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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