Loyola College Statistics For Management Question Papers Download
Loyola College B.Sc. Commerce April 2011 Statistics For Management Question Paper PDF Download
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – COMMERCE & BUSIN. ADM.
FOURTH SEMESTER – APRIL 2011
ST 4208 – STATISTICS FOR MANAGEMENT
Date : 05042011 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
SECTION A (10 X 2 = 20 marks)
Answer ALL questions.
 Define probability and give an example.
 State addition theorem on probability.
 State the Central Limit Theorem.
 Explain the term standard error.
 Define index number and discuss their importance.
 Discuss any two steps in the construction of a cost of living index by the family budget method.
 Distinguish between the control limits and tolerance limits.
 Distinguish between np chart and p chart.
 Define the term feasible solution.
 What is meant by balanced and unbalanced transportation problem.
SECTION B (5 X 8 = 40 Marks)
Answer any FIVE questions
 State and prove Baye’s theorem.
 A subcommittee of 6 members is to be formed out of a group consisting of 7 men and 4 women calculate the probability that subcommittee will consist of.
 a) exactly 2 women b) at least 2 women.
 Two Urns contain respectively 10 white, 6 red and 9 black and 3 white 7 red and 15 black balls.
One ball is drawn from each Urn. Find the probability that (i) Both balls are red (ii) Both balls
are of the same colour.
14.If a random variable X follows a Poisson distribution such that P[ X = 2 ] = P[X=1].
Find P[X=0]. ( e ^{2} ^{ }= 0.13534).
 In a survey of 200 boys, of which 75 are intelligent, 40 of the intelligent boys have skilled fathers while 85 of the unintelligent boys have unskilled fathers. Do these figures support the hypothesis that
skilled fathers have intelligent boys. Use chisquare – test of 5 % level.
 From the following data of the whole sale prices of wheat for the ten years construct
Index numbers taking (a) 1979 as base and (b)by chain base method
year  1988  1989  1990  1991  1992  1993  1994  1995  1996  1997 
Price of
Wheat 
50  60  62  65  70  78  82  84  88  90 
 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.
 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.
SECTION C (2 X 20 = 40 Marks)
Answer any TWO questions
19.(a) A Company has four production sections viz. S1, S2, S3 and S4 , which contribute 30%, 20%, 28% and 22% of the total output. It was observed that those sections respectively produced 1%, 2%, 3% and 4% defective units. If a unit is selected at random and found to be defective, what is the probability that the units so selected has come from either S1 or S4.? (10)
19.(b)The customer accounts of a certain departmental store have an average balance of Rs.120 and a standard deviation of Rs.40. Assuming that the account balances are normally distributed, find
 What proportion of accounts is over Rs.150?
 What proportion of accounts is between Rs.100 and Rs.150?
(iii) What proportion of accounts is between Rs.60 and Rs.90 ? (10)
 (a) The sales manager of a large company conducted a sample survey in states A and B taking 400
Samples in each case. The results were as follow
State A State B
Average sales Rs.2500 Rs.2200
Standard Deviation Rs.400 Rs.550
Test whether the average sales is the same in the two states. Test at 1% level. (10)
20(b) The following table gives the fields of 15 samples of plot under three varieties of seed.
A  B  C 
20  18  25 
21  20  28 
23  17  22 
16  15  28 
20  25  32 
Test using analysis of variance whether there is a significant difference in the average yield of seeds
21.(a) The following data show the values of sample mean (x) and the range (R) for ten samples of size 5 each calculate the values for central line and control limits for mean chart and determine whether the process is control.
Sample  1  2  3  4  5  6  7  8  9  10 
Mean  11.2  11.8  10.8  11.6  11.0  9.6  10.4  9.6  10.6  10.6 
Range(R)  7  4  8  5  7  4  8  4  7  9 
( For n = 5 , A_{2}=0.577,D_{2 }= 0, D_{4}= 2.115)
21(b).Calculate Laspeyre’s Index number, Paasche’s price index number and MarshallEdgeworth Index and how it satisfies Time reversal test and Factor reversal test.
Commodity  1980  1981  
Price
(in Rs.) 
Quantity
(in kgs.) 
Price
(in Rs.) 
Quantity
(in kgs.) 

A  20  15  30  10 
B  30  18  40  15 
C  10  20  45  10 
D  15  25  25  5 
22(a)Find the initial basic feasible solution by Vogel’s Approximation method.
Distribution Centers
Plants  D_{1}  D_{2}  D_{3}  Supply  
P_{1}  16  19  12  14  
P_{2}  22  13  19  16  
P_{3}  14  28  8  12  
Demand  10  15  17 
22(b) Solve the following game by graphical method.
Player A
a_{1 }a_{2 }a_{3 }a_{4} _{ }
b_{1} 2 5 6 4
Player B
b_{2} 4 3 1 6
Loyola College B.Com Corporate & Secretaryship April 2007 Statistics For Management Question Paper PDF Download
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

BBA & B.Com. Corp. DEGREE EXAMINATION
FOURTH SEMESTER – APRIL 2007
ST 4203 – STATISTICS FOR MANAGEMENT
Date & Time: 19/04/2007 / 9:00 – 12:00 Dept. No. Max. : 100 Marks
SECTION A
Answer ALL questions. (10 x 2 =20 marks)
 Define equally likely events and give an example.
 The mean of a Binomial distribution is 4 and variance is 3. Find P(X = 15).
 What is the objective of statistical quality control?
 Name some variable control charts.
 State the addition theorem of probability.
 What are index numbers? What do they measure?
 State any two methods of constructing weighted index numbers.
 State the minimaxmaximin principle in game theory.
 Find the value of the game:
B_{1}  B_{2}  
A_{1}  0  2 
A_{2}  1  4 
 What are the two types of errors in testing of hypothesis?
SECTION B
Answer any FIVE questions. (5 x 8 =40 marks)
 An urn contains 6 white, 4 red and 9 blue balls. If 3 balls are drawn at random, find the probability that,
 2 of the balls drawn are white, (ii) one is of each colour
 none is red, (iv) atleast one is white
 For a Binomial distribution with parameters n = 5, p = 0.3, find the probabilities of getting, (i) atleast 3 successes, (ii) atmost 3 successes
(iii) exactly 3 failures, (iv) exactly 3 successes
 Construct a control chart for C, ie., number of defects from the following data pertaining to the imperfections in 20 pieces of cloth of equal length in a certain make of polyester and infer whether the process is in a state of control: 2, 3, 5, 8, 12, 2, 3, 4, 6, 5, 6, 10, 4, 6, 5, 7, 4, 9, 7, 3.
 Explain quality assurance, statistical process control, and types of control charts.
 The following data relate to the prices and quantities of 5 commodities in the years 2005 and 2006. Construct the following index numbers for prices for the year 2006, taking 2005 as the base, (i) Laspeyre’s, (ii) Paasche’s, (iii) Fisher’s Ideal,
(iv) Bowleys.
Commodities

Base Year  Current Year  
Quantity  Price  Quantity  Price  
A  8  4  10  9 
B  7  3  8  5 
C  6  4  5  8 
D  5  2  7  4 
 (i) Define Linear Programming.
(ii) A company has 3 operational departments (weaving, processing and packing) with capacity to produce 3 different types of clothes namely suitings, shirtings and woolens yielding profit of Rs. 2, Rs. 4, and Rs. 3 per metre respectively. One metre suiting requires 3 minutes in weaving, 2 minutes in processing and 1 minute in packing. Similarly one metre of shirting requires 4 minutes in weaving, 1 minute in processing and 3 minute in packing, while one metre of woolen requires 3 minutes in each department. In a week, total run time of each department is 60, 40 and 80 hours for weaving, processing and packing departments respectively. Formulate the LPP to find the product mix to maximize the profit.
 Solve the following game graphically:
Player B
Player A
 Set up an ANOVA table for the following per hectare yield (in 100 Kgs) for 3 varieties of rice, each grown in 4 plots:
Variety of rice  
Plots of land  R_{1}  R_{2}  R_{3} 
1  6  5  5 
2  7  5  4 
3  3  3  3 
4  8  7  4 
Test whether there is significant difference among the average yields in the 3 varieties of wheat, at 5 % level.
SECTION C
Answer any TWO questions. (2 x 20 =40 marks)
 (i) Write down the probability distribution function of a Poisson random variable, and fit a poisson distribution to the following data: (Given e ^{_ .05} = 0.61)
X  0  1  2  3  4 
Frequency  122  122  60  15  2 
(ii) Students of a class were given an aptitude test. Their marks were found to be normally distributed with mean 60 and standard deviation 5. What percentage of the students scored:
 more than 60 marks, (b) less than 56 marks (c) between 45 and 65 marks. (12 + 8)
 From the following data calculate the control limits for the mean and range control charts and also check if the process is in control. Measurements of the units are given in cms.
S.No of Samples  
1  2  3  4  5  6  7  8  9  10 
50  51  50  48  46  55  45  50  47  56 
55  50  53  53  50  51  48  56  53  53 
52  53  48  50  44  56  53  54  49  55 
49  50  52  51  48  47  48  53  52  54 
54  46  47  53  47  51  51  57  54  52 
U
N
I
T
S
Commodity  2002  2003  2004  2005  2006 
I  2  3  5  7  8 
II  8  10  12  4  18 
III  4  5  7  9  12 
 (i) Calculate fixed base index numbers and chain base index numbers for the following
(ii) Determine the least cost allocation of the available machines to 5 jobs.
Jobs  
Machines  A  B  C  D  E 
1  25  29  31  42  37 
2  22  19  35  18  26 
3  39  38  26  20  33 
4  34  27  28  40  32 
5  24  42  36  23  45 
(10 + 10)
 There are three sources A, B, C which store a given product. These sources supply these products to four dealers D, E, F, G. The cost (Rs.) of transporting the products from various sources to various dealers, the capacities of the sources and the demands of the dealers are given below.
D  E  F  G  Supply  
A  6  8  8  5  30 
B  5  11  9  7  40 
C  8  9  7  13  50 
Demand  35  28  32  25 
Find out the solution for transporting the products at a minimum cost by using (i) NorthWest Corner Rule, (ii) Least Cost method and (iii) Vogel’s Approximation Method. Compare the costs and write down the best solution.
Loyola College B.Com April 2012 Statistics For Management Question Paper PDF Download
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 : 19042012 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
SECTION A
Answer ALL questions. (10 X 2 = 20 marks)
 State addition theorem on probability.
 Write Any four properties of normal distribution
 Explain the term standard error.
 State the assumptions made in analysis of variance.
 Define index number and discuss their importance.
 What is meant by Cost of Living Index Number?
 What is statistical quality control? Point out its importance in the industrial world?
 Distinguish between p chart and c chart.
 Mention any two applications of linear programming.
 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.
 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?
 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
 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.
 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 
 State the advantages and disadvantages of statistical quality control.
 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.
 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:
 (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 Chisquare^{ }test at 5%^{ } level to determine if any distinction is made in appointment on the basis of sex. (10)
 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)
Loyola College B.B.A. Business Administration April 2008 Statistics For Management Question Paper PDF Download
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Com.,B.B.A. DEGREE EXAMINATION – CORPORATE & BUS.ADMIN.

FOURTH SEMESTER – APRIL 2008
ST 4208 / 4203 – STATISTICS FOR MANAGEMENT
Date : 24/04/2008 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION A
Answer ALL questions. (10 x 2 =20 marks)
 Define a random experiment and give an example.
 A random experiment has the following probability function as follows, find E(X).
X  1  0  1 
P(X)  0.2  0.3  0.5 
 Differentiate between statistics and parameters.
 What are the assumptions of analysis of variance test?
 Define index numbers.
 Name any 2 methods of constructing unweighted index numbers.
 What are variable control charts? Name them.
 For a quality control process, the mean is 0.5230 cm and standard deviation is 0.0032 cm. Calculate 3σ upper and lower control limits, if the sample size is 4.
 Define a Linear Programming Problem.
B
 Solve the following game: A
SECTION B
Answer any FIVE questions. (5 x 8 =40 marks)
 Aakash can solve 3 problems out of 5, Deepak can solve 2 out of 5 and Godfrey can solve 3 out of 4.What is the probability that:
 The problem will be solved
 Only two will solve the problem
 The probability of an increase in demand of a particular product in the next year is 0.75. If this demand increase takes place, the probability that the sales will increase is 0.7. If there is no demand increase, the probability that the sales will increase is 0.5. Given that at the end of the year, the sale has risen, what is the probability that there was an increase in demand of the product?
 A college conducts both day and evening classes intended to be identical. For a sample of 100 day students, the results was: = 72.4 and σ = 14.8 and for a sample of 200 evening students, the exam results was: = 73.9 and σ = 17.9. Are the two means statistically equal at 5% level of significance?
 Edible oil is packed in tins holding 16 Kg each. The filling machine can maintain this but with a standard deviation of 0.5 Kg. Samples of 25 are taken from the production line. If the sample mean is 16.35 Kg, can we be 95 % sure that the sample has come from a population of 16 Kg tins?
 Explain the uses of index numbers, and state the problems in the construction of index numbers.
 The following table gives an inspection data on completed CD’s there were 2000 CD’s in 20 lots of 100 each. Draw a control chart for fraction defectives, and check if the process is in control.
Lot No.  1  2  3  4  5  6  7  8  9  10 
No. of defectives  5  10  12  8  6  5  6  3  3  5 
Lot No.  11  12  13  14  15  16  17  18  19  20 
No. of defectives  4  7  8  2  3  4  5  8  6  10 
 Solve the following Linear Programming Problem: Min z = 2 x + y subject to the constraints, x ≤ 4, x + y ≥ 1, 5 x + 10 y ≤ 50, x, y ≥ 0.
 Given the following data, determine the least cost allocation of the available machines M_{1}, M_{2, }M_{3, }M_{4 }and M_{5}, to 5 jobs A, B, C, D and E.
A  B  C  D  E  
M_{1}  25  29  31  42  37 
M_{2}  22  19  35  18  26 
M_{3}  39  38  26  20  33 
M_{4}  34  27  28  40  32 
M_{5}  24  42  36  23  45 
SECTION C
Answer any TWO questions. (2 x 20 =40 marks)
 (i) The screws produced by a certain machine were checked by examining samples of 128. The following table shows the distribution of 128 samples according to the number of defective items they contained:
No. of defectives  0  1  2  3  4  5  6  7 
No. of samples  7  6  19  35  30  23  7  1 
Fit a binomial distribution and find the expected frequencies if the chance of a screw being defective is ½. Also find the mean and variance of the distribution.
(ii) EastWest airlines have the policy of employing women whose height is between 62 and 69 inches. If the height of women is approximately normally distributed with a mean of 64 inches and a standard deviation of 3 inches, out of the 1000 applications receives, find the number of applicants that would be (i) too tall (> 69), (ii) too short (< 62)
 (i) A random sample is selected from each of 3 makes of ropes and their breaking strengths(in pounds) are measured with the following results:
I  70  72  75  80  83  
II  100  110  108  112  113  120  107 
III  60  65  57  84  87  73 
Test whether the breaking strength of ropes differ significantly at 5% level of significance.
(ii) Construct Laspeyre’s, Paasche’s and Fisher’s Index numbers for the following data.
2006  2007  
Commodity  Price  Quantity  Price  Quantity 
A  2  8  4  6 
B  5  10  6  5 
C  4  14  5  10 
D  2  19  2  13 
 Construct a control chart for mean and range for the following data on the basis of fuses, samples of 5 being taken every hour. Comment on whether the production seems to be under control.
Sample Number  
1  2  3  4  5  6  7  8  9  10  11  12 
42  42  19  36  42  51  60  18  69  64  61  15 
65  45  24  54  51  74  60  20  109  90  78  30 
75  68  80  69  57  75  72  27  113  93  94  39 
78  72  81  77  59  78  95  42  118  109  109  620 
87  90  81  84  78  132  138  60  153  112  136  84 
 There are three sources A, B, C which store a given product. These sources supply these products to four dealers D, E, F, G. The cost (Rs.) of transporting the products from various sources to various dealers, the capacities of the sources and the demands of the dealers are given below.
D  E  F  G  Supply  
A  3  7  6  4  5 
B  2  4  3  2  2 
C  4  3  8  5  3 
Demand  3  3  2  2 
Find out the solution for transporting the products at a minimum cost by using (i) NorthWest Corner Rule, (ii) Least Cost method and (iii) Vogel’s Approximation Method. Compare the costs and write down the best solution.
Loyola College B.B.A. Business Administration April 2009 Statistics For Management Question Paper PDF Download
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.B.A DEGREE EXAMINATION – BUSINESS ADMINISTRATION

FOURTH SEMESTER – April 2009
ST 4208/ ST 4203 – STATISTICS FOR MANAGEMENT
Date & Time: 27/04/2009 / 9:00 – 12:00 Dept. No. Max. : 100 Marks
SECTION A (10 X 2 = 20 Marks)
Answer ALL questions.
 State the axioms of “Probability”.
 Distinguish between Binomial and Poisson distribution.
 State the Central Limit Theorem.
 Write down the assumptions made in Analysis of Variance.
 Define Index Number and discuss its importance.
 What is meant by Cost of Living Index Number? What are its uses?
 What is statistical Quality Control? Point out its importance in the Industrial World.
 Distinguish between the Control Limits and Tolerance Limits.
 Mentions any two applications of Linear Programming.
 What is nondegeneracy problem in T.P.?
SECTION B (5 X 8 = 40 Marks)
Answer any FIVE questions
 Define (i) Mutually Exclusive Events.
(ii) Exhaustive Events.
(iii) Independent Events.
 Two Urns contain respectively 10 white, 6 red and 9 black and 3 white 7 red and
15 black balls. One ball is drawn from each Urn. Find the probability that
(i) Both balls are red
(ii) Both balls are of the same colour.
 An automatic machine fills in tea in sealed tins with mean weight of tea 1 kg. and S.D. 1gm. A random sample of 50 tins was examined and it was found that their mean weight was 999.50 gms.
Is the machine working properly?
 The following are Index Numbers of Prices (1988 = 100)
Year  1988  1989  1990  1991  1992  1993  1994  1995  1996  1997 
Index  100  110  120  200  400  410  400  380  370  340 
Calculate the chain base index.
 The number of defects defected 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.
 Explain the various types of control charts in use.
 Solve the following unbalanced assignment problem of minimizing total time for
doing all the Jobs.
JOBS  
J1  J2  J3  J4  J5  
A  6  2  5  2  6  
B  2  5  8  7  7  
C  7  8  6  9  8  
OPERATORS  D  6  2  3  4  5  
E  9  3  8  9  7  
F  4  7  4  6  8  
 Out of 8000 graduates in a town, 800 are females and out of 1600 graduate employees
120 are female. Use chisquare^{ }test at 5%^{ } level, to determine if any distinction is made in appointment
on the basis of sex.
SECTION C (2 X 20 = 40 Marks)
Answer any TWO questions
 (a) 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 (i) first box (ii) second box ?
(b) A machine produced 20 defective articles in a batch of 400. After overhauling, it produced 10 defectives in a batch of 300. Has the machine improved? ( 10 +10 )
 (a) Value of a Variety in two samples are given below:
Sample I  5  6  8  1  12  4  3  9  6  10 
Sample II  2  3  6  8  1  10  2  8  *  * 
Test the significance of the difference between the two population means, stating the assumptions involved.
20 (b) The following table gives the fields of 15 samples of plot under three varieties of seed.
A  B  C 
20  18  25 
21  20  28 
23  17  22 
16  15  28 
20  25  32 
Test using analysis of variance whether there is a significant difference in the average yield of seeds. ( 10 +10 )
21 (a) The following figures give the number of defectives in 20 samples ,containing 2000 items
425, 430, 216, 341, 225, 322, 280, 306, 337, 305, 356, 402, 216, 264, 126, 409, 193, 280, 389, 350.
Calculate the values for central line and the control limits for p chart.
(b) Calculate Laspeyre`s , Paasche`s and Fishers Index Number for the data given below.
Base Year  Current Year  
Commodity  Price  Expenditure  Price  Expenditure 
A  5  50  6  72 
B  7  84  10  80 
C  10  80  12  96 
D  4  20  5  30 
E  8  56  8  64 
( 10 +10 )
22 (a) Solve the following transportation problem by obtaining the initial solution
by VAM .
Source  Destination  
1 2 3 4  Supply  
A
B
C

7 3 8 5
5 2 6 11
3 6 5 2 
160
180
100 
Demand  40 100 120 180  440 
22 (b) Solve the following game by using dominance rule:
PLAYER B  PLAYER B  
Y1  Y2  Y3  Y4  
X1  19  6  7  5  
X2  7  3  14  6  
X3  12  8  18  4  
X4  8  7  13  1 
( 10 +10 )