eprints.usm.myeprints.usm.my/16382/1/MSG_162_-_APPLIED_STATISTICAL...Created Date 1/7/2010 12:15:50...
Transcript of eprints.usm.myeprints.usm.my/16382/1/MSG_162_-_APPLIED_STATISTICAL...Created Date 1/7/2010 12:15:50...
UNIVERSITI SAINS MALAYSIA
Second Semester ExaminationAcademic Session 200812009
April/May 2009
MSG 162 - Applied Statistical Methods[Kaedah Statistik G unaan]
Duration : 3 hours[Masa:3 jamJ
Please check that this examination paper consists of SIXTEEN pages ofprinted material before you begin the examination.
[Sila pastikan bahawa keftas peperiksaan ini mengandungiENAM BEL/'Smuka surat yang bercetak sebelum anda memulakan pepeiksaan ini.l
lnstructlons: Answer all four [4] questions.
Franan Jawab semua empat [4] soalan.l
...2t-
2 IMSG 1621
l. (a) A study was designed to evaluate the effectiveness of new treatments toreduce the systolic blood pressure of patients determined to have high bloodpressure. Three drugs (A, B and C) and three nondrug treatments (conholleddiet, exercise programs and biofeedback) were considered for evaluation inthe study. A group of three patients was then randomly assigned to a
combination of one of the three drugs and one of the three nondrugtreatnents. After participating in the program for 2 months, the reduction insystolic blood pressure from the blood pressure readings at the beginning ofthe program was recorded for each patient.
",1u = 48,146
(i) State a model and its assumptions.(ii) Perform an appropriate analysis at cl : 0.01.(iiD Perform a follow-up analysis.
(b) Two anticoagulant drugs are studied for their effectiveness in dissolvingblood clots. Each of six subjects receives the drugs at equally spaced timeintervals and in random order. Time periods between drug applicationspermit a drug to be passed out of a subject's body before the subject receivesthe next drug. After each drug is in the bloodstream, the length of timerequired for a cut of specified size to stop bleeding is recorded.
lndividual34 Total
IIIijk
Drug A in pill formDrug B in pill formDrug A in liquid form
Total
IIv? = 51s.335L/LI U
(i) State a model and its assumptions.(ii) Perform an appropriate analysis at a = 0.10.(iii) Perform a follow-up analysis.
808.2801.79r9.3929.2
531.0 528.8 455.8 6t3.4 7t2.8 6t6.6 3,458.4
[100 marks]
...3/-
NondrueDiet Exercise Biofeedback Total
A 322639
97
484738
133
49424l
132
362
B 35
3239
106
474844
139
484942
r39
384
c 384533
rr6
48474T
t36
404L
49130
382
Total 319 408 401 tt28
t27.5 130.6 118.3 122.5 180.7 r28.6r29.0 t29.t ttr.7 144.3 174.4 113.2135.5 138.0 110.1 162.3 181.8 191.6139.0 13l.l 115.7 184.3 175.9 r83.2
I. (a)
Wat A di dalam bentukpilUbat B di dalam bentukpilUbat A di dalam bentukcecairWat B di dalarn bentukcecairJumlah
808.2
801.7919.3929.2
531.0 528.8 455.8 613.4 7r2.8 616.6 3,458.4
3 IMSG 1621
Suatu kajian direkabentuk untuk menilai kcberkBsanan rdwaton baru bagimengurangkan tekanan darah sistolik pesakit yang dikenalpasti mengalamitelranan darah tinggi. Tiga ubat (A, B, dan C) dan tiga ranatan tanpa ubat(diet yang dikmoal, program senaman dan bio+imbalbalas)dipertimbangkan untuk penilaian di dalam knjian. Selcumpulan tiga pesahitdiumpuklran secara rm'vak kepada suatu gabungan daripada satu daripadatiga ubat dan satu daripada tiga rawatan tanpa ubat. Selepas menyertaiprogram tersebut untuk 2 bulan, pengurangan di dalam telanan darahsisitolik daripada bacamt-bacaan telanan darah pada a+al program dicatatbagi setiap pesakit.
Tanpa ubotWat Diet Senaman Bio-timbalbalas Jumlah
A 322639
97
484738
I tss
49424I
132
362
B 353239
ar06
474844
I I3:t
484942
139
384
C 384533
I tto
48474I
136
404I49
130
382
Jumlah 319 408 401 I 128
: 48,146
(i) Nyatakan suatu model serta anggapannya.(i, Lalcukan suatu analisis yang sesuai padaa : 0.01.(ii) Lakukan suatu onalisis lanjutan.
(b) Dua ubat anti pembekuan dikaji untuk keberlcesonnnnya dalam mencairkandarah beku. Setiap enam subjek menerima ubat-ubat tersebut pada selangmasa yang sama dan secara rawak. Tempoh masa antara penggunaan ubatmembolehkan satu ubat dikeluarkan dari tubuh subjek sebelum subjekmenerima ubat seterusrrya. Selepas setiap ubat berada di dalam alirandarah, panjang masa yang diperluknn bagi suatu luka yang bersaiz tertentub e r he nt i b e rdar ah dic at at.
WatIndividu34 Jumlah
141';r
>Zr; : srs,33s
Nyatalran suatu model serta anggapannya.Lakulran suatu analisis yang sesuai pada q. : 0.10.Lakulran suatu analisis lanjutan.
(,(ii)(iii)
fl00 marknhJ
...4t-
127.5 /,30.6 I18.3 122.5 i,80.7 128.6
129.0 129.1 i,1/,.7 144.3 174.4 i,13.21s5.s r38.0 il0.1 162.3 181.8 191.6139.0 131.1 115.7 184.3 17s.9 18s.2
4 IMSG 162l
2. (a) In a study to examine the quality of fish after 7 days in ice storage, ten rawfish of the same kind and approximately the same size were caught andprepared for ice storage. Two of the fish were placed in storage immediatelyafter being caughq two were placed in storage 3 hours after being caught, and
two each were placed in storage at 6,9, and 12 hours after being caught. Ameasurement of fish quality (on a 100-point scale) after the 7 days of storage
were recorded.
Quality score Storage time (in hours)
State a model and its assumptions.
Perform an appropriate analysis at a = 0.05.
(b) A clinician studied the effects of trvo drugs used either alone or together on
the blood flow in human subjects. Six healthy middle-aged males were
randomly assigned to the various drug treatments. The increase in bloodflow from before to shortly after the adminishation of the drugs weremeasured.
Individual34 Total
Both drugs A and B t4655490
Total
IIv.? = 4,524tHtH u
(i) State a model and its assumptions.(iD Perform an appropriate analysis at a :0.01.(iii) Perform a follow-up analysis using Duncan multiple range test.(iv) Determine the following effects on blood flow:
a. drug effect.b. drug combination effect.
[00 marks]
27028070373376678681 9
79984 12
85 12
(i)(iD
Drug B aloneDrug A alonePlacebo (neither
250
25 2t 24 28 25 23
108111088968101062-r0-22-l
...5t-
2. (a)
5 IMSG 1621
Di dalam suatu kajian pemeriluaan kualiti ilan selepas 7 hari di dalamsimpanan berais, sepuluh ikan mentah sama jenis yang bersaiz hampir sama
ditanglrap dan disediakan untuk simpanan. Dua daripada ikan tersebut
diletaklran di dalam simpanan sejurus selepas ditangkap, dua diletakkan didalam simpanan 3 jam selepas ditangkap dan setiap dua diletakknn didalam simpanan pada 6, 9 dan 12 jam selepas ditangknp. Suatu uhtranfualiti ilran (berdasarkan suatu skala 100) selepas 7 hari disimpan dicatat.
Wat JumlahKedua-dua ubat A dan BUbat B sahajaWat A sahajaPlaceboJumlah 250
Skor lataliti Masa simpanan (dalam jam)
(, Nyatakan suatu rnodel serta anggapannya.(iil Lalatkan suatu analisis yang sesuai pada q" : 0.05.
(b) Seorang ahli perubatan mengkaji keberkesanan dua ubat yang digunakansama ada bersendirian atau bergabungan ke atas aliran darah dalammanusia. Enam lelaki sihat pertengahan umur diumpukkan secara rav'aklrcpada rawatan ubat yang berlainan. Peningkatan di dalam aliran darahdaripada sebelum ke sejurus selepas penggunaan ubat-ubat tersebut dicatat.
Individu3,
,0
03
36699I2I2
2728707376788l7984
85
146JJ490
(,(i,(ii,
(iv)
...6r-
25 21 24I0 8 11
9682-t0
28TO
IO-2
25 23881062-l
L/L/ ij
Nyatalran suatu model serta anggapannya.Lalatknn suatu analisis yang sesuai pada a : 0.0L
Lakukan suatu analisis lanjutan menggunakan ujian julat bergandaDuncan.Tentukan kBsan berikut ke atas aliran darah:a. kesanubat.b. kesangabunganubat.
fl00 markahJ
6 IMSG 1621
3. (a) An advertising executive is interested in the effect of colour on
advertisement appeal. Six individuals are selected randomly and asked torate each of four magazine layouts in order of eye appeal, with a rank of Ibeing given to the most appealing advertisement. The layouts are identical
except for the colour scheme involved.
AdvertisementIndividual34
No colorRed predominantYellow predominantMixed colorsTotal
IIv.? = zsota tL/ u
(D State a model and its assumptions.(ii) Perform an appropriate analysis at cl = 0.05.(iii) Perform a follow-up analysis using Tukey HSD test.
(b) [t was known that a toxic material was dumped in a river leading into a large
salt-water commercial fishing area. Civil engineers studied the way thewater canied the toxic material by measuring the amount of the material (inparts per million) found in oysters harvested at three randomly selected
locations, ranging from the estuary out into the bay where the majority ofcommercial fishing were carried out.
Total
Total 374
IIv? : 8.390LILJ U
(D State a model and its assumptions.(ii) Perform an appropriate analysis at a :0.01.(iii) Perform a follow-up analysis.
[00 marks]
Totalt2l62622
I23
45
6
7l6754625565
3412452153542533
l1224554
Location
t9l5l0l6ll20
22262426l5t7
302620202928
.,.71-
lMsG 1621
3. (a) Seorang pegawai pengiHanan berminat dalam kesan warna ke atas tarikaniHan. Enam individu dipilih Eecara rav'ak dan dikchendaki untuk menilaisetiap daripada empat lakaran majalah yang menarik hati mengikutperingkat, dengan pangkat I diberikan kepada iHan yang paling menarilcLakaranJaknran tersebut odalah sama melainkan pada skema warrw yangdigunakan.
IHanIndividu34 Jumlah
Tiadawarna I2I62622
Jumlah
Warna utarna merahlV'arna utama htningWarna
(,(ii)(ii,
7I675462JJ65
374
I23456
412521354533
II3224455542
IIr' :2sol-/ a-,/ ij
Nyatalran suatu model serta anggapcmnya.
Lakukan suatu analisis yang sesuai pada a : 0.05.Lakulran suatu analisis lanjutan menggunakan uiian Tulcey HSD.
(b) Dilretahui bahawa suatu bahan tolcsik dibuang ke dalam sebuah sungai yangmegalir ke dalam suatu kawasan perniagaan penangkopan ikan air masinyang luas. Jurutera-jurutera sivil mengkaji cara air mernbawa bahan toksikdengan mengukur amaun bahan (dalam bahagian periuta) yang terdapat didalam kerang di tiga lokasi yang dipilih secara rawak, daripada muarahingga lrcluar kz kmrtasan teluk, tempat kebanyaknn penangkapan ikanlromersial dilahtkan.
Jumlah
Jumlah
IIr' : B.3sot-/ z-/ ij
(, Nyatakan suatu model serta anggapannya.(ii) Lakukan suatu analisis yang sesuai padau : 0.01.(ii, Lakukan suatu analisis lanjutan.
p00 markahJ
Lokasi
302620202928
t9I5IOI6It20
22262426I5I7
153 91 130
...8t-
4.
I IMSG 1621
For many years, educators have suggested that home environment contribute
heavily to the educational achievement of students. In a study, averages on areading test were compared with the percentage of students with three or more
types of reading material at home (books, encyclopedias, magazineso
newspapers) and the percentage of students who watch television (TV) for sixhours or more per day. The following data were collected for second year
students in 32 states:
TV watchl8t220n9t218
33l9t72023
7il8
l4l9t9t47
6
9l3l72l610
l527l6L6
8
Refer to the appendix output for question 4.
(i) Perform an appropriate analysis to obtain the model and its assumptions.
Use cr :0.025.(ii) Obtain an estimation interval and prediction interval for a state with 75
percent of students with three or more types of reading material at homeand l0 percent of students who watch television for six hours or more per
day.
[100 marks]
5259565667706l3l55
58
3l5l72677856466064768076696l508l6658l8645674
787377688586837673
80
6469848488
78768384
88
88
888479789086707682
80
86
...9/-
e IMSG 1621
Untuk beberapa tahun, para pendidik telah menyaranlran bahawa suasanarumah paling banyak merryumbang kepada pencapaian pendidilmn para pelaiar.Dalam suatu kajian, purata bagi suatu ujian bacaan dibandingkan denganperatusan pelajar yang mempunyai tiga atau lebih ienis bahan bacaan dirumah (buku, encyclopedia, suratkhabar) dan peratusan pelaiar yang metnntontelevisyen (TV) selama enam jam atau lebih sehari. Data berikut dihmpul bagipelajar tahun dua di 32 buah negeri.
Slar Bacaan Menonton W525956566770
6I3I55583I5T
72
67785646606476
8076696I508I6658r8645674
18I220IT9
T2
t833T9I720237
IIII419I9I4
69I317216
10I52716t68
Rujuk lrcpada output oppendil<s untuk soalan 4.
(, Lahtkan suatu analisis yang sesuai untuk mendapatkan model dananggapanrrya. Guna a :0.025.
(iil Dapatlran suatu selang anggaran dan selang ramalan bagi sesebuahnegeri dengan 75 peratus pelajar yang tnempunyai tiga atau lebihienisbahan bacaan di rumah dan I0 peratus pelajar yang menonton televisyenuntuk enam jam atau lebih sehari.
[100 markahJ
7873
77688586837673
8064698484887876
8384888888847978908670
76828086
...10/-
10
APPEI\DIX: OUTPUTOuestion 4
Predictor Coef SE Coef tConstant 24.58 17.81 1.38MateriaL 0.7263 0.L967 3.59I]V -1.5351 0.2058 -7.43
S = 5.794L1 R-Sq = 84.72 R-Sq(adj) = 83.5t
Analysis of VarianceSource DF SS MS
Regression 2 5377 .4 2588.7Error 29 973.5 33.5Total 31 6351-.0
I q.+soos -o.lo32o -0.0774s 1| -"--'- |
rx,x)-r = l-0.10320 0.001153 0.000731 |
I
l-0.0774s 0.000731 0.0012734J
lMsG 1621
...11t-
1.
11
APPENDIK FORMT'LAS
Completely Randomized Design
lMsG 1621
,,
Y-SST : IIV?LrLr-ij Nij
))Y: Y-SSA:t t'
? n. Nll
For any contrast :
SSL =
SSR
[t ".o.(.? r r'
L = I c.Y.tLJ I l.i
r2I
I
)2c.
\a l'
+n.ll
Completely Randomized Block Design
Y2: I I v?.?? IJ NlJ
Y? Y2: \r l'
? b NI
Y2. Y2:5 'J
laNJ
Latin Square Design
Y2: Itl"i:u - o.i jk '
Y? Y2: \a l"
+ a NI
Y2. Y2:5 .J.
?aNJ
2ZY-. Ysr '.^\_T a N
...12i-
Two-way Factorial DesigntY-
lMsG 1621
df = degtees offreedom
df = degrees offreedom
12
ssr = III"'Uu 1.li jk
ss"",, :Y?,
ss rJ'++ nrJY? Y2
SSA : t r"? bn N
I
Y2. Y2SSB : 5' ':'
?anNJ
ssE = IIL"?,,i jk tJ*
5. Distributions
Tukey HSD: 9a,a,df '
Scheffe':
Y2..
N
Y?.lJ.
a = number of treatments
. a: number of treatments
Duncan multiple range: ro,p,df , p = range df = degrees offreedom
6.
r:
t=l
Correlation
SSxy
/SS SSltlxY
a - l) Fo,u-r,ar
n-2--7l- r'
...13t-
13 IMSG 1621
7, Regression
SSb,==* , bo=Y-b,X,SS
(I*,)Er)sS*, I",", -
SS : IX? -E\.Lx-tn
(r v,fSS = IY.2 -
\! -iy-tn
Var(b,) : *
8. Kruskal-Wallis Test
r: J=I{:(N+r1N(N+l) 7 "i
9. Friedman Test
r : ,)?rrl*3 :u(a+r)ba(a+l) ?
10. Cochran Test
a(a- r)2n! (a- r)N2IT:
aN I s?AJJ
11. Spearman Test
ur oi: :1-' n("'-t)
...14t-
14
APPE|IDIX: TABLES
Duncan Multiple Range Table
r.6(p, fl
lMsG t62l
20 50 lo0
3.89 4.o9 4.16 4,22 4.32 4.36, 4.41 4.45 4.48. 4.65 4.7r 4.713.82 3.99 +.10 4.r7 424 4.3O +.34 *.37 4.+l 4.59 +.69 4.693.76 392 4,O3 4.12 4.r7 4.23 427 4.31 4.34 4.53 4.66 +.663.77 3.86 3.98 4.06 4.11 4.tT 4.2r 4.25 4.29 4.48 46r+ 4.653.64 3.80 3"90 3.98 4.04 4.09 4.L+ 4.17 +.ZO 4.4t 4.60 4.68
10
1 90.O 90.O 9o.O 9o.O 90.O 90.0 90.0 90.0 90.0 90.0 90.0 90.O
2' r4.O r4.O r+"O 14O 14O 14.O 14.O !4.0 ,1{.O 14.O l4O l4.O3 8.26 8.5 8.6 . .8.7 8.8 8.9 8.9 93 9.0 9.3 9.3 9.3
4 6.s1 6.8 6.9 7 .O 7.1 7 .r 7.2 7 .Z 7 .3 7.5 7.5 7 .5
5 5.70 5.96 6.11 6.18 6.26 6.33 6.40 6.44 6.5 6.8 6.8 6"8
6 5.24 5.51 5.65 5.73 5.81 5.88 sgs 6.00 6.0 6.3 '6.3 6.t7 +.95 5.?2 5.37 5.45 5.53 5,67 5f9 5.73 5.8 6.0 .6.0 6.08 +.74 s.oo 5.L+ 5.23 S.3Z s.40 5.47 5.51 5.5 5.8 5.8 .5.8.9 +.60 4.86 4.99 5CI8 5.r7 525 532 s.36 s.4 5.7 '5.7
.5.?10 +.48 4.73 4.88 '4.96 5.06 5.13 5.20 5.24 S.Z8 s.55 5-55 5J5
tL +.39 +.63 4.77 +.8d +.94 5.01 5.06 3.lZ 5.15 5.39. 5.39 5.3912 4.rZ 4.s5 4.68 +.76 +,84 +.92 4.96 '.5.02 s.O7 5,26 s26 5.2613 4.26 4.48 4.62 4.6,9 4"74 4.& +.A8 .4.94 4.98 5.15 5.r5 5.1st4 +.2t +rtz 4.55 4rt3 4.7o 4.78 t+.83 4.87 +.91 5o7 . 5.07 S"O7
t5 +,t7 4.37 4.50 4.58 464 4.?2 +.77 4.81 4.84 500 5.00 ' 5.O0
16 4,73 4.34 4.45 4.54' 4.60 4.67 4.72 4:16 4.?9 4.94 191- 4.9.4
L7 /t.10 4.30 4.41 4.50' 4.56 4.63 4.68 4.73 1.?5 4.8, 4.8t' 4.8918 +.O7 +.77 4.38 4.46 4.s3 4"59 4.64 4.68 4.77 4.85 4.85 4,8st9 4.O5 +.24 4.35 4.43 4.50 4.56 4.57 4.64 +.67 4.82 4.82 4.8220 4.Q2 4.22 4.33 4.40 4,47 4.53 4.58 4.61 4.65 4.79 4.79 4.79
304060
to0E
.f = dcgrecs of freedom.
...15r
lMsG 162115
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Tukev HSD Table
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titlErk
lltiqF
B()EdcIAFgEE€Fss,E ul
3!FT63T1ode}
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16 IMSG 1621
Spearman Table
.005.00r .010 .050 .100
45
67
I9
t0
.r*t
.9286
.9000' .8667
.8364
.8182
.79t2
.?570
.7464
.7265
"70E3.6904.6737.6586
.6455
.63t8
.6t 86
.6070
.5962
.5856
.5757
.5660
.s567
.5479
:
,9429.8929.8571.8167.78t 8
J545.7n3"6978.6747.6536
.632/
.6152
.s975
.5825
.5684
.5545,5426.5306.5200.5100
.5002
.4915
.4828
.4144
.4665
.9000
.8857
.8571
.8095
,7667.7333
.7000
.6713,&29.6220.6000
,3824.56t7.5480.5333.520X
.5078
.4967,4852.4748.4654
.9000
.E286
.7450
.7143
.6E33
.6364
.609t
.5E04
.5549
.534t
.5179
.5000
.4853
.4716
.4579
.u5r
.4351
,424r.4t50.406t.3977
.3894
.1822
.3749,3685.t620
.8000 .'8000
.8000 .7000
.7714 .6000
.6786 .5357
.6190 .5000
.5833 .4667
.5515 ,4424
.5273 .4182
.4965 .3986
.4780 .379t
.4593 .3626
.4429 .3500
.4265 .3382
.4r l8 .3260
.3994 .3148
.3895 ,3070
.37E9 .2977
,3688 .2909,1597 .2829.3518 .2767.3435 .270/-.3362 .2646
.3299 .2588
.3736 .2540l
.3175 ,?Al90
.3r 13 .2/r''3
.3059 .2400
ill2l3l4l5
t6t7l8l920
2l222t24
25
2627282930
.4564
.4481,&or.4320.4?'51
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