STAISTICAL ANALYSIS

M. Com. (Semester-I) Examination

STAISTICAL ANALYSIS

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 15 students in two subjects According and Statistics are given below. The two numbers within brackets denote the ranks of the same student in two subjects respectively :

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

Find the Spearman’s Rank Correlation Coefficient. 8

(b) Calculate Coefficient of concurrent deviation from the following data :

Price Imports

368 22

384 21

385 24

361 20

347 22

384 26

395 24

403 29

400 28

385 27

OR

1. For 100 students of a class the regression equation of marks in Statistics (x) on the marks in Accountancy (y) is 6y - 10x + 360 = 0. The mean marks in Accountancy is 70 and variance of marks in Statistics is 9/16th of the variance of marks in Accountancy. Find the mean marks is Statistics and the coefficient of correlation between marks in two subjects. 16

1. The manufacturer of a certain make of electric bulbs claims that his bulbs have mean life of 25 months with a standard deviation of 5 months. A random sample of 6 such bulbs gave the following values :

Life in months :

24, 26, 30, 20, 20, 18

Can you regard the producer’s claim to be valid at 1% level of significance? (Given that the table values of the appropriate test statistics at the said level are 4.032, 3.707 and 3.499 for 5, 6 and 7 degrees of freedom respectively.)

16

OR

2. To test the significance of the variation of the retail prices of a commodity in three principal cities, Mumbai, Kolkata, and Delhi, four shops were chosen at random in each city and prices observed in rupees were as follows :-

Mumbai : 16 8 12 14

Kolkata : 14 10 10 6

Delhi : 4 10 8 8

Do the data indicate that the Prices in three cities are significantly different? (The value of F 0.05 for V1 = 2, V2 = 9 is 4.26 16

3. From the following data of the wholesale prices of wheat for ten years, construct index numbers taking (a) 1994 as base and (b) by chain base method.

Year Price of Wheat

(Per 10 kg. Rs.)

1995 60

1996 62

1997 65

1998 70

1999 78

2000 82

2001 84

2002 88

2003 90 16

OR

3. (a) In an examination at which 500 candidates appeared, boys outnumbered

girls by 14 per cent of all candidates. Number of passed candidates exceeded the number of failed candidates by 300. Boys failing in examination numbered 80. Calculate the coefficient of association between boys and success in the examination. 8

(b) The number of scooter accidents per month in a certain town was as follows:

12, 8, 20, 2, 14, 10, 15, 6, 9, 4.

Use Chi-square test to determine if these frequencies are in agreement with the belief that accident conditions were the belief that accident conditions were the same during 10 month period. (Use 5% value of X2 for 9 df. = 16.92) 8

4. (a) Amravati Municipal Corporation installed 2000 bulbs in the streets of Amravati

If these bulbs have an average life of 1000 burning hours, with a standard deviation of 200 hours, what number of bulbs might be expected to fail in the first 700 burning hours? The table of area of the normal curve at selected values is as follows : -

_

x - x Probability

___

(b) A Salesman has a 60 percent chance of making a sale to each customer.

The behaviour of successive customer. The behaviour of successive customer is independent. If two customers ‘A’ and ‘B’ enter, what is the probability that the salesman will make a sales to ‘A’ or ‘B’? 8

OR

4. The following table gives the population of a town during the last 5 censes.

Estimate the population for the year 1986 : -

Year Population (000)

1951 120

1961 150

1971 200

1981 270

1991 390

2001 520

Use Newton’s-Gauss (Backward) Formula. 16

5. What do you mean by control charts? Explain in brief the types of control charts. 16

OR

For the following table :-

(i) Fit a straight line trend by the method of least squares.

(ii) Calculate the trend values.

(iii) Assuming the same rate of change continues what would be the Predicted Production for the year 2006 :

Year Production

(in 000 tonnes)

1997 12