STAISTICAL ANALYSIS : AB-0330

M. Com. First Semester

STAISTICAL ANALYSIS

Paper - 102

P. Pages : 8

Time - Three Hours] [Full Marks - 80

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

(2) All questions carry equal marks.

1. (a) The ranks of the same 16 students in tests in mathematics & statistics were follows, the two numbers within brackets denoting the ranks of the same students in mathematics & statistics respectively. 8

(1, 1), (2, 10), (3, 3), (4, 4), (5, 5), (6, 7), (7, 2), (1, 6), (9, 8), (10, 11), (11, 15), (12, 9), (13, 14), (14, 12), (15, 16) (16, 13).

Calculate the rank correlation coefficient for proficiences of the group in

mathematics & statistics. 8

(b) If co-efficient of correlation between x & y series is 0.6 & n = 64 find out probable error & standard error. 8

OR

Price indices of cotton & wool are given below for 12 months of a year. Obtain the equations of lines of regression between the indices & also calculate co-efficient of correlation. 16 Income of cotton Index of wool

78 84

77 82

85 82

88 85

87 89

82 90

81 88

77 92

76 83

83 89

97 98

93 99

2. Two random samples drawn from normal populations are :

Sample I : 100, 110, 95, 105, 90, 97, 103, 102, 108, 90

Sample II : 85, 90, 95, 96, 108, 108, 106, 95, 105, 108, 104.

Obtain estimates of variances of the population & test whether the two populations have the same variance. (Table value of N1 = 9 & N2 = 10 is 3.13) 16

(a) A sample of 400 students of the Amravati University gives a mean weight of 120 lbs. with a standard deviation of 10 lbs what inference can you draw from the data about mean weight of the students of Amravati University?8

(b) A random sample of 1000 farms in a certain year, gives an average yield of

a wheat of 2000kgs. Per hec. with S. D. of 192 kgs. A random sample 1000 farms in the following year gives and average yield of 2100 kgs. Per hectare with a standard deviation 224 kgs. Show that these data are inconsistent with the hypothesis that the average yield in the country as a whole were the same in two years. 8

3. The following is the result of a random survey regarding the employment of

adult males & females.

Frequency

Male employeed 160

Male unemployeed 40

Female employeed 440

Female unemployeed 360

Size of sample 1000

Does this survey reveal any association between the sex of an individual & his/her employment? (At 5% level of significance the table value of x2 for 1 D. F. is 3.841) 16

OR

Show with the help of the following data that the time & Factor Reversal Tests are satisfied by Fisher’s Ideal Formula for Index number. 16

Commodities Base Year Current Year

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

4. A delegation of 6 members is to meet the President. The two political parties

J. D. and BJP have nominated 7 and 4 persons respectively for the purpose. In how many ways can the delegation be formed. :

(i) If exactly 4 JD members are to be included in the delegation.

(ii) If at least 2 BJP members are to be included in the delegation. 16

OR

The following are the sales of a concern for a few years :

Years 2003 2004 2005 2006 2007

Sales (Thousand Metres) 125 163 204 238 282

Assuming the conditions to be the same estimate the sales for the year 2008 by using Binomial expansion method. 16

5. What is Statistical Quality Control? Discuss the need & utility of Statistical

Quality Control. 16

OR

Below are given figures sugar production (in Tonns) of sugar factory :

Year : 2001 2002 2003 2004 2005 2006 2007

Production : 170 180 192 183 194 199 192

Fit a straight line trend by the method of least squares and plot these figures and show the trend line. Also predict the production for the year 2010. 16