STAT 652-601
November14,2008
Instructor: Jeff Hart
Test 2
Instructions:
1' You may use your formula sheet, a calculator, and the tables in the back of your text.
2. In order to get full credit, show as much of your work as possible.
3. Point values are given in parentheses.
4. Unless otherwise stated. use a : 0.05 for all tests. Good luck!
1. (40) Engineers studied the effect of the composition of cement on heat evolved during
hardening. Data were collected on the following variables.
y: heat evolved per gram of cement (in calories)
z1: amount of tricalcium aluminate
z2: &mourt of tricalcium silicate
a 3: &mount of tetracalcium alumino ferrite
14; &mount of dicalcium silicate
R,eferto the accompanyingoutput to answer the following questions,
(a) (tO) Does there appear to be a collinearity problem in these data?
(b) (30) Choose an appropriate regressionmodel, and justify your choice.
G ) Yt, y',l"ru rs co//,n"orr(f, oraottgilu ? rtle/err/eat
ve/r'e//"a, Do co//e/a//rort /r" /ager /l/"n C, t ut
ua/vz, 04/ /4 /1" f"// nol"/
a/s"/"/"
t /ro t/a/fance
/4r/o/rat fr.f i= e/e /rtorehon d n ,
no/"/= o/e /"f"rs,'/12, ) on/ 3, 6"//f /orn
U ') Do
r
,2 vo/ue" clos. Q, egua
/ ) /. fi"/ af fi. f"tt .o/n/
//ru , /rf"
var/a //.
(f t ) ert/ere/ ort s/e/ J
'n
/,t,t /, slg,t, frro n/ , o4d /l " 04e Vr)
"/""
/a
n/"" e/ o4
va/ueof c,o5s',D r/ rs /u")o//.
3
e7"o'
P'oy'u,4
//nn nol*{ J /ag// /o
/"
f :g,"
"fO )/ffi,
5.
pt/erefable
2. (40) The data in this problem are from a statement by Texaco, Inc. to the Air and Water
Pollution Subcommittee of the SenatePublic Works Committe'eon June 26, 1973. Mr. John
McKinley, then President of Texaco, cited an automobile filter developed by Associated
'Octel
Company as effectivein reducing pollution. However,questionshad been raised about
the effects of filters on vehicle performance, fuel consumption, exhaust gas back pressure,
and silencing. On the last question, he referred to the data in this problem as evidencethat
the silencing properties of the Octel filter were at least equal to those of standard silencers.
The responsevariable was noise level (in decibels) and two factors were of interest: vehicle size (small:1, medium:2 and large:3) and type of silencer (standard:l and Octel
filter:2). A CRD was conducted as follows. Twelve small vehicleswere randomly selected
from a pool of small vehicles. Six of these twelve were randomly selectedand fitted with a
standard silencer, and the other six were fitted with Octel filters. Exactly the same procedure was used for medium and large cars, resulting in a total of 36 casesand the following
ANOVA table.
Source of
variation
Car size
Silencers
Interaction
Error
m
SS
MS
df
F
P-value
26051.389 2 13025.694199.119 0.0000
1056.250 1 1056.250 16.146 0.0004
402.083 6.146 0.0058
804.167 2
65.477
1962.500 30
Tleatment means and some SPSSoutput are provided in the accompanyinghandout. Also,
a plot of treatment means is given on the last page of the exam and the LSD value for
comparing two treatment means (at level 0.05) is 9.54. Provide a complete analysis of the
data, stating your conclusionsin the languageof the problem.
rc s,q o/ /1" o.of /"ve/,
fru /ny'e/acrtbn
a)
//t i, shga/e.il"' 4o /r"" of // " /4/eracfiba ,
frn 6rA/ f,//"" /"o/' /" s,g,/u=t torbz
04 o /e/aqe il", il. s/"a6r/ s'A-4cet
on/v uftn U7ey' /4 nel, u/4 sr*e/ Ca/s,
A/t./ rr/./,urn s;4 corEf,#"/ ur'fi /4"
s/or/ot/
t/"i
Sr'/encef or< rlgrsrb/ on Gveraqe
04y o//rr
corn/rrro/,bnof
o' lertceh, fir,"//,
/?t, !fr?/ //r7
a/ /r'ff". / (/srd.
car 5/z.tat/
'
cqrs e/z srgt,'frot//7
4U"
,
's'*o/l
Xr/ a dun ) / '5or/1,,,
3. (20) R.esearchers
in a veterinary school wanted to compare the effects of three different
diets for dogs. Measuresof enzyme activity were obtained for each dog in the study before
and after being fed a specific diet for three weeks. The responsevariable was the difference
between before and afber enzyme activities. Available for the study were three standard
poodles, three dachshundsand three golden retrievers.
(a) (tO) Which do you think is more appropriate for this study: a completely randomized
design or a randomized bock design? Justify your answer.
/1
(or/omr?e/ //./ . 1///"uq/ tk co,r'f /.
cer*rrt 6f //;, y'lura /s #" o/v,'orrs/asst/,//y
"1o,
/"rrd'/ /o" 04 ,/irr/ oi o /on't/
/to/
/espontiA /,r/. D //,a /s hrr, lr{"i o,
RBD m// /" a raonuz%"/,v.uo,/A {rfrr/
/, fftl e/tces / r /unurt/,aA . [u"n lf / runl
/ns rto e/firf an /esy'o,?eA /at //nru /3 oA/7
o i/nq///"1,//, essic,;fr/ a/// ir,,g on R60,
(b) (10) Describehow the dogswouldbe assigned
to dietsfor eachof the a"ffin, mentioned
in (a).
RSD: 4,n/"r/v ais/i4 //. ftrr" /,"A A
/1" il 16" /oi//rt. and do fi"
som+
/;1,.I';';::
cAc2;;l;',!r'!
d4/ 6ss/9aft"* A d,a1 J . ,(*,nd* /.
i of-"//;" 6 ,/etnd,4,,e 7
;;*:;
cb= ony' dssslt /ln,rt A /r"Y S
71. 3 fellar'rue /g. e/e nr*ruy'
r
5,'
/,a/
1"