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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MBA SEMESTER 1 EXAMINATION WINTER 2018
Subject Code: 2810007 Date: 01/01/2019
Subject Name: Quantitative Analysis I
Time: 10.30 am to 01.30 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
1.
2.
3.
4.
5.
6.
Choose the correct option.
Which of the following is a locational measure
Mean Median
Mode Geometric Mean
According to empirical rule 95% observations falls within
± 1σ limits ± 2σ limits
± 3σ limits ± 4σ limits
For independent events X Y which one is true
and

P(X U
None of the above
The mean of a distribution is 14 and standard deviation is 5. What is the value of
Coefficient of Variation?
60.4% 48.3%
35.7% 27.8%
The mean of a distribution is 23, the Median is 24 and the mode is 25.5. It is most
likely that this distribution is
Positively Skewed
Symmetrical
Asymptotic
Negatively skewed
A parameter is a measure which is computed from
Population data
Sample data
Test statistics
None of the above.
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Q.1 Answer in short.
Define Mode.
List four types of measurement scales.
Type I error in hypothesis testing
Discrete and continuous data.
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Q.1 Describe in brief assumptions of simple linear regression model. 4
Q.2 Explain characteristics of Poisson distribution. 7
Machines and C all produce the same two parts, X and Y. Of all the parts
produced, machine A produces machine B produces and machine C
produces 10%.
In addition,
40% of the parts made by machine A are X.
50% of the parts made by machine B are X.
70% of the parts made by machine C are X.
A part produced by this company is randomly sampled and was found to be part
X. Find the probability that it came from
Machine A.
Machine B.
Machine C.
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OR
The following data pertains to two distributions A and B.
Measure Distribution A Distribution B
Mean 29 32
Median 26 29
Standard Deviation 12.3 12.3
Check whether the following statements are TRUE or not.
The variation of distribution A and B are same.
The skewness of distribution A and B are same.
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Q.3 Suppose that the average tariff per day of hotel in a small town is Rs. 951 and the
standard deviation of the tariff is Rs. 96 and that the tariffs are normally
distributed.
If a hotel is selected at random, what is the probability that the tariff is
Rs. 1000 or more?
Between Rs. 900 and Rs. 1100?
Between Rsd. 825 and Rs. 925?
Less than Rs 700?
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According to market information, the market share of Oreo is 10% of the market
for cookies brand. Suppose 20 purchasers of cookies are selected randomly from
the population. What is the probability that
More than 2 purchasers choose Oreo?
Fewer than 4 purchasers choose Oreo?
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OR
Q.3 A company produces and ships 16 personal computers knowing that 4 of them
have defective wiring. The buyer that purchased the computers is going to check
thoroughly 3 of these computers. The buyer can detect the defective wiring. What
is the probability that the buyer will find the following?
Exactly three defective computers.
Two or more defective computers.
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The retail price of 250 g box of corn flake ranges from Rs. 92 to Rs. 96. Assume
that this prices are uniformly distributed.
What is the average price and standard deviation of the price?
If a box is selected at random, what is the probability that the price will be
between Rs. 93 to Rs. 95.
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3
If a box is selected at random, what is the probability that the price is Rs.
100 or more?
Q.4 A small business has 37 employees. Because of the uncertain demand for its
product, the company usually pays overtime on any given week. The company
assumed that about 50 total hours of overtime per week is required and that the
variance on this figure is 25. Company officials want to know whether the
variance of overtime hours has changed. Given here is sample of 16 weeks of
overtime data (in hours per week). Assume hours of overtime are normally
distributed. Use these data to test the null hypothesis that the variance of overtime
data is 25. Let α 0.1
57 56 52 44
46 53 44 44
48 51 55 48
63 53 51 50
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Use the following data to test the following hypothesis.
Ho: 0 Ha: 0
Sample 1 Sample 2
n1 8 n2 11
Use level of significance.
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OR
Q.4 A random sample of 81 items is taken, producing a sample mean of 47. The
population standard deviation if 5.89. Construct a 90% confidence interval to
estimate the population mean. Also determine point estimate for population
mean.
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According to US Bureau of Labor Statistics, the average weekly earnings of a
production worker in 1997 were $424.20. Suppose a labor researcher wants to
test to determine whether this figure is still accurate today. The researcher
randomly selects 54 production workers and obtains a representative earnings
statement for one week from each. The resulting sample average is $432.69.
Assuming population standard deviation of $33.90 and a level of
significance, determine whether the mean weekly earnings of production worker
have changed or not.
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Q.5 A chemical engineering is studying the effect of temperature on the yield of a
certain product in chemical process. The process is run 10 times and the
following data is observed for the temperature of each process X and the
corresponding yield Y.
Temperature
X (in º 95 110 118 124 145 140 185 190 205 222
Yield Y
(In Kg) 108 126 102 121 118 155 158 178 159 184
Obtain Regression Equation of Y on X.
Find Sum Square of Error and Standard error of estimate
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4
OR
Q.5 A management consulting company presents a three-day seminar on project
management to various clients. The seminar is basically the same each time it is
given. However sometimes it is presented to high-level managers, sometimes to
mid-level managers, and sometimes to low level managers. The seminar
facilitators believe evaluation of the seminar may vary with the audience.
Suppose the following data are some randomly selected evaluation scores from
different levels of managers who attended the seminar. The ratings are on a scale
of 1 to 10, with 10 being the highest.
High Level Middle Level Low Level
7 8 5
7 9 6
8 8 5
7 10 7
9 9 4
10 8
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Use one way ANOVA to determine whether there is a significant difference
in the evaluations according to manager level. Assume α 0.05.
Also discuss the business implications of your findings.
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