STAISTICAL ANALYSIS : W 2006

First Semester M. Com. Examination

STAISTICAL ANALYSIS

Paper - 102

Time - Three Hours] [Full Marks - 80

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

(2) All questions carry equal marks.

1. (a) From the regression lines given below estimate

x when y = 6, and y when x = 4,

x = 2y + 5 ---- (i)

2 10

y = 3 x + 3 ------ (ii) 8

(b) Find the coefficient of correlation and standard deviation of y from the following data : -

3x = y, 8y = 6x, Variance of x = 16 8

OR

(a) Given below are the monthly variation in prices of two shares ‘X’ and ‘Y’. Find the co-efficient of correlation by concurrent deviation method : -

Month : April May June July August Sept. Oct. Nov. Dec.

Share ‘X’ -4 -3 -4 0 3 -4 2 -3 -3

Share ‘Y’ 3 -3 -2 -4 -3 -4 0 -2 -3

8

(b) Find out Rank Correlation co-efficient from the following data : -

Sr. No. : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Rank Differences : -2, -4, -1, +3, +2, 0, 2, +3, +3, -2

8

2. The following are manufactured items in the various foudaries of a plant :-

Foundry No. of produced items

A 54, 30, 10, 17, 4

B 37, 62, 65, 10, 68, 30, 29, 78, 56

C 16, 63, 70

Table value of F 0.05 for V1 = 2 and V2 = 14 is 3.74, test whether the difference in produce is significant. 16

OR

(a) A sample of size of 10 drawn from a normal population has a mean 31 and

variance 2.25. On the basis of the given data is it reasonable to assume that the mean of the population is 30? Use 1% level of significance in case table value of t for 9 degrees of freedom is 3.25. 8

(b) A sample of 400 units is found to have a mean of 67.47 inches. Can it he reasonably regarded as a simple sample drawn from a large population with mean 67.39 inches and variance 1.69 inches? 8

3. In December 2005, there was an outbreak of plague in a Jail in Mumbai of

127 persons who where uninoculated, 10 contracted plague 6 of item died of 147 person who were inoculted 3 contracted plague and there were no detahs. Trace the association between :-

(i) Inoculation and contracting the disease and

(ii) Inoculation and mortality among persons who have contracted the disease. Use Yule’s Method. 16

OR

From the following data calculate Fisher’s Ideal Index Number. Does it satisfy both, Factor and Time Reversal Tests? :

2004 2005

Base Year Current Year

Item Price Quantity Price Quantity

A 6 50 10 56

B 2 100 2 120

C 4 60 6 60

D 10 30 12 24

E 8 40 12 36

16

4. Three newspapers A, B, and C are published in a city. It is known that 20%

residents read ‘A’ newspapers, 16% B, 14%, C, 8% A and B, 5% A and C, 4% B and C and 2 % read all the three newspapers. What is the probability that a person selected at rendom? :

(i) reads only ‘A’ newspaper.

(ii) reads ‘A’ but does not read ‘B’

(iii) reads only two out of the three,

(iv) does not read any of the paper 16

OR

The pressure of wind in pounds per square foot, corresponding to the velocity in miles per hour has been determined by experiment to be approximately as follows :

Velocity 20, 30, 40, 50

Pressure 2 4.4 7.9 13.2

Estimate the pressure for a velocity of 35 miles per hour. 16

5. What is Statistical Quality Control? Explain the need and importance of

Statistical Quality Control in an industry. 16

OR

(a) What do you mean by time series? Explain short term oscillation. 8

(b) Fit a straight line trend to the following data and obtain trend values:

Year : 2001 2002 2003 2004 2005

No. of : 100 120 130 140 160

Employees

Estimate the No. of Employed for the yrar 2005. 8