B.Sc Corporate Statistics Question Paper 2011

Loyola College B.Sc. Statistics April 2011 Testing Of Hypotheses Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2011

ST 5505 – TESTING OF HYPOTHESES

 

 

 

Date : 18-04-2011              Dept. No.                                                    Max. : 100 Marks

Time : 9:00 – 12:00

 

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Loyola College B.Sc. Statistics April 2011 Probability And Random Variables Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2011

ST 1503/ST 1501 – PROBABILITY AND RANDOM VARIABLES

 

 

 

Date : 06-04-2011             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

Section A                                Answer ALL the questions                                      10×2=20 

 

  1. Define mutually Exclusive events with an example.
  2. Mention any two limitations of classical definition of probability.
  3. What is the probability that a leap year selected at random will have 53 Sundays?
  4. When do we say that an event A is statistically independent with respect to an event B?

Does this mean that event B is statistically independent of the event A?

  1. If A and B are independent events, Show that Ac and B are independent events.
  2. What is the importance of the Baye’s Theorem?
  3. Explain the term Bernoulli trials.
  4. If X is a continuous random variable with probability density function f(x)      =  k x (1-x),

if  0 £          x £ 1    and 0, otherwise, find the value of k. Hence find E (x).

  1. If X and Y are two random variables such that X £ Y, show that

E(X) £ E(Y) provided they exist.

  1. State any two properties of variance of a random variable.

Section B                                Answer any FIVE questions                                                5×8=40 

 

  1. Define Probability Generating Function. (PGF). Obtain the PGF of a random variable X that

follows a Poisson distribution with parameter, l. Hence find the mean and variance of X.

  1. A box contains 6 red, 4 white and 5 black balls. A person draws 4 balls from the box at

random. Find the probability that among the balls drawn, there is at least one ball of each colour.

  1. Using axioms of probability show that, for any two events A and

B,            P (AÈB) + P (AÇB) = P (A)+P (B)

  1. From a vessel containing 3 white and 5 black balls, 4 balls are transferred into an empty vessel.

From this vessel a ball is drawn and found to be white. What is the probability that, out of four

balls transferred, 3 were white and 1 was black?

  1. A bag contains 10 gold and 8 silver coins. Two successive drawings of 4 coins are made such

that (i) coins are replaced before the second trial, (ii)  the coins are not replaced before the

second trial. Find the probability that the first drawing will give 4 gold and the second 4 silver

coins.

 

 

 

 

  1. Sixty per cent of the employees of the XYZ Corporation are college graduates. Of these, ten per

cent are in sales. Of the employees who did not graduate from the college, eighty per cent are

in sales.

  • What is the probability that an employee selected at random is in sales? (b) What is the

probability that an employee selected at random is neither in sales nor a college graduate?

  1. The odds against Manager X settling a wage dispute with the workers are 8: 6. The odds in

favour  of Manager Y settling the same dispute are 14:16. (a) What is the probability that

neither settles the dispute, if they both try independently of each other? (b) What is the

probability that the dispute will be solved?

  1. If X is a continuous random variable with probability density function, f(x) = 1 if 0 < x < 1 and

0, otherwise, Use Chebyshev’s Inequality   to obtain an upper bound for P [ |X –E(X) | > 2s ].

Compare it with the exact probability.

 

Section C                                Answer any TWO questions                                                            2×20=40 

 

  1. (a) If A, B and C are mutually independent show that AÈB and C are independent

(b) An Urn contains four tickets marked with numbers, 112, 121, 211, 222, and one ticket is

drawn at random. Let Ai (i=1, 2, 3, ) be the event that ith digit of the number of the ticket

drawn is 1. Discuss the mutual independence and pair-wise independence of the events.

 

  1. (a) State and prove Bayes theorem for future events.

(b)   Suppose that Urn I contains 1 white, 2 black and 3 red balls. Urn II contains 2 white, I black

and 1 red balls. Urn III contains, 4 white, 5 black and 3 red balls. One Urn is chosen at

random and two balls are drawn from it. They happen to be white and red. What is the

probability that they have come from I, II or III?

  1. (a) State and prove Chebyshev’s inequality. Bring out its importance.

(b) A petrol pump is supplied with petrol once in a day. If its daily volume of sales (X) (in

thousands of litres) is distributed by

f(x)     =  5 (1-x) 4,                  if  0 £  x £       1

What must the capacity be of is tank in order that the probability that its supply will get

exhausted in a given day shall be 0.01?

  1. (a) For any two events A. B and C, show that

P (AÈB÷ C )  = P (A÷ C) + P (B÷ C) – P (AÇB÷ C)

and     P (AÇBC÷ C )  + P (AÇB÷ C) = P (A÷ C).

  • Two computers A and B are to be marketed. A salesman who was assigned the job of finding customers for them has 60% chance of succeeding in the case of computer A and 40% chance of succeeding in the case of Computer B. The two computers can be sold independently. Given that he was able to sell at least one computer, what is the probability that computer A has been sold.

 

 

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Loyola College B.Sc. Statistics April 2011 Statistical Mathematics – I Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SECOND SEMESTER – APRIL 2011

ST 2502/ST 2501 – STATISTICAL MATHEMATICS – I

 

 

 

Date : 08-04-2011              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

 

Answer ALL questions                                                                                             (10×2 =20 Marks)

 

  1. Define least upper bound of a set.
  2. Define convergent sequence.
  3. Define cumulative distribution function and state any two of its properties.
  4. Give an example for a monotonic sequence.
  5. Define absolute convergence and conditional convergence for a series of real numbers.
  6. Define M.G. F of a random variable.
  7. State Roll’s theorem.
  8. Define Taylor’s expansion of a function about x = a.
  9. Define rank of a matrix.
  10. Define symmetric matrix. Give an example.

 

PART – B

 

Answer any FIVE questions                                                                                                        (5×8=40 Marks)

 

  1. Show that every convergent sequence is bounded. Is the converse true? Justify your answer.
  2. Obtain the c.d.f. of the total number of heads occurring in three tosses of a fair coin.
  3. Establish the convergence of (a)  ; (b) .
  4. Show that if a function is derivable at a point, then it is continuous at that point.
  5.  If two random variables X and Y have the joint probability density       

       

Find the marginal densities.

 

  1. Find the Lagrange’s and Cauchy’s remainder after nth term in the Taylor’s series expansion of loge(1+ x).

 

  1.  Verify whether or not the following sets of vectors form linearly independent sets:

       (a) (1, 2, 3), (2, 2, 0)

 

       (b) (3, 1, -4), (2, 2, -3)

  1. Find the inverse of a matrix  .

 

PART – C

 

Answer any TWO questions                                                                                          (2×20=40 Marks)

 

  1. (a) Prove that a non-increasing sequence of real numbers which is bounded below is convergent.

 

(b)Prove that the sequence  given by  is convergent.

 

  1. (a) State and Prove Rolle’s Theorem

 

(b) Find a suitable c of Rolle’s Theorem for the function   

 

                 .

 

  1. A random variable X has the following probability function

 

x 1 2 3 4 5 6 7
 

P(x)

 0 k 2k 2k k2 2k2 7k2+k

 

  • Find k
  • Evaluate (a) (b)  (c)  
  • If , find the minimum value of k 
  • Determine the distribution function of X.

 

  1.  (a) If  

            is the joint p.d.f. of X and Y, find the marginal p.d.f.’s. Also, evaluate                 

            P[ (X < 1)  (Y < 3) ]

(b) Find the rank of the matrix .

 

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Loyola College B.Sc. Statistics April 2011 Statistical Methods Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2011

ST 1502/ST 1500 – STATISTICAL METHODS

 

 

 

Date : 19-04-2011              Dept. No.                                          Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

Answer ALL questions                                                                                           10×2=20

  1. Write any two limitation of statistics.
  2. What is classification?
  3. Mention Various measures of central tendency.
  4. Define Skewness.
  5. Write the normal equations to fit a parabola by the principles of least squares.
  6. Explain curve fitting.
  7. Define correlation.
  8. State any two properties of regression coefficients.
  9. Find the missing frequencies from the following data, (A)=400,  (AB)=250, (B)=500,  N=1200.
  10. Explain Yule’s coefficient of association.

 

PART – B

Answer any FIVE questions.                                                                                 5×8=40

  1. Explain the various types of classification of data.
  2. Distinguish between primary data and secondary data.
  3. Find Arithmetic mean and mode for the following data:

Profit per shop:         0-10      10-20      20-30      30-40      40-50           50-60

No. of shops   :           12         18            27            20          17               6

  1. Define Kurtosis. Also explain various measures of Kurtosis.
  2. Fit a straight line trend for the following data:

Year:             1994         1995           1996               1997               1998               1999

Production      7             9                12                 15                  18                  23

  1. What is a scatter diagram? How does it help us in studying the correlation between two variables with respect to their nature of relationship?
  2. The following table gives the age of cars of certain make and annual maintenance costs. Obtain the regression equation for costs related to age:

Age of cars in years:            2          4          6          8

Maintenance cost

in Rs. Hundreds:                10          20        25        30

 

  1. Find out the coefficient of association from the following data:

Passed                       Failed             Total

Married                         90                                 65                 155

Unmarried                   260                             110               370

 

PART – C

Answer any TWO questions                                                                                  2×20=40

 

  1. a) What do you understand by Tabulation? What are the different parts of a table?

Explain.                                                                                                                               (2+8)

 

  1. b) Draw a histogram and frequency polygon to represent the following data.

 

Weekly wages:         10-15              15-20              20-25              25-30              30-35              35-40

No. of workers;           7                      19                   27                    15                     12                    8                                                                                                                                                                     (7+3)

  1. a) Calculate mean deviation from mean for the following data:

Class interval:     2-4      4-6      6-8      8-10

No. of person:     3         4          2          1                                                                        (3+5)

 

  1. b) Calculate Bowley’s coefficient of Skewness from the following data:

 

Marks:            1-10    10-20    20-30     30-40     40-50         50-60     60-70    70-80

No. of

persons:          10         25         20          15           10            35           25         10           (12)

 

  1. a) Write the procedure to fit a second degree parabola using method of least squares.

(6)

  1. b) Fit a second degree parabola to the following.

 

Year ;      1978           1979               1980               1981               1982               1983

 

Price:       100            107                  128                140                 181                  192        (14)

 

  1. a) Show that the coefficient of correlation lies between -1 and +1.       (10)

 

  1. b) The following results were obtained in a survey:

Boys               Girls

No. of candidates appeared at an examination             800                200

Married                                                                                   150                   50

Married and successful                                                       70                   20

Unmarried and successful                                                 550                 110

Find the association between marital status and the success at the examination both for boys and girls.                                                                                                                                                       (10)

 

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Loyola College B.Sc. Statistics April 2011 Statistical Process Control Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2011

ST 6605/ST 6602 – STATISTICAL PROCESS CONTROL

 

 

 

Date : 09-04-2011              Dept. No.                                                    Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION   A (10 x 2 = 20 Marks )

Answer ALL the questions

  1. What do you mean by the term “ cost of quality” ?
  2. List the characteristics of TQM derived from its definitions.
  3. When do you use Histogram ?
  4. What do you mean by frequency distribution ?
  5. Mention the purpose of the p-chart.
  6. When are C- charts used ?
  7. What are control charts ?
  8. The following are the and R values of  4 sub-groups of readings:

= 10.2 , 12.1, 10.8 and 10.9

R  =  1.1 ,  1.3  , 0.9 and 0.8

A2= 0.73 ; D3 = 0 ; D4 = 2.28  ; d2 = 2.059

Find the control limits for   chart.

  1. What does average total inspection mean?
  2. Define Consumer’s Risk and Producer’s Risk.

 

SECTION B  ( 5 x 8 = 40 Marks )

Answer any FIVE questions

  1. Explain “Cost of Prevention”.
  2. State the benefits of TQM
  3. Explain the Box Plot technique.
  4. Explain the logic behind the usage of 3 sigma control limits.
  5. What are the advantages of variable control charts over attribute control charts?
  6. Distinguish between CUSUM chart and Shewhart  control chart.
  7. What do you mean by Acceptance sampling ? Mention the situations it is most likely to be useful
  8. Explain the OC curve for a single sampling plan.

SECTION   C ( 2 x 20 = 40 Marks )

Answer any TWO questions

  1. a) State the requirements for successful implementation of TQM

 

  1. b) The following are weekly yield data from a semiconductor fabrication facility.  Construct a

Stem and Leaf-plot  by selecting the stem values 5, 6,7,8 and 9.

 

Week :  1     2      3      4      5     6      7     8   9    10   11   12   13   14     15    16    17    18    19   20

Yield   : 58   63   69   72    51   79   83   86   85   78   87   83   64   73     81    68    72    65    91   88

Week:  21     22    23   24   25    26  27   28   29   30   31   32    33    34   35   36    37   38     39    40

Yield   : 64    68    67   60   59    63   64  52   70   92   75   76    81    74   82    76   75    62    63    92

 

 

  1. a) What are p and np charts? How they are constructed?
  2. b) Discuss in detail the criteria for lack of control with respect to  -chart.

 

  1. a) Describe the operational aspects of CUSUM charts and the role of V-mask.
  2. b)  A certain product has been statistically controlled at a process average of 46 and a standard

deviation of 1.00. The product is presently being sold to two customers who have different

specification requirements.  Customer A has established a specification of 48 4.0 for the

product, and customer B has specification of 46  4.0. Use normal distribution and find what

percentage of items go outside the specification limits of (i) Customer A, (ii) Customer B.

 

  1. a) Mention the advantages and disadvantages of Acceptance Sampling.
  2. b) Explain Double Sampling Plan in detail.

 

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Loyola College B.Sc. Statistics April 2011 Estimation Theory Question Paper PDF Download

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ST 5504                       / ST 5500         ESTIMATION THOERY

 

Section A

Answer all the questions                                                                            10×2=20  

 

 

1          Define an Unbiased Estimator.

  1. Define consistency of an estimator. Mention any one of its properties.
  2. What is the importance of factorization theorem?
  3. Define a Sufficient Statistic.
  4. Briefly explain the method of moment estimation.
  5. Explain prior distributions and posterior distributions with reference to Bayesian Estimation.
  6. List out any two properties of Maximum Likelihood estimators.
  7. Define Squared Error Loss function.
  8. Define Best Linear unbiased Estimation. Give an example.
  9. Write down the normal equations of a simple linear regression model.

 

Section B

Answer any five questions                                                                    5×8=40 

 

  1. Let X1,X2, ..Xn be a random sample taken from a normal population with unknown mean and unknown variance. Examine the unbiasedness and consistency of T(x) = (Xi – )2
  2. State and prove a sufficient condition for an estimator to be consistent.

(P.T.O)

13 Let X1,X2, ..Xn be a random sample taken from a population whose probability density function is

f(x, ) =  exp{–  },  >0,  x>0

Use Factorization Theorem to obtain a sufficient statistic for .

 

  1. Show that Poisson distribution is complete.

 

  1. Explain the method of minimum chi-square estimation.

 

  1. Obtain the Maximum Likelihood estimators of the parameters of a normal distribution.

 

  1. X1,X2, X3,and X4 are four independent Poisson random variables with mean . Define T1(x) =  {X1 +3X3}

                          T2(x) ={X1 +2X2+3X3}

                          T3(x) ={X1+X2 +X3+X4}

Examine their unbiasedness and compute their variances. Which one is the best estimator among the three? Find the efficiency of T1(x) and T2(x) with respect to T3(x).

 

  1. Explain in detail Gauss-Markov model.

 

 

 

(P.T.O)

 

 

Section C

Answer any two questions                                                               2×20=40 

 

19        (a)       State and prove Chapman-Robbins inequality. Bring out its importance.

(b) Let X1,X2, ..Xn be a random sample taken from a normal population with unknown mean and unit variance. Obtain Cramer-Rao Lower bound for an unbiased estimator of the mean.                                                 (12 + 8)

 

  1. (a) Show that UMVUE for a parametric function is unique.

(b) State and Prove Rao-Blackwell Theorem.                            (10 + 10)

 

  1. (a) Obtain the moment estimators for Uniform distribution U(a, b).

(b) Show that Maximum Likelihood Estimator need not be unique with an example. Also, show that when MLE is unique, it is a function of the sufficient statistic.                                                                                       (10 + 10)

 

  1. (a) Let X1,X2, ..Xn be a random sample from Bernoulli distribution b(1, q). Obtain the Bayes estimator for q by taking a suitable prior.

(b) State and prove a necessary and sufficient condition for a parametric function to be linearly estimable.                                                     (10 + 10)

 

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Loyola College B.Sc. Statistics April 2011 Operations Research Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B. Ss. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – April 2011

ST6604 / ST6601 – OPERATIONS RESEARCH

Time: 3 hrs                                                                                                    Max.:100 Marks
PART A

Answer ALL questions:                                                                                                             (10 x 2  = 20)

 

  1. Define Basic feasible solution.
  2. What do you mean by Slack variable?
  3. When do we go for artificial variables?
  4. What are the two rules for selecting the entering and leaving variables?
  5. Write the Standard form for the given Linear programming problem.
  1. What do you understand by transportation problem?
  2. What is a traveling salesman problem?
  3. Define a Two- person zero sum game.
  4. Distinguish between PERT and CPM.
  5. What do you mean by Minimax criterion?

 

PART B

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

 

  1. Let us assume that you have inherited Rs. 1,00, 000 from your father – in – law that can be inversted in a combination of only two stock portfolios, with the maximum investment allowed in either portfolio set at Rs. 75, 000. The first portfolio has an average of 10%, whereas the second has 20%. In terms of risk factors associated with these portfolios, the first has a risk rating of 4 (on a scale of 0 to 10) and the second has a risk rating of 9. since you wish to maximize yours returns, you will not accept an average rate of return below 12% or a risk factor above 6. Hence, you face the important question. How much should you invest in each portfolio?

Formulate this as a Linear Programming Problem.

  1. Explain the Two Phase method of solving an LPP.

 

 

 

  1. Find the initial basic feasible solution for the following transportation problem using Vogel’s Approximation method.
From To
9 12 9 6 9 10 5
7 3 7 7 5 5 6
6 5 9 11 3 11 2
6 8 11 2 2 10 9
4 4 6 2 4 2  
  1. Solve the following linear programming problem by graphical method:

Maximize z = x1  + 2x2

Subject to

x1   + 2x2 £ 15

2x1  +   x2 £ 20

x1  + x2 ³ 1

x1,  x2  ³ 0

 

  1. Consider a firm having two factories. The firm is to ship its products from the factories to three retail stores. The number of units available at factories X and Y are 200 and 300 respectively, while those demanded at retail stores A, B and C are 100, 150 and 250 respectively. Rather than shipping directly from factories to retail stores, it is added to investigate the possibility of transhipment. The transportation cost (in rupees) per unit is given below:
Factory Retail Store
X Y A B C
Factory X 0 8 7 8 9
Y 6 0 5 4 3
Retail Store A 7 2 0 5 1
B 1 5 1 0 4
C 8 9 7 8 0

Find the optimal shipping schedule.

 

  1. Solve the following game graphically:

Player B

 

Player A

 

 

 

 

 

 

  1. Determine the total, free and independent floats and identify the critical path for the given project network.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Differentiate between Simplex method and Dual Simplex method.

 

PART C

Answer any TWO questions:                                                                        (2 x 20  = 40)

 

  1. a) Give the Dual for the following Primal.
Maximize z = 5x1 + 2x2

Subject to

6x1 +   x2  ≥ 6

4x1 + 3x2 ≥ 12

x1 + 2x2 ≥ 4

x1,     x2  ≥ 0

19 b) Solve the given problem using Big M method.

Minimize z = x1 + 2x2 + 3x3 –  x4

Subject to

x1 + 2x2 + 3x3 = 15

2x1 +  x2 + 5x3 = 10

x1 + 2x2 + x3 + x4  = 10

x1, x2, x3, x4 ≥ 0                                                                  (5 + 15)

 

 

 

 

 

  1. a)  Reduce a  m x n game to a linear programming problem.:

b) Solve the following assignment problem to find the minimum total expected cost.

  Men
I II III IV
            Job A 42 35 28 21
B 30 25 20 15
C 30 25 20 15
D 24 20 16 12

 

21. a) State the rules for drawing the network diagram.

 

21. b) A project consists of eight activities with the following relevant information:

 

Activity Immediate Predecessor Estimated duration (days)
Optimistic Most likely Pessimistic
A – 1 1 7
B – 1 4 7
C – 2 2 8
D A 1 1 1
E B 2 5 14
F C 2 5 8
G D, E 3 6 15
H F, G 1 2 3

 

(i)                            Draw the PERT network and find out the expected project completion time and variance

(ii)                          What duration will have 95% confidence for project completion?

 

 

 

 

$$$$$$$$

 

 

 

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Loyola College B.Sc. Statistics April 2011 Distribution Theory Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FOURTH SEMESTER – APRIL 2011

ST 4502/ST 4501 – DISTRIBUTION THEORY

 

 

Date : 07-04-2011              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

PART – A

Answer ALL Questions                                                                                                   10 x 2 =20

 

  1. Define : Independence of random variables
  2. Show that under usual notations,  .
  3. State the additive property of Binomial distribution..
  4. Write down the density function of Negative Binomial Distribution.
  5. Write E[X|Y=y] when (X,Y) has bivariate normal distribution.
  6. What is meant by Lack of Memory Property?.
  7. Write the density function of t-statistic with n degrees of freedom
  8. Define : F Statistic.
  9. Write down the general formula for the density function of the first order statistic.
  10. Mention the use of Central limit theorem.

 

PART – B

 

Answer any FIVE Questions                                                                                         5 x 8 =40

 

  1. Find E[X|Y=3], if the joint probability density function of and Y is given by

.

  1. Lethave the joint probability density function

 

 

Compute the correlation coefficient of X and Y.

 

  1. Establish the additive property of independent Poisson variates.
  2. If the moment generating function of a random variable is compute P(X=2 or X=3).
  3. Obtain the mean and variance of beta distribution of first kind with parameters m and n.
  4. Show that if X has uniform distribution defined over [0,1] then -2logx has chi-square distribution with 2 degrees of freedom.
  5. Let and be independent standard normal variates. Derive the distribution of using the moment generating function method.
  6. Find the limiting distribution of sample mean based on a sample of size n drawn from normal distribution with given mean and variance.

 

PART –  C

Answer any TWO Questions                                                                                          2 x 20 =40

 

  1. (a) Let and  be  jointly distributed with density

 

 

Find .

 

(b) Derive the moment generating function of Negative binomial distribution.

 

  1. (a) Show that if X and Y are independent Poisson variates with means and then the

conditional distribution of X given X+Y is binomial.

 

(b) Obtain the distribution of if X and Y are independent exponential variates with

parameter .

 

  1. (a) Derive the density function of F- distribution.

 

(b) Derive the moment generating function of chi-square distribution with n degrees of freedom

and hence find its mean and variance.

 

  1. Derive the distribution of sample mean and sample variance based on a sample drawn from

normal distribution. Also prove they are independently distributed.

 

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Loyola College B.Sc. Statistics April 2011 Design & Analysis Of Experiments Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – APRIL 2011

ST 6603/ST 6600 – DESIGN & ANALYSIS OF EXPERIMENTS

 

 

 

Date : 05-04-2011              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION – A

Answer ALL the questions                                                                                                 (10 X 2 = 20 Marks)

 

  1. State the assumptions used in a linear model.
  2. Distinguish between pair-wise and non-pair-wise contrasts.
  3. What do you mean by randomization in experimental designs?
  4. State the assumptions for ANOVA.
  5. What are the demerits of a completely randomized design?
  6. Give the layout of a 4 x 4 Latin Square Design.
  7. What is meant by a factorial experiment?
  8. What are the advantages of confounding?
  9. What is meant by incomplete block designs?
  10. When do we go for a BIBD?

SECTION – B

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

 

  1. In what way are contrasts helpful in the analysis of experimental data?
  2. Give the statistical analysis of a two-way classification.
  3. Derive the expression to measure the efficiency of RBD over CRD
  4. What is Latin Square Design? Carry out the analysis of LSD.
  5. Explain the least square method of estimating one missing observation in a LSD.
  6. Explain in detail the analysis of 22 factorial experiment.
  7. Give the analysis of 32 factorial experiment.
  8. Develop the intra-black analysis of a BIBD.

SECTION – C

Answer any TWO questions                                                                                  (2 x 20 = 40 Marks)

 

  1. a) Discuss clearly between one-way and two-way classifications of analysis of

variance.

 

  1. b) Describe in detail analysis of variance in one-way classification with suitable

examples.

 

  1. a) What is missing plot technique?  Derive the formula for missing value when one

observation is missing in the case of LSD.

 

  1.   b) Discuss briefly the advantages and disadvantages of a Latin Square Design.

 

  1.   a) Distinguish between  Complete and Partial Confounding.

 

  1.     b) Give the Yates method of computing the factorial effects in a 23 factorial experiment.

 

  1. a) Explain a BIBD with suitable illustration.

 

  1. b) Develop the inter – block analysis of a BIBD stating the model, Hypothesis, ANOVA

and inference.

 

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Loyola College B.Sc. Statistics April 2011 Applied Statistics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2011

ST 5502 – APPLIED STATISTICS

 

 

 

Date : 19-04-2011              Dept. No.                                                  Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer ALL questions                                                                                                  ( 10 x 2 = 20 Marks)

 

  1. State any two uses of index numbers.
  2. What are price and quantity index numbers?
  3. Define additive and multiplicative models in time series.
  4. Indicate the importance of time series in business.
  5. Explain the meaning of vital statistics.
  6. Define crude death rate.
  7. Distinguish between partial and multiple correlation coefficients.
  8. Show that 1 – R223 = (1 – r212)(1 – r213.2)
  9. Explain De Facto method of collecting census data
  10. Define national income.

SECTION  – B

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

 

  1. Explain ‘deflating of index numbers’ with suitable example. What is the need for deflating index numbers?
  2. Given the chain base index numbers, find the fixed base index numbers:

Year                       :    2000    2001    2002    2003     2004    2005

Chain index        :     105        75        71        105       95          90

  1. Explain the method of moving averages in measuring trend.
  2. A firm estimates its sales for a particular year to be Rs. 24,00,000. Given the seasonal indices, calculate the estimates of monthly sales of the firm assuming no trend.

Month                  :  jan  feb  mar  apr  may   jun   july   aug   sep  oct   nov   dec

Seasonal index  :   75   80   98    128  137   119  102  104  100   102     82     73

  1. Define reproduction rates. In what way do total fertility rate, gross reproduction rate and net reproduction rate differ from one another as measures of reproduction?
  2. Find the standardized death rate for the data given below:

Age                  Standard population                              Population A

Population    Specific               Population          Specific

(in ’000)       death rate           (in ’000)                death rate

0 – 5                       8                  50                            12                            48

5 – 15                    10                15                            13                            14

15 – 50                  27                10                            15                             9

50 and above      5                  60                            10                          59

  1. In a trivariate distribution, Find b3
  2. Write a detailed note on NSSO.

SECTION – C

Answer any TWO questions.                                                                                       (2 X 20 = 40 Marks)

 

  1. a) Explain the problems involved in the construction of index numbers.
  2. b) Calculate the price and quantity index numbers for 2005 with 2002 as base year using Fisher’s formula. Also verify whether it satisfies the factor reversal test and time reversal test.

Year           Item I                   Item II                   Item III                 Item IV

Price   qty            Price    qty           Price   qty           Price   qty

2002       5.00     5              7.75       6             9.63     4              12.5       9

2005      6.50    7               8.80      10           7.75     6              12.75     9

  1. a) Explain seasonal variation in a time series. Also explain the link relative method of computing the indices of seasonal variation.
  2. b) The population figures of a country are given below:

Year              :    1911     1921     1931     1941     1951      1961      1971

Population  :     25         25.1      27.9      31.9      36.1      43.9        54.7

(in crores)

Fit an exponential trend y = abx and estimate the population in 2011.

  1. a) Explain the method of fitting a logistic curve by the method of three selected points.
  2. b) Complete the following life table:

x   :       0        1         2          3           4          5           6

  :    100     90       80         75        60        30          0

  1. a) Explain in detail ‘livestock’ and ‘agricultural statistics’.
  2. b) State the properties of multiple correlation coefficient. Also prove that,

 

 

 

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Loyola College B.Sc. Statistics April 2011 Applied Statistics Question Paper PDF Download

by

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2011

ST 5506/ST 5502 – APPLIED STATISTICS

 

 

 

Date : 19-04-2011              Dept. No.                                                  Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer ALL questions                                                                                                  ( 10 x 2 = 20 Marks)

 

  1. State any two uses of index numbers.
  2. What are price and quantity index numbers?
  3. Define additive and multiplicative models in time series.
  4. Indicate the importance of time series in business.
  5. Explain the meaning of vital statistics.
  6. Define crude death rate.
  7. Distinguish between partial and multiple correlation coefficients.
  8. Show that 1 – R223 = (1 – r212)(1 – r213.2)
  9. Explain De Facto method of collecting census data
  10. Define national income.

SECTION  – B

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

 

  1. Explain ‘deflating of index numbers’ with suitable example. What is the need for deflating index numbers?
  2. Given the chain base index numbers, find the fixed base index numbers:

Year                       :    2000    2001    2002    2003     2004    2005

Chain index        :     105        75        71        105       95          90

  1. Explain the method of moving averages in measuring trend.
  2. A firm estimates its sales for a particular year to be Rs. 24,00,000. Given the seasonal indices, calculate the estimates of monthly sales of the firm assuming no trend.

Month                  :  jan  feb  mar  apr  may   jun   july   aug   sep  oct   nov   dec

Seasonal index  :   75   80   98    128  137   119  102  104  100   102     82     73

  1. Define reproduction rates. In what way do total fertility rate, gross reproduction rate and net reproduction rate differ from one another as measures of reproduction?
  2. Find the standardized death rate for the data given below:

Age                  Standard population                              Population A

Population    Specific               Population          Specific

(in ’000)       death rate           (in ’000)                death rate

0 – 5                       8                  50                            12                            48

5 – 15                    10                15                            13                            14

15 – 50                  27                10                            15                             9

50 and above      5                  60                            10                          59

  1. In a trivariate distribution, Find b3
  2. Write a detailed note on NSSO.

SECTION – C

Answer any TWO questions.                                                                                       (2 X 20 = 40 Marks)

 

  1. a) Explain the problems involved in the construction of index numbers.
  2. b) Calculate the price and quantity index numbers for 2005 with 2002 as base year using Fisher’s formula. Also verify whether it satisfies the factor reversal test and time reversal test.

Year           Item I                   Item II                   Item III                 Item IV

Price   qty            Price    qty           Price   qty           Price   qty

2002       5.00     5              7.75       6             9.63     4              12.5       9

2005      6.50    7               8.80      10           7.75     6              12.75     9

  1. a) Explain seasonal variation in a time series. Also explain the link relative method of computing the indices of seasonal variation.
  2. b) The population figures of a country are given below:

Year              :    1911     1921     1931     1941     1951      1961      1971

Population  :     25         25.1      27.9      31.9      36.1      43.9        54.7

(in crores)

Fit an exponential trend y = abx and estimate the population in 2011.

  1. a) Explain the method of fitting a logistic curve by the method of three selected points.
  2. b) Complete the following life table:

x   :       0        1         2          3           4          5           6

  :    100     90       80         75        60        30          0

  1. a) Explain in detail ‘livestock’ and ‘agricultural statistics’.
  2. b) State the properties of multiple correlation coefficient. Also prove that,

 

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Loyola College B.Sc. Statistics Nov 2011 Basic Sampling Theory Question Paper PDF Download

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