Final Exam
lied Si atstics
A
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1
ID:
Nanie:
(‘uvfn1ly 1und
‘T’liv IlIStl1I(tinhlS!
1 iie ali(1
oinl ( ol ists oh 1 pm
extra (redit h)roh)1(iIlS. (‘(U ii ()iii’ hwili vorthi 1(1 poili[. Pio\’id’ soliit iUli tO I
pFDl)1(’1IlS ill tii(’ -I)d(( piovjdd. All oiiiI iOli 1111151 I lll!1(i(’1it lv j(L-t ili’il to
(redir. 1Ol1 mdv HSi d (aIelJatC)1 00 thi0 (‘X((11i. 1I)fl IIIHV not (151 dliv iiitsidi
or exts. Goal Link!
IllStiii(’ti()iliS
his
(XdiiI
vih1 1:isr Ill)
iiiiilill(5
t\vo
1(’(V1V(’
10)1(5
U\oflS.
a1
Advice: If von cvt si ink on a probleimi Hoot pank! \Iovt’
at ‘F
rJgiNuii iii or
1
Points
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Extra Credit 1
Extra Crr Hit 2
on
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2.
‘\
rm’c
isis fJIits
to list for Ill)’ pleselIr)’
pelfornle(l (UI
au
1)11 all
says
ilNhiVi( 1)1(11
iVe
Sell’)
ted iIlCli’Vi( hial
)
III’
(us)’ is’
WiN)
Ill iII(IiVi(IH(lI
he (lise
Is
(hat
iOiI.:\
I 11ev
(I) 1(5
have
I (‘St 11(15
((‘NIl
lINt 1(11(5. If
(1(’VNIUIW(l
II)’ lest Is
Ill)’ )I’OlN(l)IIitV (f a )sitiVN
Iisease is •s, TI thr test is
t lIe (lisease. t hI 1)101)111 (ifItV of
Sr.
tile
Not ililVi’
test iesuit is .t)t. S)lppOs(’ tIll’ lest is perfoiitie1 011 0 Il11(fOHhiv
posit
(i
(1
IN I)UI)1a
iIUliVi(IIIHI who
let UNsuht (i.e. the tel
a’ih )l’IlIe(l
.i A
UNIV
V\r1l,)t is t he prol )a )ility that
flD)
‘pCty
I TIN test result
T’(-
PLUD)lCp)
()(QO1)
t
j
)
p(-f
(
p(c)
..p(-fiD)
(X)
(b) Suppose the I (‘st (( lilies 1)01k positive.
iIi(livi(lUiil actually TIlls the (fisease?
\V1IOI is
-
?Lf)
will he positive?
the proi lab )ilitV that the
a
red iiiarhles. o grceii iiinrhlvs, and
3. A bog coot allis
( blue
iiiorhlcs.
(a) Suppose flint tWo marbles are reiiioved from the bag of raiidoni. What is
the probability that at least one of them is red?
r(
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12
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F(1>±)j
Xkp(L)
(1)) Suppose I iou 6 iuiai’hl (5010 ienioved troni the hag at random. what is the
prohahilil V flint nil of (11(111 arc blue.’
:1:
1
‘
f
),i-
-,L5
ceW°-’,
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7 2_O)
7
2A7
)
(9)
(c) Suppose I lint one nool 1c is i (nio\’e(l houiu I lie I )iug nI rounloiti, lie i olor of
floe ni)IrI)lc is r(coi)l(d. uuoicl Inn tin nuuble is pui back into tin’ bog. If
tins po uciss is repent d uiulepemlcnt lv It) times. vhunt is the plo] ual out v
that the (0101 green is o,ei ((1110(1 niore than once?
1
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brUO,1)
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1
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Silolill! JIb.) 00
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3. Suppo X uII(1 )
1iaI)I(.
Il11(1UIti
u1(’ 1
i1I(I(’
)
(]1Ch’11
i,(.
t 1I(V ]))I
Ii
.
i(1(’11ti(1IR (1iS11i1)l1l((1 2
VX1)UI1(fltiHl(
)
(l(’ILSitV IHII(t 11)11
iaVc
0
(a)
( iipitt t 11( omt
(l(iISItV
:
ut .V wl
0 < i <
ol/1 ru’1(
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-2e
e.
5
4
1.yv 5A-
0
(H
Coiuput
l.J
2
(‘
Y•>
ii
put
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V <
•
(
Lf
22..
{mi
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1
ii
X—3
iiit
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k)
Jj
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2.
r
3
—31
e
X
2
z
6.
that 7 adult
and veig1tecl
removed from I lie populat ion at
est titote p. (lie Irisic nieoii \Veigli( 1)1
adult niale roroons. Tin wiglits of the tiuuotis ale displitved ii tlic table
I)eIciw. It iS assitiiied tltli 1 111 W(’i5lit of 1(11th rii(ooIN N nortiiohlv list tihuted.
T
)
bil(Oi(it
cr
it 1
I
Suppose
laloL)ui
Lit —c-x;
(Ws)
(a C
tOl(ttt’ i
male 10(00115 were
Ii (Ut otteitipl
2 I
j73
))‘/.
it
st Oi(iat(I ileviii 011
146
t7
Itiloi
ii
ill’
to
4
124
L) ji3
itO (‘1 vol lii //
if (1(1(1 Oil N (3
uIt) 2
Vi
is ;i
ittoed
I ;ii t
lie
I
•5: Lo37
37
±
_s
6
‘1 cV
r
—
)
t7)
(6) Cotipitte a )a/ eotihdetiee hit eival fur e if t lie stondotd cieviat 1)11
ssiii toil to 1 )( ott hi wi.
s
)
0
is
241
I
(o)
Compare the ooiihdeiioe iitervals ciniputcd in part a) and 6). Arootint
fui their (iiPeIeiI(cs by hrieHv explai nig rIte dittereiice between a I
distribution and the statidail hot itial olNthihutiohl.
cLi_
-+ -
4)
-{ia
-Pcc.f
ic
jjev.
) —r_
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44
6r
T
)cIc1
ii
—Cr4,(,J
(-lst’rdIc,LCtro
4
’
ii
1
pni-j,r,,j
cL)
4kl
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sol-
is
(‘-r
ahis( U (Ia lOIS ha iii auui
Ahoy! (‘liouohatu ullIf cookic
iii if 1(9 of ( III (((liii (‘ (Ii if
iii a I
1 s
(‘hi
23. fIn’ But tur I3usiios i3iiruai i)uliuVu that
)ahisco is actually rippiii iw oil, and that the true avuragu inulif nc of
(iloculate (flips lI a hag is fuss than 23. To prove their (‘latin. the niiuihjec of
ufio(Ofat I’ chops iii it) bags of C’fiiJ) \ hi
were i lflHt ud aiol t lie sample niuan
was 2 I .3 chips :\s1ani’ that lie stliiu(u(f deviation of fbi cfate 1 hips in a
1 iag of (hips .\hiov! i known to la’ 3.2.
((L
is
.
(a
Construct appropriate lull
1 ili(l alternative hypotheses for this situation.
\ fake sure
the null hypothesis is siiuiplu.
fI:
H,: ii—2
(Ii) P’lbocni tin’ tew fiat \tii iiutfiw’d If iove at ft’vef ri
sa IuIf)f(’ dab a..\ I aLe hal e of a n\’ a )faoxiau
i toils ilOi I
1
1 iv reteleli(tnL, the if If JR If (I tate till’ Ii ‘Ills.
M
0
.tC fi,wed
itdii
iii(f Va
s.’L-
—r
/)()
I.. (ft
Th 1IC)
-?
€
4
Oil
tin’
e t 1(1111
.
A
(‘0111 is
Suppose
fIiI)1)(cl 100 1 illics. aiid 217 of Ilios’ (ililvs 11w out coiiiv is heads.
7) I)iOhwl)ihilV 11011 ho coin W1W11 Ihipp(’(1 wjll (‘OHJt ‘l 100(15.
Ci1I
(ii
thus (1010
I/o : p
1(51
(I
1(’V(l
01
((
.5
V( ‘(‘Sits
/1 >
—.-rI
.5
A
cJ.3.
rrII;
I
1’-
t.J(o)
2.,3i
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.:
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1
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c—
çh) Detive a ¶10:
(UHI1(1V1I(
jj)
.±‘.
1
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I’ il(t(’lVOl
101’
p
loiseci
t1iisuuuipiu’
;
(eoi)
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—
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cc
lu) 13i’icllv (l(’(1il (V
(Ak....
un
3+
u—
bV(I II
01V al)p1’OlIuluI 101(5
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t
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ph
lot H ii
lildopEildEilt
lv
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(/N.
li’ulll
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h’t,m
(lESt FE (Ut
tIll) ut Iiti
((ii.
(‘
(tNt 11)111 i(It
1
.\IllI It
HII)ill
I III
(‘(I lion
lIE!
I WI) SrIIHll
lost
nl)l(. .\
12.1.
(a) [‘st
it
/I
“A
lEVEl .1
Ilsilig
this (LIt a
R’2
/Ij :j /1.2
(h) Euttiptil
tin
(St
1015(51
ii
t ii)
Nilili
iii
(lii
.
is
lit
H.
13,3 and
1U.
C1(( Iii 1) hOW 1iii1iV\VrVS H I hii’ Lu arIuI1g 7 hooks on 3 sIwhvs if
cochi sli(hi iou suipport olh 7 hooks Siuppos I hit’ 1)1(1(1 iii vhiihi the 1)OOkS ore
ho’ hoP oh hook 2 i oui shelf 1 is
Phott’hh oil ihit’ shithvts 110111015. (ii’. itook I
ihifiticuit Pout hook 2 to lb loft of hook 1 out shelf 1).
(Fxtra
.
(g(qqo