LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Com., B.B.A., DEGREE EXAMINATION – COMM. & BUSI. ADMIN.

FOURTH SEMESTER – APRIL 2012

ST 4208 – STATISTICS FOR MANAGEMENT

 

 

 

Date : 19-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION A

     Answer ALL questions.                                                                                           (10 X 2 = 20 marks)

    

1. State addition theorem on probability.

 

2. Write Any four properties of normal distribution
3. Explain the term standard error.
4. State the assumptions made in analysis of variance.
5. Define index number and discuss their importance.
6. What is meant by Cost of Living Index Number?

 

7. What is statistical quality control? Point out its importance in the industrial world?
8. Distinguish between p chart and c chart.
9. Mention any two applications of linear programming.
10. What is balanced and unbalanced Transportation problem?

 

SECTION B

     Answer any FIVE questions:                                                                      (5 X 8 = 40 Marks)

 

11.State and prove Boole’s  inequality.

 

12. Five men in a company of 20 are graduates. If 3 men are picked out from this 20 persons at random,

what  is the probability that (i) all are graduates (ii) at least one is graduate?

 

13. The following table gives the data on the hardness of wood stored outside and inside the room.

 

	Outside	Inside
Sample Size	40	110
Mean	117	132
Sum of squares of deviation from mean	8655	27244

 

Test whether the hardness is effected by weathering at 5% level

 

 

 

 

14. An IQ test was administered to 5 persons before and after they were trained. The results are given below:

Candidates	I	II	III	IV	V
IQ before training	110	120	123	132	125
IQ after training	120	118	125	136	121

 

 

 

 

 

Test whether there is any change in IQ after the training programme. Use 5% level of  significance.

 

15. From the following data of wholesale prices of wheat construct Chain base index taking 1993 as origin.

Year	1991	1992	1993	1994	1995	1996	1997	1998	1999	2000
Price(in Rs.) per quintal	50	60	62	65	70	78	82	84	88	90

16. State the advantages and disadvantages of statistical quality control.

 

17. The following table gives the number of defective items found in 20 successive samples of 100 items each

2    6   2   4   4   15   0   4   10   18   2   4   6   4   8   0   2   2   4   0

 

Comment whether the process is under control. Suggest suitable control limits for the future.

 

18. A company produces two types of pens say A and B. Pen A is a superior quality and pen B is a lower quality. Profit on pen A and pen B are Rs.5 and Rs.3 per pen respectively. Raw materials required for each Pen A are twice as that of pen B the supply of raw materials is sufficient only 1000 pens of per day. Pen A requires a special clip of only 400 clips are available per day. For pen B only 700 clips are available per day. Find graphically the product mix so that the company can make maximum profit.

SECTION   C                                    (2 X 20  =  40 Marks)

Answer any TWO questions:

19. (a) A factory manufacturing television has four units A, B, C and D. The units A, B, C and D manufactures 15%, 20%, 30%, and  35%, of the total output respectively. It was found that out of their outputs 1%, 2%, 2% and 3% are defective. A television is chosen at random from the output and found to be defective. What is the probability that, it came from unit D?                                                                       (10)

 

19.(b) Out of 8000 graduates in a town, 800 are females and out of 1600 graduates employees 120 are female.   Use Chi-square  test at 5%   level to determine if any distinction is made in appointment on the  basis of sex.                                                                                                                                 (10)

20. Develop the Two- way ANOVA  for the following data:

 

                                                                  Treatment

 

	A	B	C	D
I	3	4	6	6
II	6	4	5	3
III	6	6	4	7

 

 

 

(20)

21.(a) The number of defects detected in 20 items are given below

Item No       :  1   2    3    4     5    6   7    8     9    10    11     12    13    14   15   16   17   18  19    20

No. of defects         :  2    0   4   1      0     0   8     1    2     0      6        0     2      1    0      3    2      1   0    2

Test whether the process is under control. Device a suitable scheme for future.                 (10)

21(b)Using the following data compute Fisher’s Ideal price and Quantity Index numbers for the current

year and also verify factor reversal test.

COMMODITY	Base year price	Current Year Price	Base year quantity	Current Year quantity
A	8	12	6	4
B	10	12	8	8
C	14	18	4	4
D	4	2	6	10
E	10	14	10	8

 

 

 

 

 

 

 

(10)

22(a). A company has 4 machine to be assigned to 4 of the 4 workers available for this purpose.

The expected production from each machine operated by each workers is given below.

 

WORKERS

	W1	W2	W3	W4
I	41	72	39	52
II	22	29	49	65
III	27	39	60	51
IV	45	50	48	52

 

MACHINE

 

 

 

 

Suggest optimal assignment of workers to machine.                                                                     (10)

22(b).Solve the following Transportation problem by using Vogel’s Approximation Method.

 

	D1	D2	D3	D4	D5	Availability
A1	5	7	10	5	3	5
A2	8	6	9	12	14	10
A3	10	9	8	10	15	10
Demand	3	3	10	5	4

(10)

 

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