LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Com DEGREE EXAMINATION – COMMERCE

AT 21

FIRST SEMESTER – NOV 2006

CO 1810 – ADVANCED BUSINESS STATISTICS-I

 

 

Date & Time : 02-11-2006/1.00-4.00     Dept. No.                                                          Max. : 100 Marks

 

 

SECTION – A

Answer ALL the questions                                                                (10 x 2 = 20 marks)

 

1. Give the formula for Geometric mean.
2. Define Skewness
3. State the three axioms of probability.
4. Give the expression for expectation in the case of random variables X.
5. State any two properties of normal distribution.
6. Define null hypothesis
7. Define probability of Type-I error
8. Give the test statistic for testing equality of two means when n>30?
9. Explain the non-parametric test
10. Define probability

SECTION – B

Answer any FIVE questions                                                              (5 x 8 = 40 marks)

11.Calculate arithmetic mean from the following data

Marks scored:              0-10     10-20   20-30   30-40   40-50   50-60

No. of students:            5          10         25        30        20       10

 

12. A perfect dice is tossed twice. Find the probability of getting (i) a total of 9 (ii) a total is

multiple of 3 (iii) a total of 5 (iv) a multiple of 6.

 

13. Two boxes contain 12 white and 18 black and 15 white and 25 black balls respectively. One

box was taken at random and a ball was taken from the same.  It is a black ball.  What is the

probability that it is from the first box?

 

14. A random variable x has the following probability function.

X         0          1          2          3          4          5          6          7

P(x)     0          k          2k        2k        3k        k²            2k²    7k²+k

• Find k (ii) P(x<6) (iii) P (x ³6).

15. Five coins are tossed 3,200 times, find the frequencies of the distribution of heads and tails

and tabulate the results in a binomial.

 

 

 

16. A college conducts both day and night classes intended to be identical. A sample of 100 day

students yields examination results as   = 72,  , and a sample of 200 night students

as = 73.9 and   Are the two means statistically equal at 10% level?

 

17. Two sets of ten students selected at random from a college were taken: one set was given

memory test as they were and the other was given the memory test after two weeks of

training and the scores are given below:

Set A:	10	8	7	9	8	10	9	6	7	8
Set B:	12	8	8	10	8	11	9	8	9	9

Do you think there is nay significant effect due to training? (null and alternative

hypothesis should be stated (Given t = 2.10 at df =18, a = 0.05).

 

18. 200 digits are chosen at random from a set of tables. The frequencies of the digits are as

follows:

Digit:               0          1          2          3          4          5          6          7          8          9

 

Frequency:      18        19        23        21        16        25        22        20        21        15

Use x² test to assess the correctness of the hypothesis that the digits were distributed in

equal numbers in the tables from which they were chosen. (df @ 5% x² =16.92)

 

SECTION – C

Answer any TWO questions                                                             (2×20=20 marks)

 

19. a) Three urns contain respectively 3 green and 2 white balls, 5 green and 6 white balls and 2 green and 4 white balls. One ball is drawn from each urn.  Find the expected number of white balls drawn out.                                                             (12 marks)

 

1. b) Two cards are drawn at random with replacement from a box which contains four

cards numbered 1, 1, 2 and 2.  Let X denote the sum  if the numbers shown on the

two cards.  Find the distribution of X.  Also find E(X) and var (X).       (8 marks)

 

20. a) After correcting the proofs of the first 50 pages of a book, it is found that on the

average there are 3 errors per 5 pages.  Use Poisson probabilities and estimate the

number of pages with 0,1,2,3 errors in the whole book of 1000 pages (e^-6 = 5488).

(12 marks)

 

 

20. b) Three samples below have been obtained from normal populations with equal variances.

Test the hypothesis at 5% level that the population means are equal.

 

8   10   7   14   11

7   5   10   9   9

12   9   13   12   14

 

The table value of Fat 5% level  = 17 is 3.88. (use One Way ANOVA)            (8 Marks)

 

21 .a) Find the equation of regression lines for the following data.

X	25	28	35	32	36	36	29	38	34	32
y	43	46	49	41	36	32	31	30	33	39

 

(12marks)

 

1. b) Two salesmen A and B are working in a certain district. From a sample survey

conducted by the Head office, the following results were obtained.  State whether

there is any significant difference in the average sales between the two salesmen:

	A	B
No. of sales Average sales (in Rs.) Standard Deviation (in Rs.)	20 170 20	18 205 25

(8 marks)

 

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