STAISTICAL ANALYSIS : W 2007

M. Com. First Semester

STAISTICAL ANALYSIS

Time - Three Hours] [Full Marks - 80

N. B. : (1) All questions are compulsary.

(2) All questions carry equal marks.

1. (a) A group of eight students get the following percentage of marks in test in English and Hindi. Calculate the rank correlation of co-efficient by Spearman’s method :

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Roll No. of % of Marks in % of Marks in

Students English Hindi

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1 60 75

2 70 65

3 75 55

4 80 70

5 85 85

6 50 80

7 80 65

8 90 45

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(b) The following are the marks obtained by a group of ten students in Economics and Statistics :

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Marks in Marks in

Students Economics Statistics

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1 6 80

2 34 50

3 96 92

4 23 65

5 73 62

6 80 64

7 88 84

8 60 55

9 63 48

10 37 40

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OR

1. In a partially destroyed laboratory record an analysis of correlatoion data the following results only are legible :

Variance of x = 9

Regression Equations :

8x - 10y + 66 = 0

40x - 18y = 214.

What are (a) the mean value of x and y, (b) the standard deviation of y, and (c) the coefficient of correation between x and y? 16

2. (a) In an intelligent test administered 60 fathers and their 100 children the

following results were obtained :

Father Mean Score = 114; S. D. = 13

Son Mean Score = 110; S. D. = 11 r = 0.75

Calculate standard error and examine whether the difference is significant.

(b) Intelligent test of two groups of boys and girls given the following results.

Examine whether the difference is significant :

Girls : Mean = 84; S. D. = 10; No = 121

Boys : Mean = 81; S. D. = 12; No =81 8

OR

2. Following table given the wheat yields in bushes per acre of four varieties grown in five blocks. Test whether the mean yield of these varieties is significant :

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Block Varieties

A B C D

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1 16 14 19 20 80

2 20 23 11 27

3 26 24 23 19

4 12 29 17 21

5 21 25 20 13

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(Table value of F is 3.24)

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3. Out of 2000 people exposed to small pox in a village; 450 were attacked. Among the people 365 were vaccinated and out of them 50 were attacked.

Examine whether vaccination can be regarded as a good prevention or not

(The table value of X2 for one degree of freedom at 5% level of significance is 3.841) 16

OR

(a) In a sample of 1000 children, 400 came from higher group and the

rest from lower income group. The number of delinquent children in these groups respectively 50 and 200.

Calculate the coefficient of association between delinqency and income groups by using Yule’s formula 8

(b) From the Chain Base Index Number given below construct the Fixed Base Index :

Year Index No.

2001 85

2002 115

2003 125

2004 95

2005 145

4. (a) In a bag there are 7 white, 8 red, 5 black balls. Find out probability

that 2 balls will be white and one ball will be red in at random drawn 3 balls. 8

(b) One ticket is drawn at random from a bag containing 30 tickets

numbered from 1 to 30. Find the probability that it is a multiple of 3 or 5. 8

OR

4. From the following data of the population of a city in Lakhs find out the

population for 1986 by the Parabolic Curve method :

Year Population (in ‘000)

1971 180

1981 220

1991 250

2001 300

5. What do you mean by Statistical Quality Control? Explain in brief the methods of Statistical Quality Control. 16

OR

5. The Production is given below. Fit a straight line trend by the method of Least Square and find the trend values :

Year Production

1995 70

1996 72

1997 80

1998 76

1999 84

2000 88

2001 90

Estimate the production for the year 2005. Do these figures show a rising OR falling trend? How do you arrive at your conclusion? 16