LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 B.Sc. DEGREE EXAMINATION – STATISTICS

AB 16

FIFTH SEMESTER – NOV 2006

ST 5503 – COMPUTATIONAL STATISTICS

(Also equivalent to STA 508)

 

 

Date & Time : 01-11-2006/9.00-12.00   Dept. No.                                                       Max. : 100 Marks

 

 

Answer FIVE questions choosing  at least two questions from each section

SECTION A                                                  ( 5 x20 =100)

1] Consider a population of  6 units with values : 1, 2, 4, 7, 8, 9

[i] Write down all possible samples of size 3 without replacement from this population

[ii] Verify that the sample mean is an unbiased estimate of the population mean

[iii] Calculate  the Sampling variance and verify   that it agrees with the  variance of the

sample mean under SRSWOR.

[iv]  Also , Verify that  the Sampling Variance is less than the variance of  the  Sample

mean which is obtained from SRSWR.

2] The table given below shows the summary of data for Paddy crop census of all the 2500

farms in a state. The farms were stratified according to farm size(in acres)  into 4 strata as

given below:

Stratum Number	Farm Size (inacres)	No. of Farms Ni	Average area Under paddy crop (in acres) per farm ŸNi	Standard Deviation si
1	0-100	600	45	8
2	101-200	900	105	12
3	200-500	700	130	20
4	>500	300	180	40

[i] Estimate the total area under Paddy cultivation for the state

[ii] Find the sample sizes of each stratum under proportional allocation.

[iii] Find the sample sizes of each stratum under Nayman’s Optimum allocation

[iv] Calculate the variance of the estimated total area under Proportional allocation

[v] Calculate the variance of the estimated total area under Nayman’s Optimum

allocation

[vi] Calculate the variance of the estimated total area under un-stratified simple random

sampling without replacement.

[vii] Estimate the gain in efficiency resulting from [iv] and [v] as compared with [vi]

 

 

 

3]  Five samples were collected using systematic sampling from 4 different pools located in a

region to study the mosquito larvae  population( in ‘000/ gl) ,where the mosquito population

exhibits a fairly steady rising trend. i]  Find the average mosquito population in all four pools

and also find sample means. ii]  Compare the precision of systematic sampling , SRSWOR

and Stratified sampling.

Sample Number( mosquito nos. in ‘000/ gl)

Pool #	1	2	3	4	5
I	3	7	8	9	12
II	4	9	16	18	20
III	8	16	17	19	24
IV	14	18	23	28	32

 

4] The following data furnishes the software earnings of India (in ‘00 crore) for the time period

1996 To 2005. Fit a second degree parabola and hence predict the expected software earnings

of India for the financial year 2006.

Year	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005
Earnings(‘00Cr)	4	8	15	30	90	50	110	150	300	500

 

 

SECTION B

 

1. a.) From the following data construct an index for 2001 taking 2000 as base by the

average of relatives method using i.) arithmetic mean and ii.) geometric mean for

averaged relatives:

 

Commodity                 Price in 2000               Price in 2001

( Rs )                             ( Rs )

 

A                               50                                   70

B                               40                                   60

C                               80                                   90

D                             110                                  120

E                                20                                   20

 

b.) Construct the consumer price index number for 2003 on the basis of 2002  from the following data using ’ family budget method’.

 

Items	Price in 2002 ( Rs )	Price in 2003 ( Rs )	Weights
Food	200	280	30
Rent	100	200	20
Clothing	150	120	20
Fuel	50	100	10
Miscellaneous	100	200	20

(14+6)

 

1. a.)  The life time of 10 electric bulbs selected randomly from a large consignment gave

the following data :

Life time (Hours )   4.2     4.6       3.9       4.1       5.2       3.8       3.9       4.3                                             4.4     5.6

Test at 5% level the hypothesis that the average life time of bulbs is 4.

• In a cross- breeding experiment with plants of certain species, 240 offsprings were classified into 4 classes with respect to the structure of the leaves as follows:

Class :                I                       II                     III                    IV

Frequencey:        21                    127                  40                    52

 

According to theory, the probabilities of the 4 classes should be in the ratio

1: 9: 3: 3. Are these data consistent with the theory? Use 5% level.                                                                                                                                                               (10+10)

 

1. Two samples are drawn from two normal population. From the following data, test whether the two populations have i) Equal variance ii) Equal means at 5% level.

Sample 1         60        65        71        74        76        82        85        87

Sample 2         61        66        67        85        78        63        85        86        88        91

 

 

1. a.)  IQ Test on two groups of boys and girls gave the following results

	Mean	SD	Sample Size
Boys	73	15	100
Girls	78	10	50

 

Is there a significant difference in the Mean scores of boys and girls ? Test at 1% level.

 

• Let X denote the length of a fish selected at random from the lake . The

observed length of n=10 fish , were 5.0 , 3.9 ,5.2 , 5.5 , 2.8 , 6.1, 6.4 , 2.6 , 1.7

and 4.3. Test at 5 % level the hypothesis that the median length of fish in the

lake is 3.7 .                                                                                      (6+14)

 

 

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