LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

M.Sc., DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – NOVEMBER 2003

ST-1804/S719 – COMPUTATIONAL STATISTICS – I

13.11.2003                                                                                                           Max:100 marks

1.00 – 4.00

SECTION-A

Answer any THREE questions. 

 All questions carry equal marks                                                        

 

1. a) Compare the exact mean square error of ratio estimator with the variance of Hartely-

Ross unbiased estimator using the following population data assuming simple random

sampling is done with sample size 3.

Booth No.	Votes polled in 1991 election	Votes polled in 1996 election
1 2 3 4 5	1024 886 950 1251 684	964 931 1014 895 768

1. b) Consider a finite population of size 30 where the population units are arranged in

ascending order with respect to the levels,

Label : 1          2          3 …………..30

Y    : 13        21        29………….245

Y_I = 5+8_i,   i = 1, 2, ……. 30.

Draw a linear systematic sample of size 6 and estimate the population total using Yates

corrected estimator and give your comments.                                                     (20+14)

2. a) To estimate the volume of timer available in forest area consisting of 36 geographical

regions,  a sample of size 6 is drawn using random group method.  The following table

gives the data collected.

S.No.	No.of trees	Volume of timber (in cubic units)	Total no. of trees
1 2 3 4 5 6	46 73 50 48 36 20	112.6 143.6 121.2 98.7 76.3 42.3	243 180 140 70 107 90

Estimate the total volume of timber assuming that there are 2800 trees in the forest

area and also estimate the variance of your estimator.  (Here it is assumed that the

random groups are all of equal size).

1. b) A sample survey is conducted with the aim of estimating the total yield of paddy, the

area is divided into 5 strata and from each stratum 4 plots are selected by the method of

simple random sampling without replacement (SRSWOR).  Using the data given below

obtain the estimate of total yield along with the variance of the estimator.

Stratum No.	Total No. of plots	Yield of paddy for 4 plots
1 2 3 4 5	105 87 76 98 64	104     182     148       87 108      64       132     156 110      281     120     114 96      102     141    111 112     128      124    118

 

(17+17)

3. a) Show that (A­^-1)^T = (A­^T)^-1 for the following matrix.
4. b) Find g inverse for the given rectangular matrix.

 

1. c) Find the rank of the given matrix.

 

(14+10+10)

4. a) Find B^T A^-1 B without finding A^-1 for given matrices A and B.
5. b) A population containing 420 birds of same weight and age were taken for a stimulus

study.  The birds were divided into 60 equal groups.  They were then given the stimulus

to increase the growth.  The following data gives the frequency distribution of those

with significance increase in weight at the end of 6 weeks.  Fit a truncated binomial

distribution an test the goodness of fit at 5% level of significance.

No.of weeks:   1          2          3          4          5          6

No. of groups: 5          12        18        15        7          3

(14+20)

5. a) For the following distribution, fit a negative binomial distribution and test the goodness

of fit at 5% level of significance.

X:        0          1          2          3          4          5

F:         212      128      37        18        3          2

1. b) Fit a distribution of the type p(x) = where p₁ (x) = pq^x-1 , x = 1,2,…

0 ≤ p ≤ 1 and  Also test the goodness of fit at 5%

level.

X:        0          1          2          3          4          5          6          7          8

F:         72        110      119      58        28        12        4          2          2

(14+20)

 

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