UNIVERSITI SAINS MALAYSIA

Second Semester Examination

2012/2013 Academic Session
June 2013

MSG 162 Applied Statistical Methods

[Kaedah Statistik Gunaan]
Duration : 3 hours
[Masa : 3 jam]

Please check that this examination paper consists of SEVENTEEN pages of printed material
before you begin the examination.
[Sila pastikan bahawa kertas peperiksaan ini mengandungi TUJUH BELAS muka surat yang
bercetak sebelum anda memulakan peperiksaan ini.]

Instructions

Answer all four [4] questions.

[Arahan

Jawab semua empat [4] soalan.]

In the event of any discrepancies, the English version shall be used.

[Sekiranya terdapat sebarang percanggahan pada soalan peperiksaan, versi Bahasa Inggeris
hendaklah diguna pakai].

2/-

-2-

[MSG 162]

1. (a) Fabric regulations require that certain materials, such as those used for childrens pajamas, be
treated with a flame retardant. An evaluation of a flame retardant applied to a random sample of
three different materials was conducted at a laboratory. Six samples were tested from each of
the treated materials. The data collected was length of the charred portion of each sample.
Sample
Material
A
B
C
D

1
4.1
3.1
3.5
2.8

2
3.9
2.8
3.2
2.9

3
4.3
3.3
3.6
3.1

4
2.7
1.9
2.7
2.4

5
3.1
2.2
2.3
3.2

6
2.6
2.3
2.5
2.5

Total
20.7
15.6
17.8
16.9

Total

13.5

12.8

14.3

9.7

10.8

9.9

71.0

Y
i =1 j=1

= 218.64

ij

(i) State a model and its assumptions.

(ii) Perform an appropriate analysis at
(iii) Perform a follow-up analysis.
(b)

= 0.10.

A soft drink distributor wished to determine the advertising medium that will produce the
largest increase in sales per advertising ringgit. Three advertising agencies prepare copies or
films for each of the media: newspaper, radio and television. Small towns of roughly the same
size are selected for the experiment and two each are assigned to receive an advertisement
prepared by each agency and transmitted by each medium. The ringgit increased in sales per
advertising ringgit, based on a one-month sales period, is recorded.
Agency
A

Newspaper
10.6, 9.8
20.4

9.6, 10.7

Radio
11.2, 10.3
21.5

Television
9.5, 9.9
19.4

Total
61.3

10.5, 10.9

8.9, 9.4

60.0

20.3
C

9.9, 10.3

21.4
11.0, 10.4

20.2
Total

60.9

Y
i =1 j=1 k =1

2
i jk

18.3
9.3, 9.6

21.4
64.3

60.5
18.9

56.6

181.8

= 1,843.38

(i) State a model and its assumptions.

(ii) Determine the effects that influence the response. Test at = 0.01.
(iii) Perform an appropriate follow-up analysis using Duncan multiple range test.
[25 marks]

3/-

-3-

[MSG 162]

2. (a) The use of insecticides is a benefit but also a source of concern to the fruit industry. Insecticides
protect the fruit from insect damage but they are also toxic compounds that can be ingested by
human beings. There are government set tolerances on the amount of insecticides that fresh fruit
and fruit pulp can contain and fruit is carefully washed to meet those tolerances.
Insecticides are applied topically by spraying the fruit trees, so if the skin of the fruit has not
been broken, all of the insecticide lies on the surface. To determine the amount of insecticides
on peaches, a horticulturist sprayed an orchard according to the stated regulations and after the
fruits were harvested, ten peaches were randomly selected and their diameters (in centimeters)
were measured. He then washed each peach with a constant volume of detergent solution and
made a chemical determination of the amount of insecticides (in parts per million) in the
solution after cleaning.
Peach

10

Diameter

6.0

7.0

6.6

5.8

6.8

8.4

7.2

5.4

5.6

6.2

Amount of
insecticides

0.5

6.4

1.0

0.2

5.5

19.2

8.2

0.1

0.3

0.6

(i) State the interest of this study.

(ii) State a model and its assumptions.
(iii) Perform an appropriate analysis at 0.01 significance level.
(b)

A supermarket chain conducted an experiment to investigate customer response to the use of

different types of background music.
A:
B:
C:
D:

Soft volume, slow tempo, vocal

Medium volume, slow tempo
Medium volume, medium tempo
Soft volume, slow tempo

Each type of background music was played at five stores for a week. 100 customers were
randomly selected and questioned to determine whether they liked the music. The percentages
that liked the music and favored its continued use are shown in the table.
Store
1
2
3
4
5
Total

Y
i =1 j=1

(i)
(ii)
(iii)
(iv)

2
ij

A
77
73
74
76
87

Type of Music
B
C
84
81
89
76
82
73
90
79
78
84

D
94
97
90
86
91

Total
336
335
319
331
340

387

423

458

1,661

393

= 138,949

State a model and its assumptions.

Perform an appropriate analysis at = 0.01.
Perform a follow-up analysis using Tukey HSD test.
Determine the following effects on the response:
a. volume effect
b. vocal effect
[30 marks]
4/-

-4-

[MSG 162]

3. A study was conducted to investigate whether the growth of roses are affected by the temperature in
a greenhouse and the amount of fertilizer applied to the soil. A total of twenty-seven plots of equal
sizes are treated with fertilizer in amounts varying between 50 and 60 kilograms per plot and these
plots are mechanically kept at constant temperatures between 80 oF and 100oF. Small rose plants
(approximately 15 centimeters in height) are planted in each plot and their heights are measured
after a six-week growing period.
Amount
Temperature of fertilizer
80
80
80
80
80
80
80
80
80
90
90
90
90
90

Height
of carnation

50
50
50
55
55
55
60
60
60
50
50
50
55
55

50.8
50.7
49.4
93.7
90.9
90.9
74.5
73.0
71.2
63.4
61.6
63.4
93.8
92.1

Temperature

Amount
of fertilizer

Height
of carnation

90
90
90
90
100
100
100
100
100
100
100
100
100

55
60
60
60
50
50
50
55
55
55
60
60
60

97.4
70.9
68.8
71.3
38.7
42.5
41.4
69.8
72.5
73.2
51.6
54.1
51.4

Refer to the output in the Appendix.

(i) State the model and its assumptions.
(ii) Perform an appropriate analysis to obtain the estimated model. Use = 0.10
(iii) Obtain an estimation interval and prediction interval of the height of the roses with
temperature of 85o F and amount of fertilizer of 58 kilograms per plot.
[20 marks]

5/-

-5-

[MSG 162]

4. (a) A study was conducted to evaluate the effect of nutrition on the attention spans of year one
elementary school students. The students from different classes were randomly assigned to each
of three meal plans: no breakfast, light breakfast and full breakfast. Their attention spans (in
minutes) were recorded during a morning reading period.
Class

No breakfast

Light breakfast

Full breakfast

Total

1
2
3
4
5

8
7
9
13
10

14
16
12
17
11

10
12
16
15
12

32
25
37
45
33

Total

47

70

65

182

Y
i =1 j=1

2
ij

= 2,338

(i) State a model and its assumptions.

(ii) Perform an appropriate analysis at
(iii) Perform a follow-up analysis.
(b)

= 0.10.

Several researchers have conjectured that stem-pitting disease in citrus tree seedlings might be
related to the presence or absence of nematodes in the soil. Hence, weed and soil treatment
using herbicides might be effective in promoting seedling growth. Researchers conducted an
experiment to compare citrus tree seedling growth with soil and weeds treated with one of three
herbicides:
A: control (no herbicide)
B: herbicide without Nemagone
C: herbicide with Nemagone
The researchers randomly assigned five seedlings to each treatment. They treated soil and
weeds in the growing areas of the seedlings with the appropriate herbicide. At the end of the
study period they recorded the height (in centimeters) for each seedling.
Seedling
Herbicide
A
B
C

1
51
91
88

2
67
93
88

3
74
88
61

4
75
69
82

5
75
90
79

Total
342
431
398

Total

230

248

223

226

244

1,171

Y
i =1 j=1

2
ij

= 93,525

(i) State a model and its assumptions.

(ii) Perform an appropriate analysis at
(iii) Perform a follow-up analysis.

= 0.05.
[25 marks]
6/-

-61.(a)

[MSG 162]

Peraturan memerlukan bahawa kain yang digunakan untuk pakaian tidur kanak-kanak, dirawat
dengan suatu bahan memerlahankan pembakaran. Suatu penilaian terhadap suatu sampel
rawak tiga kain berlainan yang telah dirawat dilakukan di suatu makmal. Enam sampel diuji
daripada setiap kain yang dirawat. Data yang dikumpul adalah panjang bahagian yang
terbakar bagi setiap sampel.
Sampel
Kain
A
B
C
D

1
4.1
3.1
3.5
2.8

2
3.9
2.8
3.2
2.9

3
4.3
3.3
3.6
3.1

4
2.7
1.9
2.7
2.4

5
3.1
2.2
2.3
3.2

6
2.6
2.3
2.5
2.5

Jumlah
20.7
15.6
17.8
16.9

Jumlah

13.5

12.8

14.3

9.7

10.8

9.9

71.0

Y
i =1 j=1

2
ij

= 218.64

(i) Nyatakan suatu model serta anggapannya.

(ii) Lakukan suatu analisis yang sesuai pada = 0.10.
(iii) Lakukan suatu analisis lanjutan.
(b)

Suatu pengedar minuman ringan ingin menentukan medium pengiklanan yang dapat
menghasilkan peningkatan terbesar dalam jualan per ringgit iklan. Tiga agensi pengiklanan
menyediakan salinan dan filem bagi setiap media: suratkhabar, radio dan television. Beberapa
bandar kecil bersaiz agak sama dipilih untuk ujikaji dengan setiap dua diumpukkan untuk
menerima suatu iklan yang disediakan setiap agensi dan disebarkan oleh setiap medium.
Peningkatan ringgit dalam jualan per ringgit iklan, berdasarkan tempoh jualan sebulan
dicatat.
Agensi
A

Suratkhabar
10.6, 9.8
20.4

9.6, 10.7

Radio
11.2, 10.3
21.5

Television
9.5, 9.9
19.4

10.5, 10.9

8.9, 9.4

20.3
C

9.9, 10.3

21.4
11.0, 10.4

20.2
Total

60.9

Y
i =1 j=1 k =1

2
i jk

60.0
18.3

9.3, 9.6
21.4

64.3

Jumlah
61.3

60.5
18.9

56.6

181.8

= 1,843.38

(i) Nyatakan suatu model serta anggapannya.

(ii) Tentukan kesan yang mempengaruhi respon. Uji pada = 0.01.
(iii) Lakukan suatu analisis lanjutan yang sesuai menggunakan ujian julat berganda Duncan.
[25 markah]
7/-

-72.(a)

[MSG 162]

Penggunaan racun serangga merupakan suatu manfaat tetapi juga suatu sumber kebimbangan
kepada industri buah-buahan. Racun serangga melindungi buah daripada kerosakan serangga,
tetapi ia juga adalah bahan toksik yang boleh dimakan manusia. Terdapat tahap toleran
kerajaan keatas amaun racun perosak yang buah-buahan segar dan pulpa buah-buahan boleh
kandungi dan buah-buahan dibasuh secara berhati-hati untuk memenuhi toleran tersebut.
Racun serangga disembur ke pokok buah-buahan dan jika kulit buah tidak pecah, kesemua
racun serangga berada di atas permukaan. Untuk menentukan amaun racun serangga atas
buah pic, seorang pakar hortikultur menyembur suatu dusun mengikut peraturan yang
dinyatakan dan setelah buah dipetik, sepuluh buah pic dipilih secara rawak dan diameter
(dalam sentimeter) diukur. Dia membasuh setiap buah pic dengan suatu isipadu tetap bahan
pencuci dan membuat suatu penentuan bagi amaun racun serangga (dalam bahagian per juta)
dalam bahan tersebut selepas dicuci.
Buah pic

10

Diameter

6.0

7.0

6.6

5.8

6.8

8.4

7.2

5.4

5.6

6.2

Amaun racun
serangga

0.5

6.4

1.0

0.2

5.5

19.2

8.2

0.1

0.3

0.6

(i) Nyatakan aspek yang diminati dalam kajian ini.

(ii) Nyatakan suatu model serta anggapannya.
(iii) Lakukan suatu analisis yang sesuai pada aras signifikan 0.01.
(b)

Suatu rantaian pasaraya melakukan suatu ujikaji untuk menyelidik respon pelanggan terhadap
penggunaan jenis muzik latarbelakang berlainan.
A:
B:
C:
D:

Bunyi lembut, tempo perlahan, bersuara

Bunyi sederhana, tempo perlahan
Bunyi sederhana, tempo sederhana
Bunyi lembut, tempo perlahan

Setiap jenis muzik latarbelakang dimainkan di lima buah kedai untuk seminggu. 100 pelanggan
dipilih secara rawak dan ditanya sama ada mereka menyukai muzik tersebut. Peratusan yang
menyukai muzik tersebut dan memilih penggunaannya diteruskan ditunjukkan dalam jadual.
Jenis muzik
Kedai
1
2
3
4
5
Jumlah

Y
i =1 j=1

(i)
(ii)
(iii)
(iv)

2
ij

A
77
73
74
76
87

B
84
89
82
90
78

C
81
76
73
79
84

D
94
97
90
86
91

Jumlah
336
335
319
331
340

387

423

393

458

1,661

= 138,949

Nyatakan suatu model serta anggapannya.

Lakukan suatu analisis yang sesuai pada = 0.01.
Lakukan suatu analisis lanjutan menggunakan ujian Tukey HSD.
Tentukan kesan berikut keatas respon:
a. kesan bunyi
b. kesan suara
[30 markah]
8/-

-8-

[MSG 162]

3. Suatu kajian dilakukan untuk mengkaji sama ada pertumbuhan bunga ros dipengaruhi oleh suhu
dalam rumah hijau dan amaun baja digunakan dalam tanah. Sejumlah dua puluh tujuh plot yang
bersaiz sama dirawat dengan baja dalam amaun berbeza di antara 50 dan 60 kilogram per plot
dan plot tersebut ditetapkan secara mekanikal pada suhu malar di antara 80 oF dan 100oF. Pokok
ros kecil (anggaran 15 sentimeter tinggi) ditanam dalam setiap plot dan ketinggiannya diukur
selepas suatu tempoh enam minggu.

Suhu

Amaun
baja

Ketinggian
pokok ros

80
80
80
80
80
80
80
80
80
90
90
90
90
90

50
50
50
55
55
55
60
60
60
50
50
50
55
55

50.8
50.7
49.4
93.7
90.9
90.9
74.5
73.0
71.2
63.4
61.6
63.4
93.8
92.1

Suhu

Amaun
baja

Ketinggian
pokok ros

90
90
90
90
100
100
100
100
100
100
100
100
100

55
60
60
60
50
50
50
55
55
55
60
60
60

97.4
70.9
68.8
71.3
38.7
42.5
41.4
69.8
72.5
73.2
51.6
54.1
51.4

Rujuk output dalam Apendiks.

(i) Nyatakan model serta anggapannya.
(ii) Lakukan suatu analisis untuk mendapatkanm model anggaran. Guna = 0.10
(iii) Dapatkan suatu selang ramalan bagi ketinggian pokok ros dengan suhu 85o F dan amaun
baja 58 kilograms per plot.
[20 markah]

9/-

-94.(a)

Suatu kajian dilakukan untuk menilai keberkesanan pemakanan atas tahap tumpuan pelajar
tahun satu sekolah rendah. Pelajar-pelajar daripada kelas berlainan diumpukkan secara rawak
kepada setiap tiga pelan makanan: tanpa sarapan, sarapan ringan dan sarapan penuh.
Tumpuan pelajar (dalam minit) dicatat semasa waktu bacaan pagi.
Kelas

Tanpa sarapan

Sarapan ringan

Sarapan penuh

Jumlah

1
2
3
4
5

8
7
9
13
10

14
16
12
17
11

10
12
16
15
12

32
25
37
45
33

Jumlah

47

70

65

182

Y
i =1 j=1

(i)
(ii)
(iii)
(b)

[MSG 162]

2
ij

= 2,338

Nyatakan suatu model serta anggapannya.

Lakukan suatu analisis yang sesuai pada = 0.10.
Lakukan suatu analisis lanjutan.

Beberapa penyelidik mengesyaki bahawa penyakit bopeng batang anak pokok limau mungkin
berhubungan dengan kehadiran atau ketakhadiran nematod dalam tanah. Oleh itu rawatan
rumpai dan tanah menggunakan herbisid mungkin berkesan dalam pertumbuhan anak pokok.
Penyelidik melakukan suatu perbandingan pertumbuhan anak pokok limau dengan tanah dan
rumpai dirawat dengan satu daripada tiga herbisid:
A: kawalan (tanpa herbisid)
B: herbisid tanpa Nemagone
C: herbisid dengan Nemagone
Penyelidik mengumpukkan lima anak pokok kepada setiap rawatan. Mereka merawat tanah dan
rumpai dalam kawasan pertumbuhan anak pokok dengan herbisid yang sesuai. Pada akhir
tempoh kajian mereka mencatat tinggi (dalam sentimeter) setiap anak pokok.
Herbisid
A
B
C

1
51
91
88

Anak pokok
2
3
67
74
93
88
88
61

Jumlah

230

248

Y
i =1 j=1

2
ij

223

4
75
69
82

5
75
90
79

Jumlah
342
431
398

226

244

1,171

= 93,525

(i) Nyatakan suatu model serta anggapannya.

(ii) Lakukan suatu analisis yang sesuai pada = 0.05.
(iii) Lakukan suatu analisis lanjutan.
[25 markah]
10/-

-10-

[MSG 162]

APPENDIX: OUTPUT
Question 3

Predictor
Constant
Temperature
Amount of Fertilizer

Coefficient
66.14
-0.8328
1.3878

Standard error
52.28
0.3672
0.7344

Analysis of Variance
Source of Variation
Regression
Error
Total

X'X

df
2
24
26

SS
1789.9
6671.5
8461.4

11.259

-0.05

0.122

-0.05

0.000556

0.000

-0.122

0.000

0.0022

11/-

-11-

[MSG 162]

APPENDIX: FORMULAS
1.

Completely Randomized Design

SST =

Y
i

j
2
i.
n
i

2
ij

Y
SSA =
i

2
..
N

2
..
N

Y
-

For any contrast :

L =
i

c Y
i i.

2
c Y
i i.

SSL =

2
i.
n
i

c
i

2.

Completely Randomized Block Design

SST =

Y
i

j
Y

SSA =
i

Y
SSB =

2
i.
b

2
.j
a

2
ij

2
..
N

2
..
N

Y
-

2
..
N

Y
-

12/-

-123.

Latin Square Design

SST =

Y
i

2
i ..
a

SSR =
i

Y
SSC =

SSA =
k

2
.. k
a

2
ijk
Y

2
. j.
a

4.

[MSG 162]

2
...
N

2
...
N

Y
-

2
...
N

Y
-

2
...
N

Two-way Factorial Design

SST =

Y
i

2
i ..
bn

SSA =
i

2
. j.
an

Y
-

Y
SSB =

SSE =

2
...
N

2
...
N

Y
i

2
i jk

2
...
N

2
i jk

Y
-

2
i j.
n

13/-

-135.

Multiple Comparison Procedures:

Duncan: r

, p , df

1
q , a , df
2

Tukey:
Scheffe:

6.

[MSG 162]

a 1 F

, a -1 , df

p = range

df = degrees of freedom

a = number of treatments

a = number of treatments

df = degrees of freedom
df = degrees of freedom

Regression

SS
b1 =

XY

SS

bo = Y - b X

SS

SSE = SS -

2
XY

SS

X
X Y -

SS

XY

i i

i
2

2
i

X
-

n
2

SS

2
i

X
-

n
2

SS

Var( b 1 ) =
SS

) = 2
Var( Y
h

1
+
n

X - X
h

SS

) = MSE X' (X' X)-1 X

Var( Y
h
h

14/-

-147.

Correlation

SS
r =

SS

t = r

XY

XX

SS

YY

n 2
1 r

8.

Kruskal-Wallis Test
R

12
T =
N N+1

9.

2
i

- 3 N+1

Friedman Test
T =

10.

12
ba a+1

R
i

2
i

- 3b a+1

Cochran Test

a a -1

A
i

T =

2
i

aN -

a -1 N
B

j
11.

[MSG 162]

2
j

Spearman Test
n

6
r =
s

1 -

R X
i=1

- R Y

n n -1

1 -

d
i

2
i

n n -1

15/-

-15-

[MSG 162]

APPENDIX: TABLES
Duncan Multiple Range Table

16/-

-16-

[MSG 162]

Spearman Table

17/-

Tukey HSD Table

-17-

- ooo O ooo -

[MSG 162]

-18-

[MSG 162]