B.Sc Corporate Statistics Question Paper 2010

Loyola College B.Sc. Statistics April 2010 Econometric Methods Question Paper PDF Download

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Loyola College B.Sc. Statistics Nov 2010 Testing Of Hypotheses Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2010

ST 5505/ST 5501 – TESTING OF HYPOTHESES

 

 

 

Date : 01-11-10                     Dept. No.                                                     Max. : 100 Marks

Time : 9:00 – 12:00

SECTION – A

 

 

ANSWER ALL QUESTIONS.                                                                                        (10 X 2 =20 marks)

 

  1. What is a composite hypothesis? Give an example.
  2. Define: Critical region.
  3. Given an example of a density function which is not a member of the one parameter exponential family.
  4. When do you say a given family of density functions has MLR property?
  5. What are Type I and II errors?
  6. Define: Likelihood ratio.
  7. What are confidence intervals?
  8. State the test statistic for testing the equality of variances of two normal populations.
  9. Define: Empirical Distribution Function.
  10. Mention the use of Kolmogrov one sample test.

 

SECTION – B

 

ANSWER ANY FIVE QUESTIONS                                                                               (5 X 8 =40 marks)

 

  1. A sample of size one is drawn from a population with probability density function . To test the hypothesis against the following test is suggested: “Reject H if x > 4”. Compute the size and power of the test.
  2. Obtain the Best Critical Region for testing H: q = q1 versus K: q = q2 ( > q­1) when a sample of size ‘n’ is drawn from f(x; q ) = , 0 < x < 1 ( q > 0)
  3. Show that the family of Binomial densities has MLR property.
  4. Explain SPRT in detail.
  5. Derive the likelihood ratio test for testing against based on a sample of size 10 drawn from
  6. Explain the process of testing the significance of correlation coefficient.
  7. Obtain the confidence interval for the mean of a normal distribution with unknown variance.
  8. Explain in detail Median test.

(P.T.O)

SECTION – C

 

ANSWER ANY TWO QUESTIONS                                                                     (2 X 20 = 40 marks)

 

  1. a) State and prove Neyman Pearson lemma.
  2. b) Derive the MPT of level 0.05 for testing against based on a sample

of size two drawn from

  1. a) Show that the family of Uniform distributions  has MLR property.

 

  1. b) Derive the UMPT of level 0.05 for testing against based on a sample of size 10

drawn from

 

  1. a) Obtain the SPRT for testing H: p =1/2 versus K: p = 1/3 when a sample is drawn sequentially

from B(1,p) with α = β = 0.1.

  1. b) Explain the procedure for testing the equality of means of two independent normal populations

with common unknown variance.

 

  1. a) Explain Mann-Whitney U test.
  2. b) Write a descriptive note on non-parametric methods.

 

 

 

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Loyola College B.Sc. Statistics Nov 2010 Statistical Methods Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – NOVEMBER 2010

ST 1502/ST 1500 – STATISTICAL METHODS

 

 

 

Date : 10-11-10                     Dept. No.                                                    Max. : 100 Marks

Time : 1:00 – 4:00

 

PART – A

 Answer ALL the questions                                                                                                             [10×2=20]

 

  1. State any two limitations of statistics.
  2. Write down the types of Scaling with examples.
  3. Define measures of central tendency.
  4. What do you mean by skewness?
  5. Write down the normal equations for the exponential curve.
  6. What is curve fitting?
  7. State the assumptions underlying in Karlpearson’s correlation co-efficient.
  8. Define probable error.
  9. Examine the consistency of the following data:

N= 1000; (A)= 600; (B)= 500; (AB)= 50.

  1. Write the Yule’s Coefficient of association between the attributes.

 

PART – B

 

 Answer any FIVE questions                                                                                                           [5×8=40]

 

  1. Describe the various types of diagrammatic representation of data.
  2. Draw the cumulative frequency curve. find the quartiles for the following data:
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70
No of Students 4 8 11 15 12 6 3

 

 

 

  1. Find the missing frequencies using the median value 46 for the following data:
Variable 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Total
Frequency 12 30 ? 65 ? 25 18 219

 

  1. The first of the two samples has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation √13.44. Find the standard deviation of the second group.
  2. Show that the correlation coefficient cannot exceed unity.
  3. Obtain a straight line trend equation by the method of least squares. Find the value for the

missing year 1961.

Year 1960 1962 1963 1964 1965 1966 1969
Value 140 144 160 152 168 176 180
  1. Find the association of A and B in the following cases:
    1. N = 1000; (A)= 470;  ( B)= 620 and (AB)= 320
    2. (A)= 490; (AB)= 294; (α)= 570 and (αβ)= 380
  • (AB)= 256; (αB)= 768; ( Aβ)= 48 and ( αβ)= 144.
  1. Find the angle between the two regression lines.

 

PART – C

Answer any TWO questions                                                                                                       [2×20=40]

 

  1. a) Describe the various types of classification and tabulation of data in detail.                              (12)

 

  1. b) A cyclist pedals from his house to his college at a speed of 10Kmph and back from

the college to his house at 5Kmph. Find the average speed.                                                         (8)

 

  1. a) For a distribution, the mean is 10, variance is 16, γ1 is +1 and β2 is 4. Obtain

the first four moments about the origin. Make a comment on distribution.

 

  1. b) Calculate i) Quartile Deviation and ii) Mean Deviation from mean for the

following data:

Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70
No of Students 6 5 8 15 7 6 3

 

  1. a) The following table gives, according to age, the frequency of marks obtained by 100 students

in an intelligence test: Calculate the Correlation Coefficient.

Age 18 19 20 21 Total
Marks
10-20 4 2 2 0 8
20-30 5 4 6 4 19
30-40 6 8 10 11 35
40-50 4 4 6 8 22
50-60 0 2 4 4 10
60-70 0 2 3 1 6
Total 19 22 31 28 100

 

  1. b) Predict the value of Y when X=6 for the following data:

Σx=55; Σxy=350; Σy=55; Σx2=385 and n=10.

  1. a) Fit an exponential curve of the form Y=abx to the following data:
X 1 2 3 4 5 6 7 8
Y 1.0 1.2 1.8 2.5 3.6 4.7 6.6 9.1

 

  1.       b) 800 candidates of both sex appeared at an examination. The boys outnumbered the

girls by 15% of the total. The number of candidates who passed exceed the number

failed by 480. Equal number of boys and girls failed in the examination.

Prepare a 2×2 table and find the coefficient of association. Comment on the result.

 

 

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Loyola College B.Sc. Statistics Nov 2010 Statistical Mathematics – II Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – NOVEMBER 2010

ST 3503/ST 3501/ST 3500 – STATISTICAL MATHEMATICS – II

 

 

 

Date : 30-10-10                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

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

 

  1. Define upper and lower sums of a function on [a, b] corresponding to partition.
  2. State the linearity property of integrals.
  3. Define Gamma integral.
  4. Evaluate
  5. State the -test for an improper integral I kind.
  6. State how the mean and variance are found from the m.g.f.
  7. State the relationship between the characteristic roots and trace and determinant of a matrix.
  8. Solve: .
  9. Verify whether the following system of equations is consistent:

x – y + z – 2 = 0, 3x – y + 2z = 0,  3x + y + z +18 = 0.

  1. Find the characteristics roots of .

 

PART – B

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

  1. Evaluate  from first principles.
  2. Show that if  is a monotonically increasing  function on [ a, b], then .
  3. Discuss the convergence of for various value of p.
  4. Solve .
  5. Find the m.g.f and hence the mean and variance of a distribution with p.d.f.
  6. Discuss the convergence of : (a)   (b)  (c) .
  7. Evaluate the integralover the upper half of the circle.
  8. Find any non trivial solution which may exist:

.

(P.T.O.)

 

 

 

 

 

PART – C

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

  1. (a) If and , show that and that .

(b) State and prove the First Fundamental Theorem of Integral Calculus. Deduce the Second

Fundamental theorem.                                                                                                       (10 + 10)

 

  1. (a) Show that .                                                                                                     (10)

(b) Show that mean does not exist for the distribution with p.d.f. .   (10)

  1. a) If have jont pdf , find the p.d.f. of U=X1/X2.

(15)

  1. b) Discuss the convergence of the integral for various values of a. (5)
  1.  (a) State and prove Cayley-Hamilton Theorem.                                                                              (10)

 

(b) Find the inverse of the following matrix by using Cayley-Hamilton theorem.

.                                                                                                                       (10)

 

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Loyola College B.Sc. Statistics Nov 2010 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 – NOVEMBER 2010

ST 1503/ST 1501 – PROBABILITY AND RANDOM VARIABLES

 

 

 

Date : 12-11-10                     Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

PART – A

 

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

 

  1. What do you mean by “Random Experiments”?
  2. A letter of the English alphabet is chosen at random. Calculate the probability the letter

so chosen (i) is a vowel ;  (ii) precedes J and is a vowel.

  1. State Classical definition of probability.
  2. All cards of ace, jack and queen are removed from a deck of playing cards.  One card is

drawn at random from the remaining cards.  Find the probability that the card drawn is

  • a face card and    (ii) not a face card.
  1. If P(A) = 0.3, P(B) = 0.2, P(C) = 0.1 and A,B,C are independent events, find the

probability  of occurrence of at least one of the three events A,B, and C.

  1. Two coins are tossed. Show that the event “ head on first coin “ and event “ Coins fall alike”

are independent.

  1. A person is known to hit a target in 5 out of 8 shots, whereas another person is known to

hit in 3 out of 5 shots. Find the probability that the target is hit at all when they both try.

  1. If for three mutually exclusive and exhaustive events A,B and C;  and

P(B) = 2/3 P(C) then find P(A).

  1.  Find the standard deviation of the probability distribution
 

x = x

 0 1 2
P(x)

 

  1. Find the mathematical expectation of the number of points if a balanced die is thrown.

 

PART – B

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

 

  1. For three non-mutually exclusive events A,B, and C, prove that

P( A B C ) = P(A) +P(B)+P(C) – P(A B) – P( AC) – P(BC ) + P(A B C).

 

 

  1. Prove that
  • P( B ) = P(B) – P(A B)
  • P(A ) =  P(A) – (A B).
  1. In a random arrangement of the letters of the word “MATHEMATICS”, find the

probability that all the vowels come together.

  1. If events A and B are independent then prove that the complementary events and are

also independent.  Also show that A and   are independent.

  1. 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 independence of the events A1, A2 and A3.

  1. State and prove multiplication law of probability when the events are (i ) not independent

(ii) independent.

 

  1. Let X be a continuous random variable with p.d.f given by

f(x)   =  kx   ,                    0 £ x £ 1

=  k   ,                     1 £ x £ 2

=   kx + 3k   ,        2 £ x £ 3

=   0   , otherwise

  1. Determine the constant k
  2. Determine F(x).
  3. A continuous random variable X has the following p.d.f

f(x) = 3 x2  ,      0 < x < 1

=  0  ,         otherwise

Verify that it is a p.d.f and evaluate the following probabilities

  1. P( X 1/3 )    (ii)  P ( 1/3  X  ½ )  and  (iii)  P (X  1/2)  1/3  x  2/3 ).

 

PART – C

 

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

  1. a) Let A and B be two possible outcomes of an experiment and suppose P(A) =0.4,

P( A B) = 0.7 and P(B) = p

  • For what choice of p, are A and B mutually exclusive?
  • For what choice of p, are A and B independent?

 

  1. b) There are two bags. The first contains 2 red and 1 white ball, whereas the second bag

has only 1 red and 2 white balls. One ball is taken out at random from the first bag and

put in the second.  Then a ball is chosen at random from the second bag. What is the

probability that this last ball is red ?

  1. a) A and B play 12 games of chess of which 6 are won by A, 4 by B and 2 end in a tie.

They agree to play 3 more games.  Find the probability that (i) A wins all the three

games (ii) two games end in a tie (iii) A and B win alternatively and (iv) B wins at least

one game.

 

  1. b) For n events A1, A2 … An , Prove that

(i)  P (Ai) – (n-1)

(ii) P (Ai).

  1. a) State and prove Baye’s Theorem.

 

  1.     b) There are ‘n’ boxes each containing 4 white and 7 black balls.  Another one box has got 7

white and 4 black balls.  A box is selected at random from the (n + 1 ) boxes and 2 balls

are drawn out of it and both are found to be black.  If it is now calculated that probability

that there are 7 white and 2 black balls remaining in  the chosen box is 1/ 15.  What is the

value of ‘n’?

 

  1. a) The length of time ( in minutes) that a certain lady speaks on the telephone is found to be

random phenomenon with a probability function specified by the probability density

function f(x) as

f(x) = A e– x/5     for x  0

=  0,      otherwise

  • Find the value of A that make a p.d.f
  • What is the probability that the number of minutes that she will talk over the phone is
  • more than 10 minutes
  • less than 5 minutes
  • between 5 and 10 minutes?

 

  1. b) State and prove Chebyshev’s inequality?

 

 

 

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Loyola College B.Sc. Statistics Nov 2010 Estimation Theory Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2010

ST 5504/ST 5500 – ESTIMATION THEORY

 

 

 

Date : 29-10-10                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

Answer ALL the questions                                                                                                              [10×2=20]

 

  1. Define an unbiased estimator and give an example.
  2. Define the consistency of an estimator.
  3. When is an estimator called most efficient estimator?   
  4. Define UMVUE.
  5. State any two regularity conditions.
  6. State the invariance property of ML estimator.
  7. Explain ‘posterior’ distribution.
  8. Define Bayes estimator.
  9. State the normal equations associated with the simple regression model.
  10. Define Best Linear unbiased estimator.

PART – B

 Answer any FIVE questions                                                                                                            [5×8=40]

  1. If X1,X2, . . . Xn are random observations on a Bernoulli variate X taking the value 1 with

      probability p and the value 0 with probability (1-p), show that: is a consistent

      estimator of p(1-p).

  1. If X1,X2, . . . Xn are random observations of Poisson population with parameter λ.

      Obtain UMVUE for λ using Lehman Scheffe Theorem.                                                                                    

  1. State and prove Factorization theorem [Neymann].
  2. Write short notes about the method of minimum Chi-square estimation.
  3. Estimate α and p for the following distribution by the methods of moments:

        .

  1. Let X1,X2, . . . Xn be a random sample of size n from a uniform population with p.d.f:

                         f(x; Ө) = 1; Ө-1/2 ≤ x ≤ Ө+1/2, -∞< Ө <∞.

       Obtain M.L.E for Ө.

  1. State and prove Gauss Markoff Theorem.
  2. Explain the method of Least Squares with an illustration.

 

 

PART – C

Answer any TWO questions                                                                                                     [2×20=40]

  1. a) Obtain Cramer Rao Lower bound for an unbiased estimator of if f(x,θ) =

            

  1. b) Establish Chapman-Robbins Inequality.
  2. a) State and prove Rao Blackwell theorem and mention it’s importance.
  3. b) Let X1,X2, . . . Xn be an iid {f Ө, Ө Є Θ} and each Xi, i=1,2,3,4 has mean μ and

          variance σ2. Find the minimum variance unbiased estimator among the following.

                                    T1(x) = X1;

T2(x) = (X1+X2)/2;

T3(x) = (X1+2X2+3X3)/6;

T4(x) =(X1+X2+X3+X4)/4

  1. a) Show that UMVUE is unique.
  2. b) State and prove a sufficient condition for consistency of an estimator.
  3. a) Establish a necessary and sufficient condition for a linear parametric function to be

          Estimable.

  1. b) In Sampling from {b(1, Ө), 0<Ө<1}., Obtain Bayesian estimator of Ө taking a suitable prior

          distribution.

 

 

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Loyola College B.Sc. Statistics Nov 2010 Computational Statistics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2010

    ST 5507 – COMPUTATIONAL STATISTICS

 

 

 

Date : 09-11-10                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

Answer all the questions                                                                                          (5 X 20 =100)

1 a)  Consider  the population of 7 units with values  1, 2, 3, 4, 5, 6,7  Write down all possible of sample of 2 ( without replacement) from this population and verify that this sample population mean is an unbiased estimate of the population mean.

Also calculate its sample variance and verify that

  • It agrees with the formula for the variance of the sample mean, and
  • This variance is less than the variance obtained from the sampling with replacement.

(Or )

  1. b) The table given below presents the summary of data for complete census of all the the 2010                       farms in region. The farms were stratified according to the farm size in acres into seven strata, as shown in column 2 of the table. The number of farms in the different strata Ni are given in the column 3. The population values of the strata means (  ) and the strata standard deviation ( Si) for the area under wheat  are given the frequency table

 

Stratum  No. Farm size

( in acres )

 No. of farms Ni Average area under wheat per farm in acres

(  )

 St. Deviation of area under wheat per farm in acres  (Si)
1 0 – 40 394 5.4 8.3
2 41 – 80 461 16.3 13.3
3 81 – 120 391 24.3 15.1
4 121 – 160 334 34.5 19.8
5 161 – 200 169 42.1 24.5
6 201 – 240 113 50.1 26.0
7 More than 240 148 63.8 35.2

 

Calculate the sampling variance of the estimated area under wheat for the region from a sample of 150 farms if the farms are selected by the method of simple random sampling without stratification.

 

 

  1. a) A random variable takes values 0, 1, 2 with probabilities

+  +  + where N is a known number and α andθ are unknown parameters. If 75 independent observations on X yielded the values 0, 1, 2 with frequencies 27, 38, 10 estimate α and θ by the method of moments.

 

  1. b) If 6,11,4,8,7,6 is a sample from a normal population with mean 6. Find the maximum likelihood estimate for the variance .

                                                                        (or)

  1. c) Given below is a random sample from normal population. Determine 95% confidence interval for the population standard deviation.

160, 175, 161, 181, 158, 166, 174, 165, 172, 184, 170, 159, 169, 175, 179, 164

 

  1. d) A random sample of size 17 from a normal population is found to have 7 and

find a 90% confidence interval  for the mean of the population.

 

3(a) Calculate seasonal indices by using Ratio to trend method for the following data:

 

Quarter
Year I II III IV
2006 8 16 24 32
2007 48 36 24 12
2008 48 16 32 64
2009 72 108 114 36
2010 56 28 84 112

(OR)

 

(b) Calculate 3 yearly moving averages and also draw the graph for the following data:

 

Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Sales 200 120 280 240 160 320 360 400 320 360 360

 

(c) Fit a straight line by the method of least square and also forecast the production for the year 2010 for the following data:

Year 2000 2001 2002 2003 2004
Production 10 20 30 50 40

 

4 (a) Two random samples were drawn from two normal populations and the observations are:

 

A 66 67 75 76 82 84 88 90 92 – –
B 64 66 74 78 82 85 87 92 93 95 97

 

Test whether the  two populations have the same variance at 5% level of significance.

 

  1. b) The following table show the association between the performance and training of 870persons.Is the association significant.
Training
Performance Intensive Average Normal Total
Above average 100 150 40 290
Average 100 100 100 300
Poor 50 80 150 280
Total 250 330 290 870

 

(or)

(c)Apply the mann-whitney  -wilcoxon test  to the following data to test

X 25 30 45 52 65 75 80 42 50 60
Y 60 40 35 50 60 72 63 40 55 62

 

(d)  A group of 5 patients treated with machine A weighted 42, 39, 48, 60, 41. A second group of 5 patients treated with machine B weighted 38, 42, 48, 67, 40 kg. Do the two machine differ significantly with regard to their effect in increasing weight?

5) a) From the following data compute price index by applying weighted  average of price relatives method using:

(i) Arithmetic mean, and

(ii) Geometric mean.                                                                                                  (8)

 

Commodities p0

Rs.              

q0 p1

Rs.
Sugar 6.0 10 kg. 8.0
Rice 3.0 20 kg. 3.2
Milk 2.0 5 lt. 3.0

 

b)Construct index number of price from the following data by applying

 

  • Laspeyre’s method
  • Paasche’s method
  • Bowleys method,
  • Fisher’s ideal method,  and
  • Marshall edgeworth method

 

Commodity 2007 2006
Price Rs. Quantity Price Quantity
A

B

C

D

 

 2

5

4

2

 8

10

14

19

 4

6

5

2

 6

5

10

13

 

 

Or

  1. c) From the following data, calculate Fisher’s ideal index and prove that it satisfies both the time reversal test and factor reversal tests. (10)
Commodity 2007 2006
Price Rs. Quantity Price Quantity
A

B

C

D

 

 4

5

3

8

 

 8

10

6

5

 

 5

6

4

10

 8

12

7

4

 

d)From the following data of the wholesale prices of wheat for the ten years construct index numbers   (a) taking 1999 as base, and  (b) by chain base method.             (10)

 

Year Price of wheat ( Rs. Per 10 kg )
1999 50
2000 60
2001 62
2002 65
2003 70
2004 78
2005 82
2006 84
2007 88
2008 90

 

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Loyola College B.Sc. Statistics Nov 2010 Basic Sampling Theory Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – NOVEMBER 2010

ST 3504/ST 3502/ST 4500 – BASIC SAMPLING THEORY

 

 

 

Date : 02-11-10                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION – A

 

ANSWER ALL QUESTIONS.                                                                                       (10 X 2 =20 marks)

 

  1. What is meant by “Probability Sampling Design”?
  2. Give an example of a “Statistic”.
  3. What are the values of second order inclusion probabilities in simple random sampling without replacement when N=10 and n=3?
  4. Show that the variance of sample mean under simple random sampling with replacement is greater than its variance under simple random sampling without replacement.
  5. Under what condition PPSWR reduces to SRSWR?
  6. Suggest an unbiased estimator for population total under PPSWR.
  7. When do you recommend stratified random sampling?
  8. Suggest an unbiased estimator of population mean in stratified random sampling.
  9. List all possible circular systematic samples of size 3 when the population size is 10.
  10. What is the probability of selecting a sample consisting of 3rd and 4th population units in LSS when N=12 and n=4?

            SECTION – B

 

ANSWER ANY FIVE QUESTIONS                                                                                (5 X 8 =40 marks)

 

  1. Compare sampling and census.
  2. Explain the terms : (i) Unbiasedness (ii) Variance (iii) Mean square error and (iv) Bias.
  3. Show that under simple random sampling when N=3 and n=2 the estimator

is unbiased for the population mean and obtain its variance.

 

  1. Explain Cumulative total method of PPS selection with an example.
  2. Compare the efficiencies of under optimum and proportional allocation.
  3. Explain proportional allocation for a given sample. Derive the variance of under proportional allocation.
  4. Derive in terms of .
  5. Compare the variances of sample mean under LSS and SRS in the presence of linear trend.

 

SECTION  – C

 

 

ANSWER ANY TWO QUESTIONS                                                                     (2 X 20 = 40 marks)

 

  1. a) Establish the relationship between Bias, Variance and Mean Square error.
  2. b) Illustrate with an example that unbiasedness of an estimator is design dependent.
  3. a) Explain Lahiri’s method of PPS selection with proof.
  4. b) Derive the variance of Hansen Hurwitz estimator under PPSWR and develop its unbiased

estimator.

  1. a) A sampler has two strata with relative sizes  and  .  He believes that

and  can be taken as equal. For a given cost , assuming the stratum

sizes are large, show that

 

  1. Derive the formula for Optimum allocation.

 

  1. Write short notes on the following:
  2. Balanced systematic sampling
  3. Yates corrected estimator
  4. Neyman allocation
  5. Formation of Strata.

 

 

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Loyola College B.Sc. Statistics Nov 2010 Applied Statistics Question Paper PDF Download

by

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2010

ST 5506/ST 5502 – APPLIED STATISTICS

 

 

 

Date : 03-11-10                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

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

  1. List out the different tests in index numbers.
  2. Explain the deflating procedure of index numbers.
  3. Define Time Series.
  4. State the mathematical models applied in time series analysis.
  5. What is meant by Specific Death Rates?
  6. Define Life Table.
  7. What do you mean by partial correlation and partial regression?
  8. List out any three properties of multiple correlation co-efficient.
  9. Write some functions of Central Statistical Organization.
  10. State the merits of De Facto and De Jure methods.

 

PART – B

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

 

  1. What is the difference between the Weighted and Unweighted Indices? Also explain the construction of index number by Unweighted Indices.
  2. Describe cost of living index and also state its uses.
  3. Explain the procedure of finding trend values using the method of least squares.
  4. Describe the method of Ratio-to-Moving average to calculate seasonal indices.
  5. Explain the various methods available for the measurement of population growth
  6. In a tri-variate distribution:

σ1 = 2; σ2 = σ3 = 3; r12 = 0.7; r23 = r31 = 0.5.

Find: i) r23.1     ii) R1.23      iii) b12.3      iv) b13.2       v) σ1.23

  1. Write a note on National Sample Survey Organization.
  2. Describe the national income and social accounting.

 

 

 

PART – C                             

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

 

  1. a) Explain Fisher’s index number. Why it’s called as an ideal index numbers?
  1. b) Prove that the Factor Reversal Test and Time Reversal Test are satisfied

by Fisher’s Index.

Year Article I Article II Article III Article IV
Price Qty Price Qty Price Qty Price Qty
1982 5.00 5 7.75 6 9.63 4 12.50 9
1983 6.50 4 8.80 10 7.75 6 12.75 9

 

  1. a) Describe the procedure of cyclic variation and irregular variation.
  1. b) Calculate the seasonal indices by the method of link relatives
Quarter\ Year 1979 1980 1981 1982 1983
I 30 35 31 31 34
II 26 28 29 31 36
III 22 22 28 25 26
IV 31 36 32 35 33

 

 

 

 

 

  1. a) Describe the methods of obtaining vital statistics. Also write its uses?
  1. b) From the data, calculate the gross reproduction rate and Net

reproduction rate. [ratio Male:Female = 52:48]

Age Group No of children born to 1000 women passing through the age group Mortality rate
16-20 150 120
21-25 1500 180
26-30 2000 150
31-35 800 200
36-40 500 220
41-45 200 230
46-50 100 250

 

  1. Explain the following:
  1. a) Agricultural Statistics
  2. b) Financial Statistics
  3. c) Components of Time Series.

 

 

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