STAISTICAL ANALYSIS : W 2005

M. Com. First Semester

STAISTICAL ANALYSIS

P. Pages : 8

Time - Three Hours] [Full Marks - 80

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

(2) All questions carry equal marks.

1. (a) Obtain the rank co-efficient of co-rrelation from the following data : 10

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x y

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75 120

88 134

95 150

70 115

60 110

80 140

81 142

50 100

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(b) Calculate the co-efficient of concurrent derivation from the follwoing data :

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Year Supply (Unit) Price (Rs)

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1992 160 292

1993 164 280

1994 172 260

1995 182 234

1996 166 266

1997 170 254

1998 178 230

1999 192 190

2000 186 200

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OR

You are given the following information about advertising expences & sales:

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Adr. Exps (x) Sales (y)

(in Lakhs Rs.) (in Lakhs Rs.)

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Mean 10 90

S. D. 3 12

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Co-efficient of co-rrelation = +0.80.

(a) Calculate two regression lines

(b) Find out most Likely sales when advertising expenditure is Rs. 15 Lakhs.

(c) What should be the advertising expenditure for the sales target of Rs. 120 Lakshs? 20

2. A random sample of 1000 farms in a certain year give an average yield of a

barely of 2000 Lbs. per-acre with standard Deviation of 192 Lbs. A random sample of 1000 farms in the following year gives an average yields of 2100 Lbs. Show that these data are inconsistent with the hypothesis that the average yields in the country as a whole were the same in the two years. 20

OR

The following table gives the yields of four plots each of three varieties of wheat. Find out if the variety differences are significant.

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Plots Plot Yields Total

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A 26 27 28 31 112

B 18 19 21 22 80

C 16 18 19 19 72

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Total 264

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(Table value of four given degree of freedom at 5 % level of significance is 4.26) 20

3. The following Table shows the condition of home and condition of child.

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Condition of Child Condition of Home

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Clean Not clean Total

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Clean 76 43 119

Fairly clean 38 17 55

Dirty 25 47 72

Total 139 107 246

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Do these results suggest that the condition of the home has a bearing on the condition of the child. (At 5% level of significance, the value of x2 is 5.991 for two degrees of freedom.) 20

OR

In an examination at which 600 candidates appeared, Boys out numbered girls by 16 percent of all candidates. Number of Passed candidates exceeded the number of failed candidates by 310. Boys failing in the Examination numbered 88. Construct the two-fold association between male-sex and success at Examination, using yule’s formula. 20

4. (a) A bag contains 5 Black and 7 white balls. A ball is drawn out of it and replaced in the bag. Then a ball is drawn again. What is the probability that :

i) Both the balls drawn were black?

ii) Both were white?

iii) The first ball was white and the second black?

iv) The first ball was black and seconds white? 10

b) Eight balls numbered form 1 to 8 are placed in the bag and two are drawn at random. What is the probability that they are numbered 1 and 2? 10

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 Pressure

20 2

30 4.4

40 7.5

50 13.2

Estimate the pressure for a velocity of 35 miles per-hour, by using parabolic curve method of Interpolation. 20

5. a) What are the components of a time series? 10

b) What do you understand by Statistical Quality Control? 10

OR

Below are the given fires of production (in thousnad tons) of a Sugar Factory :

Year Production

(in thousand tons)

1993 80

1994 90

1995 92

1996 83

1997 94

1998 99

1999 92

Find the trend values by least square method & also find out the production for the year 2000 20