GUJARAT TECHNOLOGICAL UNIVERSITY
MBA – SEMESTER 01– • EXAMINATION –
SUMMER 2016
Subject Code: 2810007 Date:
21/05/2016
Subject Name: QUANTITATIVE ANALYSIS - I
(QA-I)
Time: 10.30 AM TO 1.30 PM Total
Marks: 70
Instructions:
1.
Attempt all questions.
2.
Make suitable assumptions wherever
necessary.
3.
Figures to the right indicate full
marks.
Q.1 (A) Answer the following questions with most
appropriate options: [06]
1.
The range of data set is 252 and the
largest value in the observation is given by 396. What is the smallest value in
the observation?
A.
244 B.
236
C.
136 D.
144
2.
Which method of sampling is
appropriate when the population consists of well-defined group such that the
groups are similar to each other and there is considerable variation within
groups?
A.
Systematic Sampling B. Simple Random Sampling
C.
Stratified Sampling D. Cluster Sampling
3.
Which of the following is the correct
representation of alternative hypothesis for right tailed test of mean using
sample? (m0 = hypothesized value of the population mean)
A.
H1: m = m0 B.
H1: m ≠ m0
C.
H1: m > m0 D.
H1: m < m0
4.
A chie square can never be negative
because,
A.
Differences between expected and
observed frequencies are squared
B.
Observed and expected frequencies are
always positive
C.
The absolute value of the difference is
computed
D.
None of these
5.
If the coefficient of correlation
between two variables between -1 and 0 then covariance between them is
A.
Positive B. Negative
C.
Zero
D.
Lesser in magnitude than the variance
of each of the variables.
6.
The statistical measures like mean,
median, mode and standard deviation which are used to describe the
characteristics of a sample known as,
A.
Parameters B. Constants
C.
Statistics D. Measures
(B)
Answer the following questions with required
calculations. [04]
1.
The probability distribution of
possible returns of an investment is given below:
|
Return (Ri)
|
5%
|
10%
|
20%
|
30%
|
|
Probability
|
0.20
|
0.30
|
0.40
|
0.10
|
What
is the expected return on investment?
2.
In the test of difference between two
proportions, two samples are under consideration. In the first, a sample size
of 250 shows 50 success, in the second sample size of 200 shows 60 successes.
What is the value of 
for this situation?
for this situation?
3.
For a simple linear regression
equation Σ(Y-Ŷ)2 = 195.40 and there are 20 pairs of observations,
what is the standard error of estimate ?
4.
If P(A) = P(B) = K and P(A Ç B)= P(A’Ç B’) = 1/10
Find
the value of K?
(C)
Write a note on Simple Random Sampling [04]
Q.2 (A)
What
is statistics? Describe the various applications of statistics in various field
of management? [07]
(B)
A study investigated the perception of
corporate ethical values among individuals specializing in marketing area. Use
5% level of significance and test significant difference among three groups for
following data: [07]
|
Marketing Managers
|
6
|
8
|
7
|
6
|
4
|
9
|
|
Marketing Research
|
5
|
6
|
4
|
3
|
4
|
5
|
|
Advertising
|
6
|
7
|
6
|
5
|
7
|
8
|
OR
Q.2 (B) 120 students are selected from the students
enrolled in MBA programs were cross classified by age group and grade point. [07]
|
Grade Point
|
Age
|
Total
|
||
|
19-21
|
21-23
|
23-25
|
||
|
Up to 7
|
12
|
28
|
10
|
50
|
|
7-8
|
10
|
50
|
15
|
75
|
|
Over 8
|
08
|
12
|
05
|
25
|
|
Total
|
30
|
90
|
30
|
150
|
1.
Calculate a table of observed and
expected frequency for the above information.
2.
State null and alternative hypothesis.
3.
Calculate chie square statistics.
4.
At 5% significant level, what is your
conclusion regarding age and grade point. Is there any association between age
and grade point?
Q.3 (A) Write a note on following : [07]
1.
Uniform Distribution
2.
Hyper Geometric Distribution
(B)
SUDA installed 20,000 LED lamps to reduce
the electricity consumption and provide better facilities to the citizens of
Surat in the western region. These lamps have an average life of 1800 burning
hours with standard deviations of 300 hours. Assuming Normality, what number of
LED lamps might be expected to fail? [07]
1.
In the first 1500 burning hours.
2. Between 1400 to 1700 hours.
3.
After what period of burning hours
would you expect that 2000 of the LED lamps would still be burning?
OR
Q.3 (A) What is non random sampling? Explain any two
methods of non random sampling. [07]
(B)
In India financial scenario is changed
after the stable government is elected. In the last two quarters, our growth is
positive, S&P has also improved the credit rating of our country. Even
though 40% of the financial experts believe that still we are in recession. A
sample of 10 independent financial experts are selected at random, find the
probability that: [07]
1.
Note more than 2 financial experts
think we are in recession.
2.
At least 5 financial experts think we
are in recessions.
3.
How many financial experts would you
expect to say we are in recession?
Q.4 (A) Write a note on Type I and Type II error. [07]
(B)
A leading cola company fills cola 2 liter
into bottles in an automatic bottling plant. A consumer advocate wants to test
the null hypothesis that the average amount filled by the machine into bottle
is at least 2 liter (2000 c.m.). A random sample of 40 bottles selected from
the plant and exact content of selected bottles are recorded. The sample mean
was 1999.6 c.m. The population standard deviation is known from past experience
to be 1.30 c.m. [07]
1.
Test null hypothesis at 5%
significance level.
2.
Assume that the population is normally
distributed with the same S=1.30 c.m. Assume that the sample size is only 20
and sample mean is same 1999.6 c.m. conduct the test once again with 5% level
of significance. If there is a difference in two results, explain the reason
for the difference.
3.
Derive confidence level and interpret
the values.
OR
Q.4 (A) What is composite hypothesis? Write detailed
note on one tailed test and two tailed test. [07]
(B)
Until few years ago, the market of
consumer credit was considerable to be segmented. With higher income group,
higher spending people tended to be HSBC platinum card holder and lower income
and lower spending people were usually ICICI gold card holders. In the last few
years, ICICI gold card has intensified its efforts to break into the higher
income segment of the market by using magazine and television advertisement to
create higher class image. A consulting firm was hired by ICICI to determine
whether average monthly charges on HSBC platinum card are equal to average
monthly charges by ICICI god card. A random sample of 1200 HSBC platinum card
holders were selected and sample monthly charges was found to be Rs.452 with
standard deviation of Rs.212. An independent sample of 800 gold ICICI card holders
revealed a sample mean of Rs. 523 with standard deviation of Rs 185. Is there
evidence to conclude that the average monthly charges in the entire population
of HSBC platinum card holders Is different from the average monthly charges of
ICICI gold card holders? Test the belief at 1% level of significance. [07]
Q.5 “Hindustan
transport corporation” a transport service provider company owned about 15,000
trucks. HTC Is known for safe and fast delivery of goods. The maintenance
manager observed that several thousand rupees were being spent on maintenance
of trucks of which majority expenditure was on tyre servicing. The tyres were
being reliable. Sometimes the tyres had to be changed much before their life as
claimed by the supplier, as the journey was long and the load to be born was
high. The bumpy, zigzag and mountainous roads increase the threat to the tyre.
However the maintenance manager felt that the quality of the tyres could be
better when the purchasing manager conveyed this matter to the supplier
company, “J.K.Traders Pvt Ltd” Ahmedabad. He bluntly turned it down. The
marketing managers of J.K.Traders told that they were supplying the tyres of
the best quality in the industry to HTC. The improvement in the quality can not
be thought in the near future. With this negative response from J.K.Traders,
HTC felt its supplier was becoming dominant and dictating the terms. Quality is
a very crucial parameter which HTC never compromised with so, the managing
director, Mr Karan directed Mr Yatharth to look out for alternative suppliers
“Road star pvt ltd” and “King tyre pvt ltd”. When the two suppliers of tyres
tested in simulated environment, the results were as follows:
|
Life of Tyres
(Thousand of KM)
|
Number of Tyres
|
|
|
Road Star Pvt. Ltd.
|
King Tyre Pvt Ltd
|
|
|
5-10
|
2
|
4
|
|
10-15
|
3
|
7
|
|
15-20
|
10
|
11
|
|
20-25
|
15
|
25
|
|
25-30
|
17
|
10
|
|
30-35
|
9
|
2
|
|
35-40
|
4
|
1
|
Find
the following:
1.
Construct histogram and frequency
curve for both tyre suppliers, compare the symmetricness.
2.
Compute and compare mean, median and
mode life of the tyres supplied by the two suppliers and interpret the values.
3.
Derive the standard deviation and
variance of life of tyres supplied by the two suppliers.
4.
Which supplier would you choose if you
were the GM of HTC? Why? Justify your decision with appropriate quantitative
tools.
OR
Q.5 According
to the Capital Asset Pricing Model (CAPM), the risk associated with a capital
asset is proportional to the slope β1 (or simply β : Regression coefficient Y
on X) obtained by regressing the assets past returns with the corresponding
return of the average portfolio called the market portfolio. (The return of the
market portfolio represents the return earned by the average investor. It is a
weighted average of the returns from all the assets in the market. The larger
the sloop of β on of an asset, the larger is the risk associated with that
asset. A β of 1.00 represents average risk. The return from IT firm’s stock and
the corresponding returns for the market portfolio for the past 10 years are
given below:
|
Market Return (X)
|
16
|
12
|
11
|
17
|
14
|
13
|
18
|
15
|
08
|
10
|
|
Stock’s return (Y)
|
21
|
17
|
14
|
22
|
16
|
15
|
24
|
18
|
05
|
08
|
Answer
the following questions:
1.
What are the independent and dependent
variables?
2.
Construct scattered diagrams based on
the relationship of market return and IT stock return and interpret the
diagrams.
3.
Carry out the regression and find the
β for the stock. What is the regression equation?
4.
Does the value of the slope indicate
that the stock has above average risk? (in the range of 1± 0.1, interpret the
risk.)
5.
If the market portfolio return for the
current year is 25%, what is the stocks return?
6. Calculate the coefficient of the
determination and state its interpretation.
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