Loyola College M.Sc. Statistics Nov 2012 Statistics For Economists Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – NOVEMBER 2012

ST 3902 – STATISTICS FOR  ECONOMISTS

 

 

Date : 10/11/2012            Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION- A

 

Answer ALL the following:                                                                                                  (2 X 10 = 20)

 

1) State any two measures of central tendency.

2) Give the formula for rank correlation coefficient.

3) Define independent events.

4) What are the parameters of normal distribution?

5) Define probability of type II error.

6) What is the test statistic for equality of means in large sample test?

7) Write the four components of time series.

8) Give the formula for Fisher’s ideal index number.

9) Define Optimal solution of an Linear Programming Problem.

10) State any two method of obtaining I.B.F.S of a transportation problem.

 

SECTION- B

Answer any FIVE of the following:                                                                                         (5 X 8 = 40)

 

11) Find the mean deviation about mean for the following data given below.

 

Marks 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
No. of students 3 8 9 15 20 13 8 4

 

12) Find the coefficient of correlation between X and Y for the following data:

X 10 12 13 16 17 20 25
Y 19 22 26 27 29 33 37

 

13) Five men in a company of 20 are graduates. If 3 are picked out from this 20 persons

random, what is the probability that (i) all are graduates (ii) exactly 2 are graduates and (iii)

atleast one is a graduate.

 

14) A random variable X has the following probability function.

x 0 1 2 3 4 5 6 7
p(x) 0 m 2m 2m 3m m2 2m2 7m2+m

(i)Find the value m (ii) Evaluate (a) p( X < 6 ) (b) p( X ≥ 6) (c) p( 0 < X < 5 )

 

15) Number of road accidents during a month follows Poisson distribution with mean 6. Find the

probability that in a certain month number of accidents will be (i) not more than 3, (ii)

between 2 and 4 and (iii) exactly 5?

 

16) The customer accounts of a certain departmental store have an average balance of Rs.120

and a standard deviation of Rs. 40. Assuming that the account balances are normally

distributed, find what proportion of accounts is (i) over Rs.150, (ii) between Rs.100 and

Rs.150 and (iii) between Rs.60 and  Rs.90?

 

17) From the following data, calculate price index numbers for 2011 with 2008 as base year by:

(i) Laspeyre’s method, (ii) Paasche’s method and (iii) Fisher’s ideal method

 

2008 2011
Commodity Price Quantity Price Quantity
A 20 10 40 10
B 50 12 60 5
C 40 10 50 10
D 20 20 20 25

 

18) Suggest optimal assignment of the workers to jobs if the completion time (in hours) of

different jobs by different workers is as given below:

Tasks

Men I II III IV
Zico 8 7 9 10
Jay 7 9 9 8
Muthu 10 8 7 11
Febin 10 6 8 7

 

 

SECTION – C

 

Answer any TWO  of the following:                                                                                   ( 2 X 20 = 40)

 

19) (i) Find the regression line of Y on X for the following data:

X 65 66 67 67 69 71 72 70 65
Y 67 68 69 68 70 70 69 70 70

 

 

 

 

(ii) Find the standard deviation for the following data given below:

Class 10-15 15-20 20-25 25-30 30-35 35-40
Frequency 2 8 20 35 20 15

 

 

20) (i) Three urns are given. Urn 1 contains 2 white, 3 black and 4 res balls, urn 2 contains 3

white, 2 black and 2 red balls and urn 3 contains 4 white, 4 black and 1 red ball. One urn

is chosen at random and two balls are drawn from the urn. If the balls happen to be white

and red, what is the probability that they were drawn from urn 3?

(ii) If 10% of the screws produced by an automatic machine are defective, find the

probability that of 20 screws selected at random, there are (i) exactly two defectives, (ii)

at the most 3 defectives and (iii) between one and four defectives. Find the mean and

variance of the number of defective screws?

 

 

21)  (i) 10 Accountants were given intensive coaching and four tests were conducted in a month.

The scores of tests 1 and 4 are given below:

S.NO. 1 2 3 4 5 6 7 8 9 10
Marks in I test 50 42 51 42 60 41 70 55 62 38
Marks in IV test 62 40 61 52 68 51 64 63 72 50

Does the score from test I to test IV show an improvement?

(ii) A random sample of 200 tins of coconut oil gave an average weight of 4.95 kgs with a

standard deviation of 0.21 kgs. Do we accept the hypothesis of net weight 5 kgs per tin at

1% level?                                                                                                    (12+8)

 

22) (i) Using the three year and five year moving averages determine the trend for the following

data:

 

Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Sales

(‘000 Rupees)

21 22 23 25 24 22 25 26 27 26

 

(ii) Determine an initial basic feasible solution to the following transportation problem using

the Vogel’s approximation method.

Distribution centres

Factory Mumbai Bangalore Delhi Chennai Available
Kolkatta 20 22 17 4 120
Cochin 24 37 9 7 70
Ranchi 32 37 20 15 50
Requirement 60 40 30 110

 

(10+10)

 

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