LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

YB 35

FIRST SEMESTER – April 2009

ST 1812 – STATISTICAL COMPUTING – I

 

 

 

Date & Time: 04/05/2009 / 1:00 – 4:00       Dept. No.                                                       Max. : 100 Marks

 

 

Answer ALL the questions.  Each carries THIRTY FOUR marks

                                                                                        

1. a). In a population containing 490 live birds of same weight and age, the birds were divided into 70 equal groups.  They were then given a stimulus to increase the growth rate.  The following data gives the frequency distribution of birds with significant weights at the end of 6 weeks.  Fit a truncated binomial distribution and test the goodness of fit.

No of birds	1	2	3	4	5	6	7
Frequency	6	15	21	17	8	2	1

 

b). The following are the marks of 135 students of B.Com in a city college.

Marks	No. of Students
0-10	5
10-20	15
20-30	30
30-40	40
40-50	25
50-60	10
60-70	6
70-80	4

Fit a normal distribution by ordinate method and test the goodness of fit at                                    5% level of significance.

(OR)

c). Fit a truncated Poisson distribution to the following data and test the                            goodness of fit at 1% level of significance.

x	1	2	3	4	5	6
f	86	52	26	8	6	1

d). Fit a distribution of the form, where

, x=0,1,2,…,  > 0 and

; x=1,2,…, 0<p<1,

to the following data:

 

x	0	1	2	3	4	5	6	7	8
f	72	113	118	58	28	12	4	2	2

 

 

1. a). Find the inverse of the following symmetric matrix using partition method.

 

b). Obtain the characteristic roots and vectors for the matrix

 

 

 

 

(OR)

c). Find  for the following matrices:

i).

ii).

d). Draw a random sample of size 10 from the exponential distribution having the    density function

.

Also find the mean and variance of the sample observations.

 

1. a) The following data were collected on a simple random sample of 10 patients with hypertension.

 

Serial No.	mean arterial blood pressure (mm/Hg)	weight (kg)	heart beats / min
1	105	85	63
2	115	94	70
3	116	95	72
4	117	94	73
5	112	89	72
6	121	99	71
7	121	99	69
8	110	90	66
9	110	89	69
10	114	92	64

i). Fit a regression model and estimate effect of all variables / unit of measurement,        taking blood pressure as the dependent variable.

ii). Find R² and comments on it

(OR)

1. b) The following table explains a company monthly income based on their advertisement

on V-Slicer product.

 

Serial No.	Monthly Income on sales ($’000)	Advertisement on TV ($ ‘000)	Advertisement on News Paper ($ ‘000)
1	5.5	0.2	0.1
2	6.7	0.5	0.2
3	8.0	1.2	0.8
4	10.1	2.0	0.9
5	15	3.0	1.4
6	18.0	4.0	2.0
7	23	5.0	2.5
8	28	6.2	3.8
9	32	8.0	4.1
10	35	10.0	5.2

 

1. Draw a scatter diagram for the above data.
2. Fit a regression mode taking TV advertisement and News paper advertisement as independent variables and estimate monthly income when TV advertisement is 15 and News paper advertisement is 7 in 1000 dollars.

 

 

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