1. For what value of the BLUE of p and P2 are uncorrelated for the model p o P 2



0

1

2

2. Let y. where i 3,. . . n be n independent standard normal variates, and y'Ay be a quadratic form where A is an idempotent matrix, then what will be the distribution of y'Ay

Normal distribution

Chi-square distribution

Bivariate Normal distribution

Rectangular distribution

3. A certain task can be accomplished in a factory by four different workers on five different types of machines. A sample study in context of a two-way design without repeated value is being made with two fold objectives of examining whether the four workers differ with respect to mean productivity and whether it is same for five machines. The researcher involved in this study reports gathered data as under Sum of squares for variance between machines 35.2 Sum of squares for variance between workers 53.8 Sum of squares for total variance 174.2 The F-statistic between machines is equal to

0.95

1.24

1.48

1.75

4. The following data pertain to a test involving analysis of variance Estimate of population variance based on variance among the sample means 18.50 Estimate of the population variance based on the variance within the samples 12.50 The F-ratio for the sample is equal to

0.68

1.48

6.00

31.00

5. In the Gauss Markov linear model, let y denote the vector of fitted values and £ denote the vector of residuals. Consider the following statements

1. The components of y are pairwise uncorrelated.

2. The components of £ are pairwise uncorrelated. Which of the above statements is/are correct

1 only

2 only

Both 1 and 2

Neither 1 nor 2

6. Suppose b1, b2, b3, ... bn are independent a random variables and c(j are independent t2) random variables for i 1 2 3 k and j 1 2 3 n. Suppose we observe only X b s.. for i J y 1 y 3 k and j 3 n. Then which of the following assertions are true

1. VarCXjP a 2 t 2 for all j

2. Cov(Xjj5 Xjtj.) 0 for all j except when i and j ..-X

3. y— is an unbiased estimator 2 of a 2 for j Select the correct answer using the code given below

1 and 2 only

1 and 3 only

2 and 3 only

1,2 and 3

7. Which of the following statements are correct about generalized inverse of a matrix

1. A generalized inverse of a matrix is defined as AAA =A.

2. A generalized inverse is not unique.

3. A matrix to have generalized inverse must be non-singular.

4. A matrix to have generalized inverse may be either square matrix or rectangular matrix. Select the correct answer using the code given below

1 and 3

1 and 4

3 and 4

1 and 4

8. Which of the following statements are associated with residuals of regression model

1. The sum of the residuals in any regression model that contains an intercept is always zero.

2. The sum of the observed values is not equal to sum of the fitted values yi

3. The sum of the residuals weighted by the corresponding regressor variable is zero.

4. The sum of the residuals weighted by the corresponding fitted values is zero. Select the correct answer using the code given below

1 and 3

1 and 4

1 and 4

3 and 4

9. For a simple linear regression model y p 0 p,x consider the following statements where PQ and pj are estimates of p0 and p

1. Cov 0

2. Cov

3. P0 P,x

4. P0 y P x Which of the above are correct

2 and 3

1 and 4

3 and 4

1 and 4

10. Which o f the following statements are correct in order to obtain the hypothesis H0 0 for the model y i p 0 p Ei

1. yi is N(p0 P1xj, a

2. isN n 2 r V i=l

3. n 2 6 2 2 is* a n 2

4. Pj and d are not independent Select the correct answer using the code given below

1 and 3

1 and 2 only

1 and 4

3 and 4 3 x (Contd.)

For the next three items that follow A company used three different methods to train its employees. The number of units of output produced by different employees trained by the three training methods is given below

Method A 50 45 55 44
Method B 64 48 52 56 44
Method C 46 42 48 45 57 42

It has to be tested whether the three different methods are satisfactory at level of significance Given F2.12 at 0.05 3.89 as the critical value)

11. Which of the following is/are the null and alternate hypothesis for testing whether the mean number of units produced per hour is different for the three different training methods

1. Ho • Me

2. H0 56 Hb He

3. H1 |iB and fic are not all equal

4. H1 IV Ij b Hc

Select the correct answer using the code given below:

1 and 3

1 and 4

1 and 2

2 and 3

12. The estimate of the population variance on the basis of the variance among the sample means for the above methods is

45.25

48.36

52.58

55.65

13. The estimate of the population variance within the samples for the different methods

25.67

31.07

38.646

39.097

14. In the Gauss-Markov linear model, what is the possible number of distinct solutions of the normal equations

Either 0 or 1 or infinite

1 only

Infinite

Either 1 or infinite

15. If in a linear model y. p0 e. for i 1 E(ej5 e.) 0 for all i then which of the following statements are correct for the method of estimation by least squares

1. The least square estimates o f the parameters P0 and Pj are determined by minimising the sum of squares of residuals.

2. The observations y. are pairwise uncorrelated.

3. The observations y. are jointly independent and each is a normal random variable.

Select the correct answer using the code given below

1 and 2 only

2 and 3 only

1 and 3 only

1,2 and 3

16. If in a linear model y. P0 p s. for i ..., n where are normal and independently distributed random variables with mean 0 and variance a the maximum likelihood estimators of P0 and a 2 are denoted by b0, and d respectively, then which of the following are correct for these estimators

1. The estimators are jointly complete sufficient statistics.

2. is independent of d .

3. 2)62 is a Chi-square random variable with degrees of freedom. Select the correct answer using the code given below

1 and 2 only

2 and 3 only

1 and 3 only

1,2 and 3

17. What is R in linear hypothesis H0: Rp r with two restrictions a 0 2a, and 3a, 4 a3 in three variable linear model

1 2 0 0
0 3 0 4

0 2 0 0
1 3 0 4

3 0 1 0
0 2 4 0

1 0 2 0
3 0 4 0

18. Mean square error criteria are used for selection of which one of the following

Explanatory variables

Model

Estimates

Response variables

19. In which one of the following assumptions do the general linear model and generalized linear model differ

Linearity

Homoscedasticity

Unbiasedness

Nonmulticollinearity

20. Consider the following statements associated with R2 and —R 9 criteria

1. R^2 increases with the inclusion of relevant explanatory variable only.

2. R^2 increases whether the included explanatory variable is relevant or irrelevant.

3. R^2 decreases if the included explanatory variable is irrelevant.

Which of the above statements are correct

1 and 2 only

1 and 3 only

2 and 3 only

1,2 and 3 5 x (Contd.)

21. LetX,,X2, X3, ..., Xnbe i.i.d. variables. Which of the following statements are correct n

1. T Xj is a complete sufficient i=l statistic for X — T

2. X — is the unique UMVUE for X n

3. is the unique UMVUE for X

Select the correct answer using the code given below

1 and 2 only

2 and 3 only

1 and 3 only

1,2 and 3

22. Consider the following statements

Statement-I Where the parent distribution is discrete, the non-randomised tests may not exactly attain a given level of significance a.

Statement-II a usually has a low value like 0.01 or 0.05. Even inclusion of any single discrete point with positive probability in the critical region often makes the level greater than the prescribed value. Which one of the following is correct in respect of the above two statements

Both Statement-I and Statement-II are true and Statement-II is the correct explanation for Statement-I

Both Statement-I and Statement-II are true but Statement-II is not the correct explanation for Statement-I

Statement-I is true but Statement-II is false

Statement-I is false but Statement-II is true

23. Consider the following statements

Statement-I Sequential Probability Ratio 9 Test (SPRT) requires, on an average, smaller number of observations than a nonsequential test with identical error controlling properties.

Statement-II SPRT can be carried out graphically.

Which one of the following is correct in respect of the above two statements

Both Statement-I and Statement-II are true and Statement-II is the correct explanation for Statement-I

Both Statement-I and Statement-II are true but Statement-II is not the correct explanation for Statement-I

Statement-I is true but Statement-II is false

Statement-I is false but Statement-II is true

24. Let X2, X3, ... Xn be independent random variables distributed uniformly on the interval 0). If n is odd, which of the following is/are the unbiased estimator(s) of 0

1.

2.

Select the correct answer using the code given below

1 only

2 only

Both 1 and 2

Neither 1 nor 2

25. If X2, X3, X n be independent random variables distributed as then which of the following statements are correct n

1. T Xj is sufficient for p i=l n

2. Xj is complete for p

3. T^2 is unbiased for p2

Select the correct answer using the code given below

1 and 2 only

2 and 3 only

1 and 3 only

1,2 and 3

26. For testing the hypothesis H0:0 0O against the alternative 0 X is the likelihood ratio; A and B B are the constants. Under the SPRT criteria, consider the following statements

1. If X we terminate the process with the acceptance of H0

2. If X we terminate the process with the rejection of H0

3. If B X we continue sampling by taking an additional observation

Which of the above statements is/are correct

1,2 and 3

1 and 3 only

2 and 3 only

3 only

27. If X1, X2, X3, ..., Xn is a random sample of size n from Cauchy distribution with pdf f x o o x o o then n[l — J which one of the following is true for estimating

Sample mean is a consistent estimator but not sample median

Sample median is a consistent estimator but not sample mean

(c)Both sample mean and sample median are consistent estimators

Neither sample mean nor sample median is a consistent estimator

28. If and T2 are independent and unbiased estimators of parameter 0 with a 2 and 2g2, then the unbiased estimator of 0 given by T AT, X)J2 has minimum variance if X equals

2/3

1/2

1/3

1/4

29. Consider the following statements pertaining to likelihood ratio tests

1. The likelihood ratio criterion offers a method o f constructing tests of hypotheses which do not fall within the purview of Neyman-Pearson Lemma

2. The likelihood ratio test statistic X is the ratio of the supremum of the likelihood under H0 to the supremum of the likelihood in the unrestricted parametric space

3. The critical region of the likelihood ratio test is the left hand tail of the distribution of A.

Which of the above statements are correct

1 and 2 only

2 and 3 only

1 and 3 only

1,2 and 3

30. Let X1,X2...,Xn be a random variable 32. I n with pdf 1 A e xa_1;x 0 a I a 0 s otherwise What is the consistent estimator for p2 P li

i=l

na(a I I i=l na2(a u 5>i

i=l

na(a n i=l n2a(a

31. Which one of the following sampling designs is used in conducting the Consumer Expenditure Survey by the National Sample Survey Office (NSSO)

Simple Random Sampling

Quota Sampling

Stratified Multi-stage Random Sampling

Judgement Sampling

32. Given a random sample from
f — 2(a 0 x a .

What is the MLE for a

x

2x

x/2

None of the above

33. Consider the following statements

1. Size of Type-I error is P {rejecting H01H0 is true}

2. Power of a test is P {rejecting H0 1 is true}

3. n n0 is a right tailed hypothesis Which of the statements given above are correct

1 and 2 only

2 and 3 only

1 and 3 only

1,2 and 3

34. The Manager of a cyber cafe says that the number of customers visiting on the weekdays followed a Binomial distribution. Which one of the following techniques can be used to test the hypothesis at a given level of significance

Test of significance of mean

Chi-square test as a test of goodness of fit

Test of significance o f difference between two means

Correlation analysis

35. What is an unbiased estimator of 0 for the distribution, x 0

1

1

1

1

36. Consider the following statements regarding the properties of an estimator

1. Every consistent estimator is unbiased.

2. If an estimator tn based on n n observations is a consistent estimator of then for any E Prob tn 0 tends to one as n oo

3. Since consistency is a limiting property, no consistent estimator actually exists as sample size is finite. Which of the above statements are not correct

2 and 3 only

1 and 3 only

1 and 2 only

1,2 and 3

37. Consider a random sample X1, X2, X3, ..., Xn of size n from the statistic T xi xi^2=l for 0 is

Sufficient and complete

Sufficient but not complete

Not sufficient but complete

Neither sufficient nor complete

38. In usual notations, if a quantity exists, whose distribution is independent of then which of the following are correct

1. is called a confidence interval.

2. is a pivotal quantity.

3. can be used to define 100% confidence interval for 0.

Select the correct answer using the code given below

1 and 3 only

1 and 2 only

2 and 3 only

1,2 and 3

39. Consider the following statements with respect to Neyman-Pearson Lemma if C is a critical region of size a and k is a constant.

1. Lo/L1 k inside C

2. Lo/L1 k outside C

3. C is a most powerful critical region of size a for testing 0 0O against 0

Which of the above are correct

1,2 and 3

2 and 3 only

1 and 3 only

3 only

40. To compare the quality of LED TVs of Brand and Brand a statistician collects the following data
X1, X2 ..., Xn are the number of dead pixels in a random sample of n Brand TVs and Y., Y„ ..., Y are the number m of dead pixels in a random sample of m Brand TVs.
Assuming that the Xts and Y.s are independent Poisson random variables with mean and X2 for Brand and Brand TVs respectively, the statistician decides to test the hypothesis H0 A., X2 versus H W Here H0 and are, respectively

Simple and simple

Simple and composite

Composite and simple

Composite and composite

41. If Xi follows be a random sample for i 3,..., then what is an unbiased estimator of 0

X

X/2

2X

sqrt(x)

42. X has a Poisson A distribution. Then where X is the sample mean based on a random sample of size n and s^2 Z (Xi X is an unbiased n estimator of

0

A/n





43. An unbiased estimator of —U for the distribution 0(1 0 x ..., go; 0 0 1 is 1

1/x

1/nx

nx

x

44. If X1, X2, X3, X n is a random sample from then

Sample mean X is unbiased for p but not consistent

Sample mean X is consistent for p but not unbiased

Sample mean X is unbiased and consistent for p

Sample mean X is neither unbiased nor consistent for p

45. Consider the following statements

1. If T is an unbiased estimator of then T2 is an unbiased estimator of 02

2. If T is a consistent estimator of then T^3 is a consistent estimator of 0^3

Which of the above statements is/are correct

1 only

2 only

Both 1 and 2

Neither 1 nor 2

46. What is the MLE of 0 based on a random sample of size n drawn from a population Af with pdf as
f 0 0 x <oo
0 otherwise

x

1/x

Largest observation

Smallest observation

47. If population variance of an infinite population is a 2 and a sample of 25 items is selected from this population, then what is the standard error of sample mean

O^2/25

O/5

O/25

O

48. Consider the following statements

Statement-I An SPRT always provides a decision.

Statement-II Probability of terminating an SPRT is one.

Which one of the following is correct in respect of the above two statements

Both Statement-I and Statement-II are true and Statement-II is the correct explanation for Statement-I

Both Statement-I and Statement-II are true but Statement-II is not the correct explanation for Statement-I

Statement-I is true but Statement-II is false

Statement-I is false but Statement-II is true 11 (Contd.)

49. Consider the following statements

1. The purpose of hypothesis testing is to make a judgement about the difference between the sample statistic and the hypothesized population parameter.

2. When the Null hypothesis is rejected the alternate hypothesis is accepted.

3. The purpose of hypothesis testing is to test the correctness of the computed value of the sample statistic.

4. If the Null hypothesis is not rejected, this does not ensure that the Null hypothesis is true.

Which of the above statements are correct

1,2 and 3

1,3 and 4

1,2 and 4

3 and 4

50. Which one of the following statements is correct?

The mean of the sampling distribution of mean is greater than the population mean.

The sampling distribution of mean approaches normality as the sample size decreases.

As the standard error o f mean increases, the value of any sample mean will be closer to the value of the population mean.

As the standard error o f mean decreases, the precision of the sample mean as an estimator of the population mean increases.

51. Suppose X1, X2, X3, ..., X10, Y1,Y2,Y3, ...,Y10 are independent random variables where X(s have density f —1 e x 0 and Y(s have density f 1 y — e y 0. 2 What is MLE of X based on all X I s and Y ls

X Y

X Y

2X Y/4

X 2Y

52. In a normal population a with a 2 in order to test the null hypothesis jj. [i0 against the alternative x where based on a random sample of size the value of k such that x k provides a critical region of size a 0.05 is

M0 1.645/sqrt(n)

M0 3.290/sqrt(n)

M0 1.96/sqrt(n)

M0 3.92/sqrt(n)

53. For testing the null hypothesis H0 ji 55. against the alternative n0 at Q level o f significance on the basis of a random sample of size n from a normal population with known variance ct2 consider the following statements with respect to likelihood ratio criteria

1. The value of A is

2. The null hypothesis is rejected if A 0 k 1

3. A is a ratio of the maximum likelihood function for all values of M in parameter space and maximum likelihood function for all values of M under H0

Which of the above statements are correct

1 and 2 only

2 and 3 only

1 and 3 only

1,2 and 3

54. Consider the following statements

1. If X1, X2, X3,X n is a random sample from normal population, then the sample variance S2 is consistent estimator of a^2.

2. If X1, X2, X3, Xn is a random sample from normal population with mean 0. Xi^2/n is unbiased estimator of O^2

3. If X1, X2, X3, ..., Xn is a random sample from an exponential population with probability density function
f(x 1 q e e x>0 then X is 0 otherwise
consistent estimator for parameter 0.

4. If X1, X2, X3,..., Xn is a random sample from then the nth order statistic Yn is unbiased estimator of p.

Which of the above statements are correct

3 and 4

1,2 and 4

1,3 and 4

1,2 and 3

55. Cramer Rao lower bound of variance for the parameter 0 of the distribution with pdf

f(x 1/n 1/1 where -oo x oo is

1/n

2/n





56. An estimator with large variance is preferred in which one of the following cases

X follows gamma

X follows

X follows gamma

X follows gamma

57. Let X1, X2, X3, X n be independently and normally distributed with mean 0 and variance a 2. What is the minimum variance unbiased estimator of a^2

E xi^2

1/n E xi^2

1/n



58. If X2 and X3 is a random sample of size 3 from a population with mean p. and variance ct2. What is the value of X for which T3 +X2 is an unbiased estimator for M

1/4

1/3

1/2

1

59. If X and S2 are the mean and variance of a random sample of size n from a normal population with mean and standard deviation ct, then consider the following statements

1. X is unbiased and consistent estimator of |i.

2. S2 is consistent estimator of ct2.

3. The random variable —— has a CT2 Chi-square distribution with degrees of freedom. Which of the above statements are correct

1 and 2 only

2 and 3 only

1 and 3 only

1,2 and 3

60. If the pdf of a random variable X is l 0 x and if we reject H0:0 1/2 against Ht 3/4 whenever x then what is the power of the test

15/16

1/2

7/16

9/16

61. Consider the following statements

Statement-I Fisher's Index number is known as ideal Index number.

Statement-II Fisher's Index number is the arithmetic mean of Laspeyre's Index number and Paasche's Index number which show upward bias and downward bias respectively.

Which one of the following is correct in respect of the above two statements

Both Statement-I and Statement-II are true and Statement-II is the correct explanation for Statement-I

Both Statement-I and Statement-II are true but Statement-II is not the correct explanation for Statement-I

Statement-I is true but Statement-II is false

Statement-I is false but Statement-II is true 14 x (Contd.)

62. If X1, X2, X3, ..., Xn is a random sample from then which one of the following statements is correct n

Xi^2 to is minimal sufficient statistic for a^2

Xi is minimal sufficient statistic i=l for ct^2

X is minimal sufficient statistic for a^2

There is no minimal sufficient statistic for ct^2

63. If X2, X3, ..., Xn is a random sample from the uniform distribution on where a e then which of the following statements are correct

1. Maximum likelihood estimator of is. same as the moment estimator of

2. Maximum likelihood estimator of is Max{X1, X2, X3,... Xn a

3. is an unbiased estimator of n where a is maximum likeklihood estimator of

4. Method of moments estimator is unbiased estimator of

Select the correct answer using the code given below

3 and 4

1,3 and 4

1,2 and 4

1,2 and 3

64. Randomised test is used for testing parametric hypothesis regarding distribution of a random variable X

Whenever X has a discrete distribution

Whenever exact size a test is required

When X is a discrete random variable and exact size a test is required

When X is a continuous random variable and exact size a test is required

65. If X2, X3, ..., Xn is a random sample from Poisson distribution with parameter then the maximum likelihood estimator of log k is given by

to

log Exi/n(i=1 to

e^Exi(i=1 to

log Exi(i=1 to

66. Agriculture Census in India is conducted at an interval of

3 years

5 years

8 years

10 years

67. Which one o f the following sampling designs is used for General Crop Estimation Survey (GCES)

Simple Random Sampling

Judgement Sampling

Stratified Multi-stage Random Sampling

Quota Sampling

68. Which of the following are the components of the scheme 'Improvement of Agricultural Statistics'

1. Timely Reporting Scheme

2. Improvement of Crop Statistics

3. Establishment of Agency Reporting Agricultural Statistics (EARAS)

4. Studying cost o f cultivation of principal crops in India

Select the correct answer using the code given below

3 and 4

1,3 and 4

1,2 and 4

1,2 and 3

69. Minimum Support Prices of major agricultural products are recommended to the Government by

Directorate o f Economics and Statistics

Directorate o f Marketing and Inspection

Commission for Agricultural Costs and Prices

Directorate of Rice Development 16

70. Which one of the following index numbers is used for calculating the Dearness Allowance of Central Government Employees

1. Consumer Price Index (Rural, Urban, Combined)

2. Consumer Price Index (Industrial Workers)

3. Wholesale Price Index

4. Index of Industrial Production

Select the correct answer using the code given below:

2 only

1 and 2 only

1,2 and 3

1,3 and 4

71. Consider a single observation from the population 0e-0x, 0 x oo. Let x 1 be the critical region for testing H0 0 2 against 0 1. What are the values o f type I and type II errors respectively



1/e e





72. Which one of the following organizations of the Government is responsible for collection, compilation and dissemination of Trade Statistics in India

Central Statistical Office

Directorate General of Commercial Intelligence and Statistics

Department of Industrial Policy and Promotion

Tariff Commission

73. What are the major sources of data on Official Statistics

1. Census and Sample Surveys

2. Administrative Records

Select the correct answer using the code given below

1 only

2 only

Both 1 and 2

Neither 1 nor 2

74. Which o f the following are the major sources on 'Health Statistics' in India

1. Sample Registration System

2. Civil Registration System

3. National Family Health Survey (NFHS)

Select the correct answer using the code given below

1 and 2 only

2 and 3 only

1 and 3 only

1,2 and 3

75. Which of the following is/are correct for Consumer Price Index (Rural, Urban, Combined)

1. Base year is 2012

2. Weights have been derived from the Consumer Expenditure Survey conducted by NSSO during 2011 -2012

Select the correct answer using the code given below:

1 only

2 only

Both 1 and 2

Neither 1 nor 2

76. Which of the following are part of mandate ofSDRD?

1. Planning of Survey

2. Formulation of Sample Design

3. Conducting of Sample Survey

4. Preparation of Survey Reports

Select the correct answer using the code given below

1,2 and 4

1,2 and 3

1,3 and 4

3 and 4

77. Which of the following equations are correct in respect of National Accounts

1. NDP GDP CFC

2. GNI GDP net factor income from abroad

3. NNI GNI CFC

Select the correct answer using the code given below

1 and 2 only

2 and 3 only

1 and 3 only

1,2 and 3

78. The first phase of Population Census is associated with which of the following

1. House listing

2. Housing Census

3. Population Enumeration

Select the correct answer using the code given below

1 and 2 only

2 and 3 only

1 and 3 only

1,2 and 3

79. Which of the following is/are correctly matched

1. Population Census Office of Registrar General and Census Commissioner

2. Economic Census Central Statistics Office

Select the correct answer using the code given below

1 only

2 only

Both 1 and 2

Neither 1 nor 2

80. The Unified District Information System for Education which is an important source of school education data, has been developed by which one of the following

National Council of Educational Research and Training

National University of Educational Planning and Administration

University Grants Commission

National Sample Survey Office