lnstructlons: Answer all four [4] - EPrints USM

UNIVERSITI SAINS MALAYSIA Second Semester Examination

Academic 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

of

printed material before you begin the examination.

[Sila

^pastikan

bahawa

^keftas peperiksaan ini

mengandungiENAM BEL/'S muka

surat yang

bercetak

sebelum anda memulakan

pepeiksaan

ini.l

lnstructlons:

^Answer

all four

[4] questions.

Franan Jawab semua

empat

[4]

^soalan.l

2

IMSG ¹⁶²¹

l. (a) A

^{study was designed}

to

^{evaluate the} effectiveness

of

new treatments to reduce the systolic blood ^pressure of patients determined to have high blood pressure. Three drugs (A, B and C) and three nondrug treatments (conholled diet, exercise programs and biofeedback) were considered for evaluation in

the

study.

A

^group

of

^{three patients was}

then

^{randomly assigned}

to

^a

combination

of one of the three

drugs

and one of the

three nondrug treatnents. After participating in the program for 2 months, the reduction in systolic blood ^pressure from the blood ^pressure readings at the beginning

of

the 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

dissolving blood clots. Each

of

six subjects receives the drugs at equally spaced time intervals

and in

random order.

Time

periods between

drug

applications permit a drug to be ^passed out of ^a subject's body before the subject receives

the

next drug.

After

each drug

is in the

bloodstream,

the

length

of

time required for a cut of specified size to stop bleeding is recorded.

lndividual

34

Total

III ijk

Drug

A

in

pill

form Drug B in

pill

form Drug

A

in liquid form Total

IIv? =

^51s.335

L/LI U

(i)

^{State a model and its} assumptions.

(ii)

Perform an appropriate analysis at

a

= 0.10.

(iii)

Perform a follow-up analysis.

808.2 801.7 9r9.3 929.2

531.0 528.8 455.8 6t3.4 7t2.8

6t6.6 3,458.4

[100 marks]

...3/- Nondrue

Diet Exercise Biofeedback Total

A

32

26 39

97 48 47 38

133 49 42

4l

132

362

B ³⁵

32 39

106 47 48 44

139 48 49 42

r39

384

c

38

45 33

rr6

48 47

4T

t36

40 4L 49

130

382

Total 319 408 401

tt28

t27.5 130.6 118.3 122.5 180.7

r28.6

r29.0 t29.t ttr.7 144.3 174.4

113.2

135.5 138.0 110.1 162.3 181.8

191.6

139.0 13l.l 115.7 184.3 175.9

r83.2

I.

^(a)

Wat A di dalam bentukpil Ubat B di dalam bentukpil Ubat A di dalam bentukcecair

Wat

B di dalarn bentukcecair Jumlah

808.2 801.7 919.3 929.2

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 bagi mengurangkan tekanan darah sistolik pesakit yang dikenalpasti mengalami telranan 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 pesahit diumpuklran secara rm'vak kepada suatu gabungan

daripada

satu daripada

tiga

ubat

dan

satu daripada

tiga

rawatan tanpa ubat. Selepas menyertai

program

tersebut untuk

2

bulan, pengurangan

di

^dalam

telanan

^darah

sisitolik daripada bacamt-bacaan telanan darah pada a+al program dicatat bagi setiap pesakit.

Tanpa ubot

Wat Diet

Senaman Bio-timbalbalas Jumlah

A 32

26 39

97 48 47 38

I tss

49 42

4I

132

362

B 35

32 39

ar06

47 48 44

I I3:t

48 49 42

139

384

C 38

45 33

I tto

48 47

4I

136 40

4I

49

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 mencairkan darah beku. Setiap enam subjek menerima ubat-ubat tersebut pada selang masa yang sama dan secara rawak. Tempoh masa antara penggunaan ubat membolehkan

satu ubat

dikeluarkan

dari

tubuh subjek sebelum subjek menerima

ubat

seterusrrya. Selepas setiap

ubat

berada

di

dalam aliran darah, panjang masa yang diperluknn bagi suatu luka yang bersaiz tertentu

b e r he nt

i

^{b e} rdar ah dic at at.

Wat

Individu

34

^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)

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,13.2

1s5.s r38.0 il0.1 162.3 181.8

191.6

139.0 131.1 115.7 184.3 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 raw

fish of the

same

kind

^and approximately

the

same size were caught and prepared

for

ice storage. Two

of

the fish were placed

in

storage immediately after 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.

A

measurement

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

blood

flow from

before

to

shortly

after the

adminishation

of the

drugs were measured.

Individual

34

Total

Both drugs

A

and B

t46

55 49 0 Total

IIv.? =

^4,524

tHtH 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]

270 280 703 733 766 786

81

⁹

799 84

¹²

85

¹²

(i)

(iD

Drug B alone Drug A alone Placebo (neither

250

25 2t 24 28 25

²³

108111088

96810106 2-r0-22-l

...5t-

2.

^(a)

5

IMSG ¹⁶²¹

Di

dalam suatu kajian pemeriluaan

kualiti ilan

selepas 7

hari di

^dalam

simpanan 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

di

dalam simpanan 3

jam

selepas ditangkap dan setiap

dua

diletakknn

di

dalam simpanan

pada 6, 9

dan 12

jam

selepas ditangknp. Suatu uhtran

fualiti

ilran (berdasarkan suatu skala 100) selepas 7 hari disimpan dicatat.

Wat

^Jumlah

Kedua-dua ubat A dan B Ubat B sahaja

Wat A sahaja Placebo

Jumlah 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 digunakan sama

ada

bersendirian

atau

bergabungan

ke atas aliran darah

dalam manusia. Enam

lelaki

sihat pertengahan umur diumpukkan secara rav'ak lrcpada rawatan ubat yang berlainan. Peningkatan

di

dalam

aliran

darah daripada sebelum ke sejurus ^selepas penggunaan ubat-ubat tersebut dicatat.

Individu

3,

,0 0 3 3 6 6 9 9

I2 I2

27 28 70 73 76 78

8l

79 84 85

146 JJ 49 0

(, (i, (ii,

(iv)

25 21

²⁴

I0 8

¹¹

2-t0 968

28

TO

IO -2

25

²³

106 88

2-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

berganda Duncan.

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 to rate each

of

four magazine layouts in order

of

eye appeal,

with

a rank

of

I being given

to

the most appealing advertisement. The layouts are identical except for the colour ^scheme involved.

Advertisement

Individual

34

No color

Red predominant Yellow predominant Mixed colors Total

IIv.? =

^zso

ta 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

the water canied the toxic material by measuring the amount of the material (in parts

per million)

^found

in

oysters harvested

at

three randomly selected locations, ranging from the estuary out into the bay where the majority

of

commercial fishing were carried out.

Total

Total 374

IIv? :

_LILJ ^8.390

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]

Total

t2 l6

26 22

I

2 3

4

5 6

7l

67 54 62 55 65

3412 4521 5354 2533 22 l1

45 54

Location

t9 l5 l0 l6 ll

20

22 26 24 26

l5 t7

30 26 20 20 29 28

.,.71-

lMsG

¹⁶²¹

3. (a)

^{Seorang pegawai} pengiHanan berminat dalam kesan warna ke atas tarikan iHan. Enam individu

dipilih

Eecara rav'ak dan dikchendaki untuk menilai

setiap daripada empat lakaran

majalah

yang menarik hati

mengikut peringkat, dengan pangkat

I

diberikan kepada iHan yang

paling

menarilc LakaranJaknran tersebut odalah sama melainkan pada skema warrw yang digunakan.

IHan

Individu

34

^Jumlah

Tiadawarna

I2

I6

26 22 Jumlah

Warna utarna merah lV'arna utama htning Warna

(,

(ii)

(ii,

7I

67 54 62 JJ 65 374

I

2 3 4 5 6

412 521 354 533 224 II3

455 542

IIr' :2so

l-/ 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 yang megalir ke dalam suatu kawasan perniagaan penangkopan ikan

air

masin yang luas. Jurutera-jurutera sivil mengkaji cara

air

^mernbawa bahan toksik dengan mengukur amaun bahan (dalam bahagian

periuta)

yang terdapat di dalam kerang

di tiga

lokasi yang

dipilih

secara rawak, daripada muara hingga lrcluar

kz

kmrtasan

teluk,

tempat kebanyaknn penangkapan ikan lromersial dilahtkan.

Jumlah

Jumlah

IIr' :

^B.3so

t-/ z-/ ij

(,

Nyatakan suatu model serta anggapannya.

(ii)

Lakukan suatu analisis yang sesuai

padau :

_0.01.

(ii,

Lakukan suatu analisis lanjutan.

p00

markahJ Lokasi

30 26 20 20 29 28

t9 I5

IO

I6 It

20

22 26 24 26

I5

153 91

¹³⁰

I7

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 a reading 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 six hours

or

more

per

day.

The following

data were collected

for

second year students in 32 ^states:

TV watch

l8 t2

20

n

9

t2

18 33

l9 t7

20 23

il

7 8

l4 l9 t9 t4

7 6 9

l3 l7 2l

6 10

l5

27

l6

L6 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 home and

l0

^{percent of students} who watch television for six hours or more per day.

[100 marks]

52 59 56 56 67 70

6l 3l

55 58

3l 5l

72 67 78 56 46 60 64 76 80 76 69

6l

50

8l

66 58

l8

64 56 74

78 73 77 68 85 86 83 76 73 80 64 69 84 84 88 78 76 83 84 88 88 88 84 79 78 90 86 70 76 82 80 86

...9/-

e

IMSG ¹⁶²¹ Untuk beberapa tahun,

para pendidik telah

menyaranlran bahawa suasana rumah paling banyak merryumbang kepada pencapaian pendidilmn para pelaiar.

Dalam

suatu kajian,

purata bagi

suatu

ujian

bacaan dibandingkan ^dengan peratusan

pelajar yang

mempunyai

tiga atau

lebih

ienis

^bahan

bacaan di

rumah (buku, encyclopedia, suratkhabar) ^dan peratusan pelaiar yang metnnton televisyen (TV) selama enam

jam

atau lebih sehari. Data berikut

dihmpul

bagi

pelajar

tahun dua di 32 buah negeri.

Slar Bacaan Menonton

W

52 59 56 56 67 70

6I 3I

55 58

3I

5T 72 67 78 56 46 60 64 76 80 76 69

6I

50

8I

66 58

r8

64 56 74

18

I2

20 IT 9 T2

t8

33 T9

I7

20 23

II

7

I

I4

19

I9 I4

6 9

I3

17 21

6 10

I5

27 16

t6

8 Rujuk lrcpada output oppendil<s untuk soalan 4.

(, Lahtkan suatu

analisis

yang

sesuai

untuk

mendapatkan model dan anggapanrrya. Guna

a :0.025.

(iil

Dapatlran suatu selang anggaran

dan

selang ramalan

bagi

sesebuah negeri dengan ⁷⁵ peratus pelajar yang tnempunyai tiga atau lebihienis bahan bacaan di rumah dan I0 peratus pelajar yang menonton televisyen untuk enam

jam

atau lebih sehari.

[100 ^markahJ 78

73 77 68 85 86 83 76 73 80 64 69 84 84 88 78 76 83 84 88 88 88 84 79 78 90 86 70 76 82 80 86

10

APPEI\DIX: OUTPUT

Ouestion ⁴

Predictor Coef

^SE

Coef t Constant 24.58 17.81 1.38

MateriaL 0.7263 0.L967 3.59

I]V -1.5351 0.2058 -7.43

S = 5.794L1 R-Sq = 84.72 R-Sq(adj) = 83.5t

Analysis of Variance

Source DF SS

^MS

Regression 2

⁵³⁷⁷

.4 2588.7

Error 29 973.5 33.5

Total 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

_N

ij ))

Y: Y-

SSA:t ? n.

_ll

t'

^N

For any contrast :

SSL

=

SSR

[t ".o.

(.? r r'

L = I

_tLJ

c.Y.

_{I l.}

i

r2

I

I

) c.

2

\a l'

+n.

_ll

Completely Randomized Block Design

: I I ?? v?. IJ Y2

_N

lJ

Y? Y2

: \r l'

? b

^N

I

Y2. Y2

:5

^'J

laN

J

Latin

Square Design

: Itl"i:u - i jk ' Y2

^o.

Y? Y2

: \a l"

+ a

_I ^N

Y2. Y2

:5

^.J.

?aN

J

Y-. 2Z

Y

sr

\_

'.^

T a

^N

Two-way Factorial Design

Y- t

lMsG

¹⁶²¹

df

= degtees offreedom

df

= ^degrees offreedom 12

ssr = III"'Uu

^1.l

i jk

ss"",,

: ss ++ rJ Y?,

ⁿ

rJ'

Y? Y2

SSA : t ? bn r"

^N

I

Y2. Y2

SSB : 5' ?anN ':'

J

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 SS

ltlxY

a

- l)

^Fo,u-r,ar

n-2

--7

l- r'

...13t-

13 IMSG ¹⁶²¹

7,

^Regression

b,==* ,SS

SS

, bo=Y-b,X

(I*,)Er)

sS*, I",", -

SS

_x-tn

: IX? -E\.L

(r v,f

SS = IY.2 - \!

^-i

y-tn

Var(b,) :

*

8. Kruskal-Wallis

Test

r: J=I{:(N+r1 N(N+l)

7 "i

9.

^Friedman Test

r : ,)?rrl*3 ba(a+l) ? :u(a+r)

10.

Cochran Test

a(a- r)2n! (a-

^r)N2

T:

I

aN I AJ s?

J

11.

Spearman Test

ur oi

: :1-

' n("'-t)

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

^4.71

3.82 3.99 +.10 4.r7 424 4.3O +.34 *.37 4.+l 4.59 +.69

^4.69

3.76 392 4,O3 4.12 4.r7 4.23 427 4.31 4.34 4.53 4.66

^+.66

3.77 3.86 3.98 4.06 4.11 4.tT 4.2r 4.25 4.29 4.48 46r+

^4.65

3.64 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.O

3 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.t

7 +.95 5.?2 5.37 5.45 5.53 5,67 5f9 5.73 5.8 6.0 .6.0

^6.0

8 +.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

^5.39

12 4.rZ 4.s5 4.68 +.76 +,84 +.92 4.96 '.5.02 s.O7 5,26 s26

^5.26

13 4.26 4.48 4.62 4.6,9 4"74 4.& +.A8 .4.94 4.98 5.15 5.r5

^5.1s

t4 +.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'

^4.89

18 +.O7 +.77 4.38 4.46 4.s3 4"59 4.64 4.68 4.77 4.85 4.85

^4,8s

t9 4.O5 +.24 4.35 4.43 4.50 4.56 4.57 4.64 +.67 4.82 4.82

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20 4.Q2 4.22 4.33 4.40 4,47 4.53 4.58 4.61 4.65 4.79 4.79

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30 40 60

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16 IMSG ¹⁶²¹ Spearman Table

.005

.00r .010 .050 .100

4 5 6 7

I

9

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

il

l2

l3

l4

l5 t6 t7 l8 l9

20

2l

22

2t

24 25 26 27 28 29 30

.4564 .4481

,&or

.4320 .4?'51

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