StatisticsSemesterTwo Review
Name:
Usethe following to answerquestions1-2.
n
A notedpsychicwastestedfor ESP. The psychicwaspresented
with 200 cardsfacedownand
askedto determine
if the cardwasongof five symbols:a star,.rorr, .ffi
squareor threewavy
lines. The psychicwas correctin 59tases. Let p represent
the probabilitythat the psychic
correctlyidentifiesthe symbolon the card in a randomtrial.
1. Supposeyou wished to seeif there is evidencethat the psychic is doing betterthanjust
guessing. To do this you test the
Ho ;p:4.20, Ha:p > 0.20.
The P-value of your test is
A) b etween.l0and.05.
(!) between.05 and .01.
C ) b etween.0land.00l.
D) b elow.00l.
A
SIRr
-rE:t
p-Vcll^&_
S
-: ,tl$gS"
2. Basedon theresultsof the test,?2jZo confidence
intervalforp is (assuming
thatthe 200
trials can be treatedas an SRS from the populationof all guesses
his lifetime)
r o.o6o. (
@ o.zs
B) 0 . 2 5+ 0 .0 5 5 .
c) 0.25* 0.050.
ld make in
lrttg , isor)
-3
.3lb$i
- ,AS
2 .6 tCI5 g l
D) We can assertthatp:0.20 with 100% confidencebecausethe psychic is just guessing.
Page I
Use the following to answerquestions3-4.
When a police officer respondsto a call for help in a caseof spousalabuse,what shouldthe
officer do? A randomized controlled experimentin Charlotte, North Carolina studied three
police responsesto spousalabuse:adviseand possibly separatethe couple, issuea citation
to the accused,and arrestthe accused. The effectivenessof the three responseswas
determinedby re-arrestrates. The table following showstheserates.
AssignedTreatment
Number of
subsequentarrests
0
I
2
Itat
1 75
36
t8t
2
7
I
2
0
0
187
24
JJ
a
0
i
+
b
3. This is an r x c table. The number r has value
i
A) 2.
\./
B) 3 .
c) 4.
*ob
rst^)ii
@s
A
4. Supposewe wish to test the null hypothesisthat the proportion of subsequentarrestsis
the same,regardlessof the treatmentassigned.Under the null hypothesis,tb&ecled
number of times no subsequentarrestwould occur for the treatment"Advisel'Separate"is
@) t?z
B) 1 81
.
c) 1 87.
D) s43.
JnJ
ntd*1
€t i-r A
4-rv.fu-.-obs
z-'
GlF Srfr
vc"l"uu,s
rnbT
J"'d
fr\ofri x
tbrt
6ee,
TS
€-l(-P Y4-LLL[A
Page2
c
Use the following to answerquestions5-7.
To study the export activity of manufacturingfirms in Korea, questionnaireswere mailed to
a SRS of firms in eachof four industriesthat export many of their products. The response
rate was low, and to comparethe industriesit is important that the responseratesfrom the
different industriesbe similar. Do the datain the Minitab output shown in the following
table provide evidenceof a differencein responserate betweenthe four industries?
The output includesthe cell counts,the expectedcell counts,and the chi-squarestatistic.
Expectedcountsare printed below observedcounts.
Industrv
Machinery
Responded
ta
JJ
32.54
Eleckicalequipment
?1
J)
94
94.46
TotalMailed
121
25.62
79
74.38
100
Precisioninskuments
41
31 00
80
90.00
121
Transportation
equipment
18
23.83
75
69.17
C h i S q : 0 .0 1 1+6 0 0 0 2+
0834+ 0287+
3 .2 2 2+ 1 1 1 0 +
1 .4 2 6 +0 .4 9 1 =1 .3 81
L
!\
Didn't Respond
5. This is an r x c table. Thenumberr hasvalue
A)L
B) 2.
c) 3.
@+
Page3
R
thatthe probabilityof responseis the samefor
6. TheP-valuefor testingthe null hypothesis
the four industriesagainstthe alternativethat the probabilityis different for the four
(refe-r .+o .+ ./
Srftr" TEST- Cindustries
)
t
ir sreaterthan0.05.
f}r
=
.
Obn7
*B)
f/-VG-l-L\-t
0.025and0.05.
i, f,etween
0.010and0.025.
C) is between
D) cannotbe determinedbecausetheseare not the hypothesesbeing testedby the chisquaretest.
7. The appropriatedegreesof freedom for the chi-squarestatisticis
A) l .
B) 2.
/Aa
\g/ r.
D ) 4.
Use the following to answerquestion8.
A study examinesthe personalgoals of children in grades4,5, and6. A random sampleof
studentswas selectedfor eachof the grades4,5, and 6 from schoolsin Georgia. The
studentsreceived a questionnaireregarding achievementof personalgoals. They were asked
what they would most like to do at school:make good grades,be good at sports,or be
popular. Resultsare presentedin the following table by the sex of the child.
Make good grades
Be popular
Be good in sports
Boys
96
)z
94
Girls
295
45
40
rLt
8. The
"
A) 3 .8 4 .
B) s.ee.
c) 1 6.105.
@ ar.roo.
for this tableis
(re€-eq- +- o**)
STn-T-
T-E,ST q-
Page4
bs
To assessthe accuracyof a laboratoryscale,a standardweight known to weigh 1 gram is
repeatedlyweigheda total of zztimes, and the mean F of the weighingsis computed.
Supposethe scalereadingsare normally distributed,with unknown meanm and standard
de via tiono:0.01g@ sothata95 o h c o n f id e n c e in t e rv a lf o rrn h a s a
marginof errorof * 0.0001?
A) 1oo
B) 1 ,96
c) 10,000
n:
r=*5,$
-J
'r-f,t"1
=( /
L) e*'- tgts (So"", i"Sr*)
t q to ( ,ol)r
*=
3"'J lG
-c:oe -J
C_D:s,+ro
Use the following to answerquestion10.
A study examinesthe personalgoalsof children in grades4, 5, and6. A random sampleof
studentswas selectedfor eachof the grades4,5, and6 from schoolsin Georgia. The
studentsreceiveda questionnaireregardingachievementof personalgoals. They were asked
what they would most like to do at school:make good grades,be good at sports,or be
popular. Resultsare presentedin the following table by the sex of the child.
Make good grades
Be popular
Be good in sports
R
Bovs
96
32
94
Girls
295
45
40
10. Wlrl.h hy_pothqqer b"i
by the chi-square
test?
-.
(D fn. null hypothesis
is that personal goals and genderare independent,and the
alternative is that they are dependent.
B) The null hypothesisis that the mean personalgoal is the same for boys and girls, and
the alternative is that the meansdiffer.
C) The distribution of personalgoalsis different for boys and girls.
D) The distribution of genderis different for the three different personalgoals.
Page5
Use the following to answerquestionsll-14.
A food company is developing a new granola bar, and its market analysts are currently
working on preliminary studiesof the packaging design. To help with a marketing strategy,
the company was first interestedin whether the appeal of the packaging design for the new
product (and hencethe appealof the product itself was relatedto a person'sgender. There
were 100 male and 100 femalevolunteersavailablefor purposesof evaluation. Both males
and femalesratedthe designon a scaleof I to 10, I being "very unappealing"and 10 being
"very appealing." The meanrating for maleswas f , = 7.4, with a standarddeviation s1 :
L5. The meanrating for femaleswas 7" = 8.0, with a standarddeviation s2 = 2.0. Let lt1
andp2 representthe mean ratings we would observefor the populationsof males and
females,respectively,and assumeour samplescan be regardedas samplesfrom these
popuiations. J Scr-r
+d_l*
r-y^t-tCr_n
Il. A 90% confidenceintervalfor ltr
TEST'
b-rffi
A ) - 0 .6+0 .2 5 .
B) - 0 . 6 t0 .3 2 .
o
C-r ,CIr'3i .-"itt r)
O -0.
6*0.42.
D) * 0.6 r 0 . 5 .
N
ltt is
,-ol8t-'l *
(-" b) =
"yr33
n. Suppose
the researcher
had wishedto testthe hypotheses
Ha:/,*t
5T{\T TdS1
, Hu:y,1./'ra,
The f-value forlhe test is
A) largerthan0.10.
B) between0.10and 0.05.
C) between0.05and 0.01.
6 ) be low0.01.
.t
p-.vc*l-rr*f = " Oot?
\J
O13
If we had used the more accuratesoftware approximation to the degreesof freedom, we
would have used which of the followine for the number of desreesof freedom for the /
procedures?
A) 1 9 8
B) 191
df = lt 3, bo'
rr+
@
D) 99
Page6
I
B
hadwishedto testthe hypotheses
the researcher
14. Suppose
Ho,f=f
Th.
A) 2.00.
,^"
(9) 2.40.
o 3.2s.
, , Hu:y, ljaa
it
t:7
D) 9.60.
Use the following to answerquestion15.
The American Veterinary Medical Associationconducteda survey of veterinaryclinics to
estimatethe proportion that do not treat large animals (cows, horses,etc.). The survey was
mailed to a random sampleof l!0 veterinaryclinics throughoutthe country and of these,88
respondedthat they ao not treat?argeanimals.
^
A * aY^.o= "-lJ3
15. The standarderror SErof the proportionp of clinicsthat do not treatlargeanimalsis
A) 0.02.
B) 0 . 0 3 .
56*
= , c)Yo.l
@ o,o+.
D) 0.05.
16. Is the mean ageat which American children can first read now qgderyllgglg? If the
population of all American children has mean age ofp years until they begin to read and
standarddeviation oyears, one would test which of the following null and altemative
hypothesesto answer this question?
A) H s: p:4 vs.l/u: 1t> 4
@ nr lL:4vs.Hu:trt<4
C) Hs: lt:4 vs.llu: p + 4
D) Hs:p:4 vs.F/u:p- 4 * r , assuming
oursample
sizeis n
Page 7
Use the following to answerquestions17-19.
A researcherbelievesthat college studentsspendless time participating in extra-curricular
activitesthan they did ten yearsago. An SRS of 100 college studentsfound that in the past
year the averagenumber of hours spentper semesterin extracurricular activities was f :
107 hours, with standarddeviations : 45 hours. Assumethe distribution of the number of
hours spentby college studentsper semesterparticipatingin extracurricularactivities is
approximatelynormal, with mean1t. Are thesedata evidencethat phas lowered from the
value of 120 hours of ten yearsago? To determinethis, we test the hypotheses
Ho: F:
120,Ha: l"L< 120.
on€"
ruSl_4-l
L
b
17. Thelryalgefor theone-sample
/ testis
A) largerthan0.10.
B) between0.10and 0.05.
C) between0.05 and 0.01.
6) below0.01.
t3
l-5" ST I
p*v'cuL^.-r-- .OOA4
18. The appropriate
deqrees
of freedomfor this testare
A) 4s.
@l l
c) 100.
D) r20.
R
51-fir
df - n- l
a l o o -l
-q q
19. Basedonthe data,thevalueof the
"@
A) 3 . 41 .
fR1z.se.
t-- - 3,Kg
Tt z.et.
D ) 2 . 38 .
ft
20. ,!n formulatinghypotheses
for a statisticaltestof significance,
the null hypothesisis often
@) " statementof 'onoeffect" or "no difference."
B) the probabilityof observingthe datayou actuallyobtained.
C) a statementthat the dataareall 0.
D) 0.05.
Page8
Use the following to answerquestions2l-23.
A random sampleof 1400Internetuserswas selectedfrom the recordsof a large Internet
provider and askedwhetherthey would use the Intemet or the library to obtain information
about health issues. Of these,872 saidthey would use the Internet.
n 814/
p -- - 'Z.ioo=.b)]9
N
2t.If the Internetproviderwantedan estimateof the ryportton
g that would usethe Internet
ratherthanthe library,with a marginof errorof at most0.01in a99Yoconfidence
interval,
how larsea samplesizewouldberequired?
A) 1400
:(4j(,J:)
:] ffi:,l, Y1
@ 16,seo
= (esrb).(,*,
: tre.K?q{"
\
b
22. The proportion
A) 0 .0 13.
B) 0.2s.
c) 0.485.
itthatwould use the Intemet rather than the library is
A
tl' -.
*
A 1J,.
4 {oo=.ta}3
@ o.azt.
S
T.
The standarderror SE, of the proportionit thatwould use the Internet rather than the
librarvis
@l 0 .013.
B) 0.25.
c) 0.485.
D) 4.623.
O
56=,@=re-r
n
v
t LloCI
- . O lf gs
24.Supposewe want a90Yo confidence interval for the averageamount of time (in minutes)
spent per week on homework by the studentsin a large introductory statistics course at a
large university. The interval is to have a margin of error of 2 minutes, and the amount
spenthas a normal distribution with a standarddeviation o: 30 minutes. The numberof
requiredis closestto
observations
A) 2s.
B) 30.
@eor.
D) 86s.
Page9
Use the following to answerquestions25-27.
A SRS of 20 commutersto the Los Angeles metropolitan areaareselected,and each is asked
how far they commute to work each day. In the sample,the mean distanceis 64 miles and
the standarddeviation is 12 miles. Assumethat in the population of all commutersto the
Los Angelesmetropolitanarea,daily commutingdistancefollows a normal distribution,
with some meanP.
onA- *.:,G-/yLp.LL
,^|4_e*a_J4
25. The standnrderror of the meanis
A ) 14 .3 1 .
B) 7.20.
@ z.ot.
bE = $/6 ='%G1
J.rots
D ) 0 .6 0 .
e-Ze . We are interestedina95Yo confidenceinterval for the populationmeancommutingdistance.
The marein
of error associatedwith the confidenceinterval is
.--€
A) 2.68miles.
B\ 4.64miles.
fr\=$g*)
@ s.ezmiles.
D) 6.84miles.
= J.os3 ('%)
n-:ao
dS-rQ
95?o*7dtr= J.o ? 3
= $ . [ o, 55
A 9iolo confidence interval for the population mean commuting distancebasedon thesedata
is
A) 64+ 2.68miles.
1A
l*l
-.
o+
f 4.o4 mlles.
C) 64* 5.62miles.
D) 64* 6.84miles.
s-TRr' -rESr *
(sq,'3b,t"x,br)
bt . t sq-Lo. l= 4. t 'J
Pagel0
Use the following to answerquestions28-29.
A large MidwesternUniversity studiedstudentperformancein a statisticscourserequired
by its mechanicalengineeringmajors. Of interestis the time spentin extracurricular
activitiesand whethera studenteameda B or betterin the course.
ExtracurricularActivities
(hoursoer week)
Grade
B or better
BelowB
A
<2
47
2to 12
48
80
26
> 12
31
70
28. This is anr x c table. Thenumberr hasvalue
G\ z.
'-lJ
B) 3 .
c) 4.
D) 6.
n 2s.Supposewe wish to test the null hypothesisthat there is no associationbetweensuccessin
the courseand the time spentin extracurricularactivities. Under the null hypothesis,the
expectednumber of successfulstudents(B or
extracuricular activitiesis /
r
ffi
4 2.6 .
frefer -t-{t+)
c) s3.4.
D) s8.e.
C
x
30. An sRS of?i male faculty members atalargeuniversity found that lb felt that the rl
university was supportive*
of female and minority faculty. An independentSRS of 2b'x
female faculty found that"f felt that the university was supportive of female and minority
faculty. Let p 1 Md pz representthe proportion of all male and female faculty, respectively,
at the universi$ wh6 felt that the university was supportive of female and minority faculty
at the time of the survey. Lj5%
confidenge!g!9ry4!.!glzt_pz is
A) 0 .1 3 5* 4 .2 7 0 .
B ) 0 .1 3 5+ 0 .2 6 3 .
Q o.rs! o.z7o.
D ) 0 .1 5* 0 .2 6 3
*ut:c> ST.p,La?ro?o,^*ra-rrS
TI-AT r-&Si- b
(*.tI).{rt.lg)
0,- Ps="'{-As:.IS
PageI I
"Llt qqy - *; S : . J b g f y
Use the following to answerquestion31.
{\
A newspaperconducted a statewide survey conceming a proposal to raise taxes to prevent
budgetcuts to education. The newspapertook a random sample(assumeit is an SRS) of
1200registeredvoters and found that 5r[0 would vote to raise taxes. Let p representthe
proportion of registeredvoters in the statethat would vote to raise taxes.
CrY\C- ba_In-{ota_
Pt-t:-perfz
en
3 1. A 90% confrdenceinterval for n is
A ) 0 .4 8 3+ 0 .0 1 4 .
@ o . + s+: 0 . 0 2 4 .
c ) 0 .4 8 3* 0 .0 2 8 .
D ) 0 .4 8 3*0 .2 4 9 .
:-]-R-T' Tg5T
fl
(,4s9[el,,=-c-'"to)
. 5 o *? c> L ) - _ .lY 3 =
"O 1 q Ob
32.
Usethefollowingto answerquestion
A TV newsprogramconductsa call-in-pollabouta proposedcity banon smokingin public
places.Of the 2467 callers,1900wereopposed
to the ban.
b
32. Letp be the proportionof citizensin the city opposedto the ban on smokingin public
places.To determineif the lq4igri* o:lcilizensin the citv opposethe_banon smokingin
publicplaces,
A) testthe hypotheses
p:0.50, Hu:p* 0.50.
F1s:
,4.
l1e:p = 0.50,Hu:p> 0.50.
( B) testthe hypotheses
ffe:p : 0.77, Hu:p > 0.77.
C) testthe hypotheses
D) noneof theabove.
A
'
I. there evidencethat the proportion of freshmenwho graduatedin the bottom third of their
high school classin 200i was reducedbecauseof the tougheradmissionstandardsadopted
in 2000, comparedto the proportion in 1999? To determinethis, you test the hypotheses
HO:Pt = P2, H;. pt > p2.
The P-value of your test is
A) between.10and.05.
B) between.05and.0t.
C) between.0land .001.
D ) b elow.001.
Page 12
Use the following to answerquestion34.
n
q*{
of 1750adultsfoundthat I 140usedtheInternet.Of those
A random-digit
dialingsaqrple
q+ilJaia
who usedthJnternet,
theyexpectbusinesses
to haveWeb sitescontaining
productinformation;329of the 610nonusers
saidthis too.
[.*
I,t
.S
8.. scr.*r4r,Lq
Proper-ti yw1
34. Let p, andp, betheproportionof all partsusersandnonrrr.rr,respectively,
that expect
to haveWeb sitescontainingproductinformation. A 90%confidenceinterval
businesses
%
.T'Ftr'r-€:r' b
ffi0.023.
(. f,rorg begor)
,"
@ ol99t 0.038.
C) 0.300+ 0.045.
.33804
D) 0.300+
0,054.
5
"
*"jeq3=.e$Tby
when
it istrue,
l,t#,'.:ltilT:"uu hypothesis
(9
ur."pting the null hypothesiswhen it is false.
C) incorrectly specifying the null hypothesis.
D) incorrectly speciffing the alternativehypothesis.
F*'-! '*o re
rl- tr'a-t**l
$cJ
tLo
Use the following to answerquestion36.
A newspaperconducteda statewidesurveyconcerninga proposalto raisetaxes to prevent
budgetcuts to education. The newspapertook a random sample(assumeit is an SRS) of
I 200 registeredvoters and found that 580 would vote to raise taxes. Let p representthe
proportion of registeredvoters in the statethat would vote to raise taxes.
t
- b 3 6 .to e sti m atepwithmarginoferror0. 0 lwit h 9 5 %
confidence?
A)n:4;
B)n: r5oo
C ) n :4 8 0 0
Q
,:e604
/*\sz^--\(
r) :- (+6)-
2
as)
tH^( rs)
: Q loc>4
Page13
"l
\-'
t=t .QG
Usethefollowingto answerquestion37.
In a largemiflwesternuniversity(theclassof enteringfreshmen
is 6000or morestudents),
an SRSof 100'enteringfreshmenin 1999foundthat flfinished in the bottomthird of their
highschoolcl-ass.
Admissionstandards
at $e universityweretightenedin 1995.In 200I,
an SRSof lUfenteringfreshmenfoundthailO finishedin the bottomthird of theirhigh
schoolclass.Let p, andp, betheproportionof all enteringfreshmenin 1999and2001,
respectively,who graduatedin the bottomthird of their high schoolclass.
J sa-n-pt-qF.oPet- fr t-rn
37. Is there evidencethat the proportion of freshmenwho graduatedin the bottom third of their
high schoolclassin 2001 has beenreduced,as a result of the tougheradmissionstandards
adoptedin 2000, comparedto the proportion in 1999? To determinethis, you test the
hypotheses
HO:Pt = P2, Hat pt > pZ.
is
The vable of_lhezqlAlistic"fortestingthesehypotheses
A) z - 1 .2 0 .
B) z : 1 .6 5 .
x z--_I
c) z :
@
1 .9 6 .
z: L98.
5'AT
TL:T
to
z= | 9843
Use the following to answerquestion38.
We wish to seeif, on average,traffic is moving at the postedspeedlimit of 65 miles per
hour along a certain stretchof Interstate70. On eachof four randomly selecteddays,a
randomly selectedcar is timed and the speedof the car is recorded. The observedspeeds
{-
Pt^+''n
L1
65,70,and75 milesperhour. Assumingthatspeeds
arenormallydistributed
with
--are.7A,
*"i;" {1,*"t"st w[Ether,on average,
traffic is movingat 65 milesper hour,by testingthe
hypotheses
On-a_ lFrnj.*CLJ,1
H o :l t : 6 5 , H u :1 t* 6 5 .
38. Basedon the data,the vqlujfthq)re:sample
A) 5.
B) 4 '90'
/-<
/ statistic,is
\r
' t= I
( c) 2.4s.
STtrT, TES.i- J
bgrr?
L=J +'+1
D ) r.23.
-a/
Page14
Use the following to answerquestions39-40.
A scientistwas curiousif youngercoupleswith at leastone child were becomingmore
prevalentin urban areas. He decidedto seeif the meanage of the older spouseof couples
with at leastone child living within the city limits of a large metropolitanareawas lower
than that of the elder spouseof coupleswith at leastone child living outsidethe city limits.
He selectedan SRS of 100 coupleswith at leastone child living within the city limits and
determinedthe meanageto be x, : 39 years,with a standarddeviationsl : 8 years. He
also selectedan independentSRS of 100 coupleswith at leastone child and determinedthe
meanageto be 7, : 40 years, with a standarddeviation s2 : 10 years. Let l\ and1t2
representthe mean agesof the populations of all couples with at least one child living inside
and outside the city limits, respectively. Supposethe researcheris interestedin testing the
hypotheses
J n*"^+tt
fv\-a_ct'-'r/1.
HO:ltt: [LZ,Ha'.$t < FZ.
A 39. The numericalvalue of the / statisticis
G,
B) - 0.61.
6TRT
-a
tr-
Q!
B)
C)
D)
largerthan0.10.
between0.10 and 0.05.
between0.05 and 0.01.
below0.01.
{
t = --.'l8O?
c) - 0.33.
D) * 0 .11.
A 40.,^.The P-valuefor the testis
TEST
p*va-L*o= .Jtr.7
Page15
Use the following to answerquestions4l-42.
Do women and men treat female and male children differently? An observational study was
conductednear the primate exhibit at the Columbus Zoo onweekends in 1997. The data are
from 39 groups of three- one adult female, one adult male, and one toddler, in which the
toddlerwas being carried. Recordedbelow is which adult (male of female)was carryingthe
toddler by the sex of the toddler.
Sexof adultcarryingtoddler
Male
Female
n
H
Sex of Toddler
Female
Male
8
6
11
tt
8
41. Supposewe wish to test the null hypothesisthat the proportion of male adults and the
proportion of female adults carrying a toddler is the same,regardlessof the sex of the
toddler. Under the null hypothesis,the expectednumber
carrying a male toddler accordingto the table is
e.
\A)
B) 8 .
reQr
*o +4
c) 6.
D) s.
R
42.rhe
uare statistic for testing independenceof sex of the adult of
sex of the toddler is
@ o.+oo.
B) 0.498.
c) 3 .94.
D) 39.27.
n
+l
$.
,XL
= "159r
$ we rqiectthe-ryll-byell$is when,in fact,it is t!ue,we have
a TYPeI error'
@) .otntnitted
B) committeda TYPeII error.
C) a probabilityof beingcorrectthat is equalto theP-value'
D) a probabilityof beingcorrectthat is equalto 1 -P-value'
/\
!*+
Page16
Re6wf *c,^o fio-" .I
fil
|* rer6"uS
Fa-lsr l{,,,
JT
Use the following to answerquestions44-45.
Recentrevenueshortfallsin a Southernstateled to a reductionin the statebudgetfor higher
education. To offset the reduction,the largeststateuniversity proposeda25oh tuition
increase.it was determinedthat such an increasewas neededto simply compensatefor the
lost supportfrom the state. Random samplesof 50 freshmen,50 sophomores,50 juniors,
and 50 seniors from the university were askedwhether they were strongly opposedto the
increaseogiven that it was the minimum increasenecessaryto maintain the university's
budgetat currentlevels. The resultsare given in the following table.
Year
Stronelv Opposed
Freshman
Yes
No
39
Junior
36
t4
1l
29
18
2l
)z
an
stronglyonoosedseniors?
A) r8
(Ce{*.
\'
B) 2 5
c ) 3 0.5
D) 50
.+o+.J\
'
)
Chi-squarestatisticfor this dataequals21,p.Thel:alue
b, 45. A)Thegreater
than
is
.10.
B) between0.05 and 0.10.
C) between0 .01 and 0.05.
I P) lessthan0.01.
p * rlcu.t-u"*-=(". ?CIbq e, .*S
** .COSSls?
46. The appraisedvaluesof threerecently sold housesin the Columbusareaare (in thousands
of dollars) 260,315, and 295. The standarderror of the meanof thesethree appraised
__-_\-/_-_\_-/
values ls
p-r"rl. L-.
' L,
A) 2 9 0.00.
B) 27.54.
c) 22.73.
Ql' to.oz.
cR Lt-
cnn
iT',trT
I-VAR 5T'AT
+., S,;r,d
5= .1.1.t3tX
Page17
sfl=
*tn
)r"t
-ffi*-sEX
: l\a.01yl
Usethe following to answerquestions47-48.
The housing commission of Ashland County is interestedin finding out more about the
number of rental units that qualifu as low-income housing but do not meet the minimum
standardliving requirementsin ValrTownship and Marlin Township. Units are randomly
selectedin both townships. Of the 85 low-income units sampledin Van Township
(Township l),1t do not meet minimum requirements.Of the 80;rnits sampledin Marlin
erTownship(Township2),2-l do not meetminimum requirements.
\'I
?t*oPc:r *r Crrr
that do not meet minimum standardsin the two townships is
@
B)
C)
D)
O
t = 1 .4 5 .
z = 1 ,.6 5 .
z = 1 .9 6 .
z : 2 .3 3 .
STAr
T'6b-T t€
/='* j .* - 1 s l* p
48.The hypothesesto testthat the proportionsof low-incomerentalunits that fail to meet
minimumrequirementsin the two townshipsareejgllg
A)
4olis
Ho: pr:pz,Ho:Pt<Pz.
Ho:pr>pz.
B) Ho: h:pz,
+ pz.
Ho: pr:pz,Ho'.pt
A
D) Ho: p., * pz,Hotpt=pz.
fl
49. The mean area ltof the severalthousandapartmentsin a new developmentby a certain
b u ild erisadvertisedtobel250s q u a re f e e t . A t e n a n t g I o u p . t b in k s t @a t g ,
becauseit is basedon the squarefootage of apartmentsin an older development by the same
builder. The group hires an engineerto measurea sample of apartmentsto verifu its
suspicion. The appropriate null and alternative hypotheses,lls and Hu, for 1t arc
@
nottrr:1250andHu:1t* 1250.
B) l/6: lL= 1250andHu:1t< 1250.
C) Flo:I,L=1250andHu: 1t> 1250.
D) cannotbe specifiedwithout knowingthe sizeof the sampleusedby the engineer.
Pagel8
A5 0
Scoreson the SAT Mathematicstest (SAT-M) are believedto be normally distributed,with
meanp. The scoresof a random sampleof three studentswho recently took the exam are
olu: and4uu. 4.95%
A
c,onfidence
intervalforprbasedon thesedatais
Up*!24,*glg.
_ , _--21:u.
Psin G) ssooo+TZ as
L
B) 550.00x 142.00.
+ 1 2 8 .5 8 .
c ) 5 s0 .0 0
D ) 5 50 .0 *0 1 0 5 .0 1 .
I
STfiT Tr_5r t
\:Srn
(erb. rr,1 )3 g.?)
Ouestions51 to 55 are BONUS!
fv\9<crr\
[- sc-*,+Lq
-t )3 .tQ *,sso
a- l-l 3,9 ?
5l. Supposethe time it takescollegestudentsto completetheir degreefollows a normal
distribution,with mean ltand standarddeviation o:1.2 years. Basedon random sampleof
collegestudents,you constructa95o/oconfidenceinterval forpr and find it to be l.l5 + 0.08.
Which of the followins is true?
(t.<t1 r.&3
A) A test of the hypotheses.F/s:lt: 1.2,Hu: lt * 1.2would be rejectedat the 0.05 level.
B) A test of the hypothesesF16:p: l.l, Hu: Ir * 1.1would be rejectedat the 0.05 level.
4) e test of the hypothesesfls: p : 0, Ha: [t + 0 would be rejectedat rhe 0.05 level.
L
D) All theabove. R%e-d
E
rlu t^:\nu.r
.l-hs- C-f
7,r" Lb {tc1t i.,"
52. Alevel c two-sidedsignificance
testrejectsthe null hypothesis
F/s:p= l.16exactlywhen
A) the z test statisticdiffers from p6.
@ ttt" value g4 falls outside a level l-aconfidence interval for 1t.
C) the z test statistic differs from p.
D) the value p falls outside a level l-a confidenceinterval for pa.
r',
l)
53. In testinghypotheses,
if the consequences
of rejectingthe null hypothesisare very serious,we
should
4)
tfl
C)
D)
/4:i
usea verylargelevelof significance.
usea verysmaillevelof significance.
insistthattheP-valuebe smallerthanthe levelof significance.
insistthatthe levelof significance
besmallerthantheP-value.
Page19
_-.
n
D
the lifetimesof a randomsampleof 100tiresratherthan25.Which
I hadmeasured
54. Suppose
is true?
of the following statements
intervalwould increase.
A) Themarginof errorfor our 95o/oconfrdence
for our 95% confidenceintervalwould decrease.
ffr.
of
error
@
intervalwouldstaythe same,sincethe level
marginof errorfor ow 95%confidence
C) The-*!n
ofconfidencehasnotchansed.
D) owould decrease.
t.*"%"- lc"rn\pt -5 hq.n.{- i-rno*ll.sr
V@-rt
, 5c
hU.-r-<-
Use the followins to answerquestion55.
u-
&
ft\L\u2l*
la-ntA-qr se"'lftls_
"% €f {-oc
LpLU
A large Midwestern University studiedstudentperformancein a statisticscourserequired
by its mechanicalengineeringmajors. Of interestis the time spentin extracurricular
activitiesand whether a studenteameda B or betterin the course.
Extracurricular Activities
(hours per week)
Grade
B or better
Below B
H
<2
47
26
2to 12
48
80
>12
3l
70
55. Supposewe wish to display in a graphic the proportion of time successfulstudentsspend
in the three levels of extracurricularactivities. Which of the following graphical displays is
best suited to this purpose?
/-.
u pie chart
(9
B) a histogram
C) a boxplot
D) a stemplot
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