio
nS
tan
dard
ized
No
rma
l D
istr
ibu
tio
n
�if
π
= 0
.4
an
d
n =
20
0,
wh
at
is
P(0
.40 ≤
p ≤
0.4
5)
?
(co
ntin
ue
d)
Use s
tanda
rdiz
ed n
orm
al ta
ble
:
P(0
≤Z
≤1.4
4)
= 0.4
25
1
0.4
00
p
Basic
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ess S
tatistics, 11e ©
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rentice-H
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Chap 7
-45
Cha
pte
r S
um
mary
�D
iscusse
d p
roba
bili
ty a
nd n
onpro
bab
ility
sam
ple
s
�D
escri
bed four
com
mon p
roba
bili
ty s
am
ple
s
�E
xam
ine
d s
urv
ey w
ort
hin
ess a
nd
types o
f surv
ey
err
ors
�In
troduced s
am
plin
g d
istr
ibutions
�D
escri
bed the s
am
plin
g d
istr
ibution o
f th
e m
ean
�F
or
norm
al pop
ula
tion
s�
Usin
g t
he C
entr
al Lim
it T
heore
m
�D
escri
bed the s
am
plin
g d
istr
ibution o
f a p
roport
ion
�C
alc
ula
ted p
roba
bili
tie
s u
sin
g s
am
plin
g d
istr
ibutions
