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C O N F I D E N T I A L
S I S E P
2014 /QMTI8 I /212 /216 /STAIO4
i\
U N I V E R S 1 T 1 T E K N O L O G I M A R A
F IN A L E X A M I N A T I O N
C O U R S E
C O U R S E C O D E
E X A M I N A T I O N
TIME
: IN T R O D U C T I O N T O S T A T I S T IC S / B U S IN E S S
S TAT I S T I CS
: Q M T I 8 I /2 1 2 / 2 1 6 /S T A I 0 4
: S E P T E M B E R 2 0 1 4
: 3HOURS
IN S T R U C T IO N S T O C A N D I D A T E S
1 .
Th is quest ion paper cons is ts o f five 5 ) quest ions.
2 .
AnsW er ALL quest ions in the Answ er Book le t. Sta r t each answ er on a new page.
3.
Do n o t b r in g a n y m a te r ia l i n to t h e e x a m i n a t io n r o o m u n i e ss p e r m i ss i o n i s g i ve n b y t h e
i n v i g i l a t o r .
4 .
Cand ida tes a re a l lowed to use ca lcu la to r .
5 .
Please ch eck to make sure tha t th is examina t ion pac k cons is ts o f :
i)
the Quest ion Paper
ii )
a th ree - page Ap pend ix 1 Fo rmu la L i s t)
i i i )
an A nsw er Book le t - p rov ided by the Facu l ty
iv )
graph p aper - prov ided by the Facu l ty
D O N O T T U R N T H I S PA G E U N T I L Y O U A R E T O L D T O D O 5 0
his exam inat ion paper cons is ts o f pr in ted pages
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O N F I D E N T I A L
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C O N F I D E N T I A L
S / S E P 2 0 1 4 I Q M TI 8 1 /2 1 2 / 2 1 6 / S TA I 0 4
Q U E S T I O N 1
a)
efine the following terms:
i sampling frame
questionnaire
iii)
inferential statistics
iv ) s a m ple su rv ey
v) prim a ry da ta
5 marks)
b)
or each of the foliowing variables, classify whether it is qualitative, quantitative
discrete or quantitative continuous variable.
i)
N umber of ri fles produced in F ebruary 20 1 4 .
ii)
Types of car manufactured by Company zz
iii)
Range of size of childrens shoe
iv )
L evel of patients satisfaction toWa rds on facil it ies provided at Hospital A A .
v) Volume of soft drink served per bottle.
5 marks)
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O N F I D E N T I A L
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C O N F I D E N T I A L
S/ SE P 2 0 1 4 / Q M TI 8 1 / 2 1 2 / 2 1 6 / STA I 0 4
c) A group of researcher wanted to investigate the perception of the married couple
towards on the factors that contributed to problems in marriage in a particular state.
The questionnaires were distributed to 500 randomly selected couples from five
districts in the state. Among the variables selected in the survey were age, gender,
occupation, number of years of marriage, number of children, the total household
income and the perception on the factors contributed to the marriage problems on a
Likert scale where 1 indicates strongly agree and 5 indicates strongly disagree. The
distribution on the num ber of m arried couples is shown in the following table.
District
umber of Married Couples
A
2 0
B
70
c
8 0
D
0 0
E
30
i) State the population and sample of the above study.
2 marks)
ii) State TWO 2) variables in the above study. Hence, identify the corresponding
scales of measurements.
3 marks)
iii) Calculate the number of married couples to be selected from each district if
stratified random sam pling is used.
5 m arks)
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O N F I D E N T I A L
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C O N F I D E N T I A L
S ISEP
2 0 1 4 / Q M TI 8 1 /2 1 2 / 2 1 6 / STA I 0 4
Q U E S T IO N 2
a)
he following data represents the total annuai income (RIVI 000) of 20 lecturers at
one of the colleges in N egeri S embilan.
36
0
0
6
2
2
8
0
7
8
59
2
3
1
1
3
0
5
5
4
i) Construct the stem and Ieaf plot for the above data.
3 marks)
ii) Based on part i), give your comment on the shape of distribution.
2 marks)
b) A group of physiotherapist intends to determine the appropriate number of hours
spend per week by their ACL (Anterior Cruciate Ligament) patients to maximize the
process of recovery their muscle flexibility. The table below depicts the distribution of
hours spend per week for A C L treatment of 50 patients at Hospital M M .
Hours Per Week
umber of Patients
O to less than 5
5tolessthan10
0
_10 to less than 15
5
15tolessthan20
3
2 0 to less than 2 5
i) Calculate the mean and standard deviation.
4 marks)
11) Construct a histogram for the above data. Using the histogram, estimate the
modal of hours spend per week for AC L treatment of the patients.
4 marks)
iii) Using the value in part i) and 11), compute the coefficient of skewness. Hence,
give your comment on the shape of distribution.
4 marks)
iv) lt is known that the mean and standard deviation for hours spend per week for
ACL treatment of the patients of Hospital ZZ is 15.3 and 7.95 hours respectively.
Using an appropriate measurement determine which hospital is more consistent
in hours spend per week for A C L treatment of the patients.
3 marks)
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C O N FI D E N T I A L
SISEP 2014 /QM TI8 I /212 /216/STAIO4
Q U E S T I O N 3
a)
psychologist wants to investigate the association between the levei of happiness of
the kindergarten students (rating: not happy - 3, neutral - 2, happy - 1) and the
number of hours spend playing per day. Th e data recorded as follows:
Student
Emotional
2
Rating
N umber of
6
0
hours
Calculate the Spearmans Rank Correlation coefficient. Give your comment on the
value obtained.
6 marks)
b)
A group of hematologist Wants to determine the relationship between the number of
blood packets ( 00 unit) at the blood bank in General Hospital and the number of
blood donors in M alaysia. The data recorded as follows:
Month
2
N umber of
blood
0
2
packets
N umber of
blood
50 510 290 315 400 410 170 325 430 360 580 380
donors
i)
S tate the independent and dependent variable.
2 marks)
ii) Compute the Pearsons product moment correlation coefficient whether there is a
linear relationship between the number of blood packets ( 00 unit) at the blood
bank at General Hospital and the number of blood donors. lnterpret on the value
obtained.
5 marks)
iii)
Given the regression equation is Y 0.012
0 02X
Using an apropriate
formula, show that the value of the slope is 0.02. Hence, explain the meaning of
the value.
5 marks)
iv)
P redict the number of blood packets if the number of biood donor is 34 5 .
2 marks)
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O N FI D E N T I A L
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C ON F I D EN T I AL
S ISEP
20141QMT181 /212 /216 /STAI04
Q U E S T IO N 4
a)
etermine the app ropriate componen ts of time series for the situation beiow.
i)
The increase on demand of the fresh chickens during Hari Raya Aidilfitri.
ii)
T he nomination of the top committee C hess S ociety for every 3 years.
iii)
The decrease in the compilation rate of cancer patients during treatment due to
improvement in stem ceIl transplants procedure.
3 ma rks)
b)
he following table indicated the trend value for air-conditioner sales ( 00 unit) from
2011 2013 for Maz Company. All calculation should in three decimal places.
¥ear
uarter
ales
rend Value
2 0 1 1
5
2
8
3
0
7.625
4
6
8 . 50 0
2 0 1 2
8
9.625
2
2
0 .875
3
5
2 .500
4
1
5.000
2 0 1 3
6
9.125
2
4
4.125
3
6
4
0
i) Calculate seasonal indices for each quarter.
8 marks)
1
lnterpret the seasonal index obtained for
s t
and
2nd
quarter.
2 marks)
iii) Predict the sales for
2nd
quarter 201 4.
4 marks)
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ON F I D EN T I AL
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C O N F I D E N T I A L
S ISEP
2 O1 4 / Q M T1 8 1 / 2 1 2 / 2 1 6 IS TA I 0 4
c)
he seasonal indices of quarterly sales at One-Ten Hypermarket are shown in the
following table:
Q uarter
easonal lndex
50
7
lf the expenses for the second quarter are 5 below the trend, find the value of x
and y.
3 m arks)
Q U E S T I O N 5
a)
he table below presents the prices, quantities and relative price index for three
types of table fan purchased by the custom ers at S eng Huap S tore. T he relative price
index for the year 2 0 1 3 using 20 1 2 as the base year;
Prices RIV I per unit)
uantities
ype of elative price
Tablefan
0 1 2
0 1 3
0 1 2
0 1 3
ndex
Alpha 50
8 5 5 2
K D K
70
8
0
1 7
Rubine
3 0
6 5
3
1 1
i) Find the values of x, y and z.
4 marks)
ii) Compute the Paasche Price lndex for the year 2013. Explain the value obtained.
4 marks)
b)
ow many different arrangements of the letters in the word PROBABILITY can be
formed if:
i)
there is no restriction,
2 marks)
ii)
the arrangement begins with the letter B.
2 marks)
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O N F I D E N T I A L
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C O N F I D E N T I A L
S/ SEP 2 0 1 4 / Q M T I 8 1 / 2 1 2 /2 1 6 / ST AI 0 4
c Syamimi intends to buy either a double storey terrace house or cluster house. The
probability that she wilI buy a double storey terrace house is 0 86 From the previous
experience of her friends, she found that if she preferred to buy a double storey
terrace house the probability that the area had the LRT is 0.45 while if she preferred
to buy cluster house the probability that the area had the LRT is 0.58.
i Construct a tree diagram for the above situation.
3 marks)
ii Find the probability that she preferred the area had LRT.
2 marks)
iii Compute the probability that she preferred the area had LRT given that she
selected a double storey terrace house.
3 marks)
E N D O F Q UE S T I O N P A P E R
Hak C ipta Universiti Tekn ologi M A RA
O N F I D E N T I A L
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C O N F I D E N T I A L
P P E N D I X 1 ( 1 )
S/SEP 2014/QMTI8 I /212 /216 /STAIO4
Sam p le Measurem en ts
:x
x
1 .
M e a n ,
=- or
n
-i
2 .
M edian , x == L
m +
0
m
A l
- L
m o
l
-
2J
ample size
ower class boundary of median class
ower class b ounary class boundary of modal class
umulative frequencies for the classes before the median class
edian class frequency
modal class freque ncy) - ( frequency for the class before the
modal class)
modal class frequency ) - ( frequenc y for the class after the
modal class)
lass size
3. M ode,
where:
Lm
Lmo
I
f
m— i
m
A1
A2
c
(1
4 .
Standard D eviat ion, s = .
x -
2
or
2
)2
-
— 1
— 1 -
n
1
s =
x - )
2
or
fx
n —
2
x
2 ]
j;
5.
C oeffic ien tofVar ia t ion, C V = - -x10 0
6 .
Pearsons Measure of Skewness =
e a n _ - M o d e
r 3( M e a n - M e d ia n )
tan dard D eviation
t a n d a r d D e v i a t io n
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C O N F I D E N T I A L
P P E N D I X 1 2 )
S/SEP 2014/QMTI8 I / 212 /216 /STAIO4
C orre lat ion and Reqression
1 Pearsons P roduct Mom ent Corre la tion Coef f ic ient
r -
LXY ) - X )
Y )
[n 2) X)2][n y2) — Y)21
2 .
Spearm ans Rank C orrelat ion:
rs=
1
3.
Th e least- squares regression l ine of Y against X,
Ya + bX
nXY XY
n d
=Y bX
n X 2
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C O N F I D E N T I A L
P P E N D I X 1 3 )
S / S E P
2 1 4 1 Q M T 1 8 1 1 2 1 2 1 2 1 6 1 S T A 1 4
l ndex Num bers
1 . LaspeyresPr ice lndex=
tqo
x l O O
q
;
2.
Paasche Price lndex
=
1 00
p q
5.
Simple Ag gregate Pr ice lndex =
1
p o
6.
W eighted Aggregate Pr ice lndex =
tw
x1
pow
where:
p
o = price of the base year
p t =
price of the current year
q
=
quantity of the base year
q
= quanti ty of the current year
w = weight
Probabi l ity Th eory,
1
onditional Prob ability
P A
I
B) - P A - B)
P B)
ultiplicative Ru le
a)
P A - B) = P B)P A IB)
b)
P A -
B ) - P B ) . P A ) ;
l f and only if A and B are independen t events
3
ayess Theorem
P A
I B )
A).P B A)
P A)P B
I
A)+ P A).P B
I
A)
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