LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

M.A., DEGREE EXAMINATION – ECONOMICS

FIRST SEMESTER – NOVEMBER 2003

ST-1900/S774 – STATISTICS FOR ECONOMISTS

13.11.2003                                                                                                           Max:100 marks

1.00 – 4.00

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:

“For Binomial distribution mean is  and variance is 5”

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

• 170
• 200
• 60
• 50
• 40

4500 and over                                       20

Draw cumulative frequency curve and find the values of all quartiles.  Also, verify it using the formula.

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

• Determine the expected demand for transistors.
• Also, obtain the variance
• 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
17. the percentage of batteries which have life time of more than 350 hours.
18. 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.

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

1. 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.
21. 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?

1. 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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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.A. DEGREE EXAMINATION – ECONOMICS

THIRD & FIRST SEMESTER – APRIL 2008

    ST 3902 / 1900 – STATISTICS FOR  ECONOMISTS

Date : 05/05/2008            Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION–A                  (10 X 2 = 20 Marks)

Answer all the Questions:

1. Briefly explain the limitations of Statistics in Economic Analysis.
2. Define the terms ‘Range ’ and ‘Standard Deviation’
3. In a distribution, the mean is 65, median is 70, Coefficient of Skewness is -0.6

Find mode and Coefficient of Variation.

4. State the merits and demerits of rank correlation.
5. Give any two applications of discrete distributions in Economics.
6. State any four properties of Normal distribution.
7. Briefly explain the terms positive and negative correlation.
8. What is meant by Test of Adequacy?
9. When do you go for Transportation Problem? Give an example.
10. What is the objective of an Assignment Model?

SECTION-B                  (5 X 8 = 40 Marks)

Answer any five Questions:

11.The frequency distribution of income in a certain factory is as  follows.   Calculate Bowley’

skewness from the following data:

Income ( Rs in 100):   0-100  100-200    200-300  300-400     400-500      500-600

No. of Persons        :     8              17               58         47             22            8

12.Discuss in detail how trend analysis plays an important role in Economic.

13.Show that the Fisher’s Index satisfies both time reversal test and factor

reversal test.

14. Explain in detail the construction of Cost of living Index numbers.

15. State Addition and Multiplication Theorem on Probability with an example.

16. Calculate the rank coefficient of correlation between X and Y from the following data:

X:    10      35        43        51        73        85        10

Y :    23      62        38        10        14        16        20

17. When do we go for Chi-square Test ? Illustrate with an example.

18. Discuss in detail, the applications of LPP in Economics.

SECTION-C                 (2 X 20= 40 Marks)

Answer any Two Questions:

19 The following data represents the daily wages of an automobile industry.

Find   ß₁,   ß₂  from  the following data and comment on the results.

Daily Wages   :    0-20        20-30      30-40    40-50       50-60      60-70        70-80

No.of workers :     12              35           58        72           49           34              17

20. Calculate the coefficient of correlation between X and Y for the

following and obtain the two regression lines.

X:        1          3          4          5          7          8          10

Y:        2          6          8          10        14        16        20

21a. Explain in detail the various steps involved in solving a Transportation problem.

21b. Construct a Transportation problem using three origin and three destinations and find the optimal

solution.

22. Write short notes on the following:

1. Kurtosis
2. Standard Error
3. Assignment Problem
4. Conditional probability

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.A. DEGREE EXAMINATION – ECONOMICS

THIRD SEMESTER – November 2008

    ST 3902 – STATISTICS FOR  ECONOMISTS

Date : 14-11-08                 Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION–A                                         (10 X 2 = 20 Marks)

Answer all the Questions:

1. Give any two industrial applications of
2. When will you go in for Median? Give an example.
3. Briefly explain the term Positive Skewness.
4. If the two regression lines are x +2y = 5 and 2x+3y = 8. Calculate the means and the regression coefficients.
5. What do you understand by the term Continuous random variable? Give an example.
6. What are the properties of Poisson distribution?
7. Briefly explain the term Business Cycle.
8. Define the following terms with examples.
9. Critical Region. b.  Level of Significance.
10. State the addition Theorem and give an example.
11. Briefly explain the objective of an Assignment Problem.

SECTION-B                                      (5 X 8 = 40 Marks)

Answer any FIVE Questions:

11. The following data relate to the profits (in Million $) of 1000 companies:

      Sales:             :      100 – 120   120-140  140-160  160-180  180-200 200-220  220-240

      No of Companies:  17                 53        199           194             327      208      2

       Calculate Bowley’s coefficient of skewness.

12. Explain in detail the various steps in the construction of Cost of living Index   

 numbers.

13. The following table gives age X  in years of Ford cars and Annual Maintenance Cost   

            Y  (in hundred $)

            Age          :      1                3                5             7             9

            Main.Cost:     15               18             21          23           22

            Plot the given data and the trend line.

14. Explain the Characteristics of the Chi-Square distribution and state the various   

applications of this distribution.

15. Explain in detail the ratio-to-trend method to calculate the seasonal indices.
16. From the following data Calculate the Rank coefficient of correlation.         

            X   :  40    50    60   70    80    90 100  120  90  60

       Y   :  185  167  132  82   38   12   34    56   54  78

17. A manufacturer of flat TV knows that 2% of his products are defective. If he sells the TV   in boxes of 100  and guarantees not more than 4 defectives, What is the probability that a  box will fail to meet the  guaranteed quality?    ( e ^–2 = 0.13534)

18. State BAYE’S theorem and give a suitable example.

SECTION-C                                                  (2 X 20= 40 Marks)

Answer any TWO Questions:

19. a. The following data relate to the life  (in hours) of 2 companies:

                Suriya:  87  45  69  38  60  58  40  60  78  98 

                Philips: 17  53  99  19  74  67   80 77  32  28       

       Which company you would  like to purchase? and comment on the results.                        (10-Marks)

1. Fit a straight line to the following data:

Year      :1995  1996  1997  1998   1999   2000  2001    2002   2003   2004    2005

Sales    :   250    592   672     824      569    968    1205   1464   1758  2058    1566

(in Million $)                Estimate the sales for 2009.                                                            (10-Marks)

20 a. In a certain sample of 2000 families from UK, 1400 families consume of tea. Out of 1800 Indian  

        families, 1236 families consume tea. Use Chi-Square test to test whether tea consumption is

        independent of the families.

   (Use Chi-Square table value = 3.841,  at 5% level)                                                                (12–Marks)

1. Distinguish between small sample tests and large sample tests with suitable illustrations. (8-Marks)

21. a) Nokia started producing cell phones at different parts of the world and supplying for the whole

         world. Construct a Transportation model.                                                                            (5 Marks)

1. Explain in detail all the steps involved in solving a transportation model to find the optimal solotion.

 ( 15-Marks)

22. Write shot notes on the following:
23. a) Kurtosis
24. b) Components of Time series
25. c) Time reversal test

d)Assignment problem                                                                                  ( 4X 5 = 20 Marks)

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         LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.A. DEGREE EXAMINATION – ECONOMICS

THIRD SEMESTER – April 2009

ST 3902 – STATISTICS FOR  ECONOMISTS

Date & Time: 29/04/2009 / 9:00 – 12:00   Dept. No.                                                 Max. : 100 Marks

SECTION–A                  (10 x 2 = 20 Marks)

Answer all the Questions:

1. State any two applications of statistics in business.
2. Define the term mode with an example.
3. When do we go for Mean deviation?
4. Briefly explain the term partial correlation.
5. What is meant by Leptokurtic?
6. State any four properties of Normal distribution.
7. When Binomial tends to Poisson distribution?
8. Define the term time reversal test.
9. Define the following terms with examples.
10. Sample space. b. Mutually exclusive events.
11. What is meant by degeneracy in a transportation problem? Give an example.

SECTION-B                  (5 x 8 = 40 Marks)

Answer any five Questions:

11. Calculate mean, median and mode from the following data:

Income (in 1000 Rs):  5-10   10-15   15-20   20-25   25-30

No of IT staff               :   5          10        20        10        5

12. The following data represent the hourly wages paid to the workers of TCS and WIPRO.

No of workers             Mean                   SD

TCS                 500                              Rs. 186                 81

WIPRO           600                              Rs. 175                100

Calculate the co-efficient of variation and comment upon your result.

13. Calculate the Karl Pearson’s coefficient of correlation from the following data:

Income :           125  137  156  112  107  136  123  108

Expenditure:    78    89    96    69    59    79    68    61

14. How do you fit the curve of the form Y = ax² +bx +c?
15. Explain in detail any five steps involved in the construction of cost of living index numbers.
16. Three coins are tossed once, Construct

i)Sample space

1. ii) Probability distribution

iii) Expectation of X.  Where X represents the number of heads.

17. Students in a Business school were given an aptitude Test. Their marks were found to be

normally distributed with mean 60 and SD 5.

What percent scored

1. i) More than 60 marks?
2. ii) Less than 56 marks?

iii) Between 45 and 65 marks?

( table value Z =0 to -0.8=0.2881:    Z=0 to -3 =0.49865:     Z = 0 to 0.3413)

18. Describe the various steps involved in solving an LP problem using graphical method.

SECTION-C                 (2 x 20= 40 Marks)

Answer any Two Questions:

19a.  Distinguish between skewness and kurtosis with suitable diagram.

1. Calculate Bowley’s coefficient of skewness from the following data:

Per capita income: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of countries   : 12       16      26      38        22     15        7        4

(10 +10-Marks)

20a. Discuss in detail the various steps involved in solving an assignment model.

1. Solve the following transportation problem and find the optimal solution.

M1      M2  M3  M4          supply

W1          19     30    50    10             7

W2          70     30    40    60             9

W3          40     8      70    20            18

Demand              5       8      7     14

(8 +12-Marks)

21 Calculate the seasonal indices by the Ratio – To – Moving average method, from the following

data:

Year

Quarters          2004    2005    2006    2007

Q1                175     862     390     100

Q2                601     652     272      278

Q3                154     623     466     172

Q4                529     380     385     193

(20 Marks)

22. Write shot notes on the following:
23. a) Rank correlation
24. b) Price relative index numbers
25. c) Baye’s theorem
26. d) Large sample tests ( 4X 5 = 20 Marks)

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