13.11.2003
1.00 - 4.00
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034
M.A., DEGREE EXAMINATION - ECONOMICS
FIRST SEMESTER – NOVEMBER 2003
ST-1900/S774 - STATISTICS FOR ECONOMISTS
Max:100 marks
SECTION-A
Answer ALL questions.
(10X2=20 marks)
1. In a moderately skewed distribution, the mean and the median are 34.5 and 38.6
respectively. Compute the most probable mode.
2. Why do we require two regression lines and when they will coincide?
3. What is the purpose of constructing Index numbers? How do you select the base period?
4. From the following data, construct an index number for 2003 taking 2000 as base by
using the price relatives method:
Commodities
Prices for 10 kgs in Rs.
2000
2003
A
70
95
B
46
80
C
130
215
D
190
380
5. State addition theorem on probability.
6. Of 12 accounts held in a file, four contain a procedural error in posting account balances.
In an auditor randomly selects two of these accounts without replacement, what is the
probability that neither account will contain a procedural error?
7. Comment on the following statement:
5
"For Binomial distribution mean is and variance is 5"
3
8. Explain briefly any two characteristics of a Normal distribution.
9. Distinguish between simple and composite hypotheses by giving suitable examples.
10. What is 'Analysis of variance' and where is it used?
SECTION-B
Answer any FIVE questions.
(5X8=40 marks)
11. The following table gives the distribution of monthly income of 600 families in a certain
village.
Monthly income (in Rs.)
No. of families
Below 750
60
750-1500
170
1500-2250
200
2250-3000
60
3000-3750
50
3750-4500
40
4500 and over
20
Draw cumulative frequency curve and find the values of all quartiles. Also, verify it using
the formula.
1
12. The following table shows the number of motor registrations in a certain territory for a
term of 5 years and the sale of motor tyres by a firm in that territory for the same period.
Motor Registration (X):
600
630
720
750
800
No. of Tyres sold (Y):
1250 1100 1300 1350 1500
Find the regression equation to estimate Y when X is known. Also, predict Y when
X = 850.
[
13. Explain in detail the main components of a time series and give suitable examples.
14. Construct a four-yearly centered moving average from the following data:
Year:
1995 96
97
98
99
2000 2001
Imported
Cotton consumption
in India:
129
131
106
91
95
84
93
(in lakh bales)
Draw original and Trend lines on the graph.
15. The monthly demand for transistors is known to have the following probability
distribution:
Demand (x): 1
2
3
4
5
6
Probability : 0.1
0.15 0.2
0.25 0.18 0.12
(i)
Determine the expected demand for transistors.
(ii)
Also, obtain the variance
(iii)
Suppose that the cost (C) of producing (X) transistors is C = 10,000 + 500 X,
find the expected cost.
16. The life time of a certain type of battery has a mean life of 400 hours and standard
deviation of 50 hours. Assuming normality for the distribution of life time, find
a) the percentage of batteries which have life time of more than 350 hours.
b) the proportion of batteries that have a life time between 300 hours to 500 hours.
17. An economist wants to test the hypothesis that the proportion of firms intending to
increase the prices of their product is the same in three industries: should the economist
accept or reject the hypothesis?
Number of firms
Decision
A
B
C
To raise price
40
50
60
Not to raise price
60
50
40
18.Seven homemakers were randomly sampled and it was determined that the distances they
walked in their housework had an average of 39.2 miles per week and a sample standard
deviation of 3.2 miles per week. Construct 95% and 98% confidence intervals for
population mean.
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SECTION-C
Answer any TWO questions.
(2X20=40 marks)
19. a) With the help of the following data, show that Fisher's Ideal Index satisfies both time
reversal and factor reversal tests:
Commodity
2001
2003
Price Quantity
Price Quantity
A
2
50
10
56
B
6
100
2
120
C
4
60
6
60
D
10
30
12
24
b) Using the method of simple average, calculate seasonal indices for all quarters:
Quarterly cement production
(in 100 lakhs tons)
Year
I
II
III
IV
1998
3.5
3.9
3.4
3.6
1999
3.5
4.1
3.7
4.0
2000
3.5
3.9
3.7
4.2
2001
4.0
4.6
3.8
4.5
2002
4.1
4.4
4.2
4.5
(10+10)
20. a) Distinguish between independent and dependent events.
b) A can hit a target with pistol 3 times in 5 shots, B 2 times in 5 shots and C 3 times in 4
shots. They fire a volley. What is the probability that two shots hit?
c) A factory has two machines and the past records show that machine - A produces 40%
of the items and machine - B produces 60% of the items. It was further found that 5%
of the items produced by machine - A were defective and only 2% of items produced
by machine - B were defective. If a defective item is drawn at random, what is the
probability that it was manufactured by i) machine - A and ii) Machine - B.
(4+8+8)
21. The following mistakes per page were observed in a book.
Number of mistakes per page:
0
1
2
3
4
Number of pages
:
211
90
19
5
0
Fit a Poisson distribution and test the goodness of fit.
22. The designs produced by four automobile designers are evaluated by three product
managers as reported below. Carry out two-way analysis and comment on your results:
Designer
Evaluator
1
2
3
4
A
87
79
83
92
B
83
73
85
89
C
91
85
90
92
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