STATISTICAL ANALYSIS : W.2003

VSJ - 49

First Semester M. Com. Examination

STATISTICAL ANALYSIS

Time - Three Hours] [Full Marks - 100

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N. B. : (1) All questions are compulsary. (2) All questions carry equal marks.

1. (a) Calculate Spearman’s co-efficient of co-rrelation between marks assigned to ten

Students by Judges x and y in a certain competitive test as shown below :

S. No. Marks by Marks by

x Judge y Judge

1 52 65

2 53 68

3 42 43

4 60 38

5 45 77

6 41 48

7 37 35

8 38 30

9 25 25

10 27 50 10

(b) Compute the co-efficient of concurrent deviation from the following data and give your comments :

Months Subject Relative

output of steel unemployed

(in 000’ tonnes) in steel

Industries

(in 000’ tonnes)

January 8.5 60

February 9.2 65

March 9.3 61

April 8.5 74

May 7.2 92

June 5.9 157

July 5.1 130

August 6.6 106

September 7.9 58

October 7.6 80

November 8.2 52

December 9.2 45 10

OR

The height of fathers and sons are given in the following table :

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Height of

Fathers 165 166 167 167 168 169 171 173

(in centimeters)

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Height of

Sons 167 168 164 168 172 170 169 170

(in centimeters)

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Calculate two lines of regression and calculate the expected average height of father is 167.5 centimeters. 20

2. The mean produce of wheat of a sample of 100 filds comes to 200 Lbs per-

acre with S. D. of 10 Lbs. Another sample of 150 filds gives the mean at 220 Lbs.; with S. D. of 12 Lbs. Assuming the Standard Deviation of the mean yield at 11 Lbs. for the Universe, Find out if these is a significant difference between the mean yields of the two samples. 20

OR

Set-up a table of Analysis of Variance and Comment on its result.

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Plots Varieties

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a b c d

1 200 230 250 300

2 190 270 300 270

3 240 150 145 180

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3. Show that there is a significant association between the temperament of Brothers and Sisters.

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Good natured Brothers Sisters Total

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Quick Good natured Sullen

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Quick 850 571 580 2001

Good natured 618 593 455 1666

Sullen 540 456 457 1453

Total 2008 1620 1492 5120

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(The Table value of x2 for given degree of freedom at 5% level of significance is 9.488 20

OR

In a Co-Education instituion, out of 1000 students 750 were boys. They appeared in an Examination and it was found that 600 Boys Passed, 50 Girls had failed. Is there any association between sex and success in the Examination? (By using Yule’s formula) 20

4. (a) A bag contains 8 white and 3 red balls. If two balls are drawn at random, find the probability that :

i) Both are white

ii) Both are red. 10

b) A problem in statistics is given to three students. R. G. T. whose chances of

solving it are 1/2, 1/3 and 1/4. What is the probability that the problem will be solved? 10

OR

From the following data Estimate the population for the year 1986 using parabolic curve method of interpulation :

Year Population (in Lakhs)

1971 18

1981 22

1991 25

2001 30 20

5. Discuss the need and utility of Statistical Quality control. 20

OR

Fit the Straight line by the method of least square to the data given below. Find the trend values and predict the sales for the Year 1997.

Year Sales

(in Crores Rs.)

1989 35

1990 42

1991 44

1992 48

1993 46

1994 49

1995 51

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