STATISTICS
UPSC CSE Mains Statistics Syllabus
(These syllabus may change from time to time. Please check with the relevant Public Service Commission websites for any changes in the syllabus)
Statistics Paper  I 1. Probability: Sample space and events, probability measure and probability space, random variable as a measurable function, distribution function of a random variable, discrete and continuoustype random variable, probability mass function, probability density function, vectorvalued random variable, marginal and conditional distributions, stochastic independence of events and of random variables, expectation and moments of a random variable, conditional expectation, convergence of a sequence of random variable in distribution, in probability, in pth mean and almost everywhere, their criteria and interrelations, Chebyshev’s inequality and Khintchine‘s weak law of large numbers, strong law of large numbers and Kolmogoroff’s theorems, probability generating function, moment generating function, characteristic function, inversion theorem, Linderberg and Levy forms of central limit theorem, standard discrete and continuous probability distributions. 2. Statistical Inference: Consistency, unbiasedness, efficiency, sufficiency, completeness, ancillary statistics, factorization theorem, exponential family of distribution and its properties, uniformly minimum variance unbiased (UMVU) estimation, RaoBlackwell and LehmannScheffe theorems, CramerRao inequality for single parameter. Estimation by methods of moments, maximum likelihood, least squares, minimum chisquare and modified minimum chisquare, properties of maximum likelihood and other estimators, asymptotic efficiency, prior and posterior distributions, loss function, risk function, and minimax estimator. Bayes estimators. Nonrandomised and randomised tests, critical function, MP tests, NeymanPearson lemma, UMP tests, monotone likelihood ratio, similar and unbiased tests, UMPU tests for single parameter likelihood ratio test and its asymptotic distribution. Confidence bounds and its relation with tests. Kolmogoroff’s test for goodness of fit and its consistency, sign test and its optimality. Wilcoxon signedranks test and its consistency, KolmogorovSmirnov twosample test, run test, WilcoxonMannWhitney test and median test, their consistency and asymptotic normality. Wald’s SPRT and its properties, OC and ASN functions for tests regarding parameters for Bernoulli, Poisson, normal and exponential distributions. Wald’s fundamental identity. 3. Linear Inference and Multivariate Analysis: Linear statistical models’, theory of least squares and analysis of variance, Gauss Markoff theory, normal equations, least squares estimates and their precision, test of significance and interval estimates based on least squares theory in oneway, twoway and threeway classified data, regression analysis, linear regression, curvilinear regression and orthogonal polynomials, multiple regression, multiple and partial correlations, estimation of variance and covariance components, multivariate normal distribution, MahalanobisD2 and Hotelling’s T2 statistics and their applications and properties, discriminant analysis, canonical correlations, principal component analysis. 4. Sampling Theory and Design of Experiments: An outline of fixedpopulation and superpopulation approaches, distinctive features of finite population sampling, probability sampling designs, simple random sampling with and without replacement, stratified random sampling, systematic sampling and its efficacy ,cluster sampling, twostage and multistage sampling, ratio and regression methods of estimation involving one or more auxiliary variables, twophase sampling, probability proportional to size sampling with and without replacement, the HansenHurwitz and the Horvitz Thompson estimators, nonnegative variance estimation with reference to the HorvitzThompson estimator, nonsampling errors. Fixed effects model (twoway classification) random and mixed effects models (twoway classification with equal observation per cell), CRD, RBD, LSD and their analyses, incomplete block designs, concepts of orthogonality and balance, BIBD, missing plot technique, factorial experiments and 2nand 32, confounding in factorial experiments, splitplot and simple lattice designs, transformation of data Duncan’s multiple range test. Paper  II 1. Industrial Statistics: Process and product control, general theory of control charts, different types of control charts for variables and attributes, X, R, s, p, np and c charts, cumulative sum chart. Single, double, multiple and sequential sampling plans for attributes, OC, ASN, AOQ and ATI curves, concepts of producer’s and consumer’s risks, AQL, LTPD and AOQL, Sampling plans for variables, Use of DodgeRoming tables. Concept of reliability, failure rate and reliability functions, reliability of series and parallel systems and other simple configurations, renewal density and renewal function, Failure models: exponential, Weibull, normal, lognormal. Problems in life testing, censored and truncated experiments for exponential models. 2. Optimization Techniques: Different types of models in Operations Research, their construction and general methods of solution, simulation and MonteCarlo methods formulation of linear programming (LP) problem, simple LP model and its graphical solution, the simplex procedure, the twophase method and the Mtechnique with artificial variables, the duality theory of LP and its economic interpretation, sensitivity analysis, transportation and assignment problems, rectangular games, twoperson zerosum games, methods of solution (graphical and algebraic). Replacement of failing or deteriorating items, group and individual replacement policies, concept of scientific inventory management and analytical structure of inventory problems, simple models with deterministic and stochastic demand with and without lead time, storage models with particular reference to dam type. Homogeneous discretetime Markov chains, transition probability matrix, classification of states and ergodic theorems, homogeneous continuoustime Markov chains, Poisson process, elements of queuing theory, M/M/1, M/M/K, G/M/1 and M/G/1 queues. Solution of statistical problems on computers using wellknown statistical software packages like SPSS. 3. Quantitative Economics and Official Statistics: Determination of trend, seasonal and cyclical components, BoxJenkins method, tests for stationary series, ARIMA models and determination of orders of autoregressive and moving average components, forecasting. Commonly used index numbers Laspeyre’s, Paasche’s and Fisher’s ideal index numbers, chainbase index number, uses and limitations of index numbers, index number of wholesale prices, consumer prices, agricultural production and industrial production, test for index numbers  proportionality, timereversal, factorreversal and circular . General linear model, ordinary least square and generalized least squares methods of estimation, problem of multicollinearity, consequences and solutions of multicollinearity, autocorrelation and its consequences, heteroscedasticity of disturbances and its testing, test for independence of disturbances, concept of structure and model for simultaneous equations, problem of identificationrank and order conditions of identifiability, twostage least square method of estimation. Present official statistical system in India relating to population, agriculture, industrial production, trade and prices, methods of collection of official statistics, their reliability and limitations, principal publications containing such statistics, various official agencies responsible for data collection and their main functions. 4. Demography and Psychometry: Demographic data from census, registration, NSS other surveys, their limitations and uses, definition, construction and uses of vital rates and ratios, measures of fertility, reproduction rates, morbidity rate, standardized death rate, complete and abridged life tables, construction of life tables from vital statistics and census returns, uses of life tables, logistic and other population growth curves, fitting a logistic curve, population projection, stable population, quasistable population, techniques in estimation of demographic parameters, standard classification by cause of death, health surveys and use of hospital statistics. Methods of standardisation of scales and tests, Zscores, standard scores, Tscores, percentile scores, intelligence quotient and its measurement and uses, validity and reliability of test scores and its determination, use of factor analysis and path analysis in psychometry. 
Recommended Books1. Statistics Paperback – 2011
by Freedman (Author), Purves (Author), Pisani (Author) 2. Fundamentals of StatisticsVol I by A.M.Gun 3. Programmed Statistics (QuestionAnswers) by B.L. Agarwal

STATISTICS MCQs
1. The names of Francis Galton and Karl Pearson are associated with
1) Probability
2) Correlation
3) Measures of Dispersion
4) Harmonic Mean
Answer: 2
2. The word Regression was used for the first time by
1) Sir Francis Galtom in 1877
2) Sir Francis Galton in 1787
3) Fredrick C. Mills in 1877
4) A.L. Bowley 1877
Answer: 1
3. If Mode and Median of a series are 22 and 21.4 respectively, what will be the value of Arithmetic Mean?
1) 15.99
2) 34.30
3) 21.10
4) 19.33
Answer: 3
4. Statistical averages are of how many types?
1) 2
2) 3
3) 4
4) 5
Answer: 2
5. Karl Pearson coefficient of Correlation is calculated on the basis of measure of
1) Arithmetic mean
2) Standard deviation
3) Arithmetic mean and standard deviation
4) Median and standard deviation
Answer: 3
6. The coefficient of variation of a series is 30% and standard deviation is 15, then its arithmetic mean is
1) 0.5
2) 5.0
3) 2.0
4) 50.00
Answer: 4
7. Statistics diagrams are the instruments of
1) Analysis
2) Interpretation
3) Presentation
4) Collection of data
Answer: 3
8. Method of analysis of variance was proposed by_
1) Sir Ronald A. Fisher(1923)
2) Sir Francis Galton(1877)
3) Wallis and Roberts(1911)
4) Karl Pearson(1932)
Answer: 1
9. Which one of the following is the correct sequence of steps of research ?
1) Problem identification, data analysis, hypothesis, conclusion
2) Hypothesis, data collection, sampling, conclusion, data analysis
3) Thinking about solution, selection of tools, hypothesis, data collection, data analysis
4) Problem identification, hypothesis, data collection, data analysis, conclusion
Ans: 4
10. In the identification of problem the researcher should decide
1) The title and the variables
2) The objectives
3) The variables, title and objectives
4) The title
Ans: 3
11. Probability is known as
1) Deliberate sampling
2) Systematic sampling
3) Stratified sampling
4) Simple random sampling
Ans: 4
12. Which aspect is not related with significance of research ?
1) Research inculcates scientific thinking.
2) Solutions suggested in research are universal
3) Research promotes the habit of logical thinking
4) Spatial and temporal aspects are basis of geographical research
Ans: 2
13. Which of the following is not a quality of good research ?
1) Systematic
2) Methods of data analysis should be appropriate
3) Based on preconceived ideas.
4) Logical
Ans: 3
14. Which is not a method of hypothesis testing ?
1) Chisquire Test
2) Circular Test
3) Student's T. Test
4) Parametric Test
Ans: 2
15. Which type of sampling is done if a population from which a sample drawn does not constitute a homogenous group ?
1) Systematic
2) Random
3) Stratified
4) Area
Ans: 3
16. Which is not a type of the measurement of scale ?
1) Simple Scale
2) Nominal Scale
3) Ordinal Scale
4) Ratio Scale
Ans: 1
17. In report writting, select the correct sequence of the following heads using codes given below : (A) Objectives
(B) Cartographic representation (C) Conclusions (D) Data Collection
1) A, B, C and D
2) A, D, B and C
3) D, A, B and C
4) A, B, D and C
Ans: 2
18. Which is not a characteristic of a research problem ?
1) Relationship between variables
2) Research problem should be in question form
3) Protection of moral judgements
4) Test ability
Ans: 3
19. Which of the following is the correct sequence of increased emphasis on practical action related to research ?
1) Applied  Pure Policy Action
2) Pure  Applied Policy Action
3) Action Applied Policy Pure
4) Policy  Pure  Applied  Action
Ans: 2
20. The sqaure of standard deviation is called :
1) Variance
2) Precision
3) Regression
4) Relative Standard Deviation
Ans: 1
21. Which of the following is not considered as determinate error ?
1) Operational Error
2) Additive Error
3) Proportional Error
4) Random Error
Ans: 4
22) Which of the following is used to denote a continuous variables?
A) Simple bar
B) Histogram
C) Pie diagram
D) Multiple bar
Ans: 2
23) Likert scale is:
A) Ordinal scale
B) Nominal scale
C) Variance scale
D) Categorical scale
Ans: 1
24) Measuring variation between two different units is done through :
A) Variance
B) Coefficient of variance
C) Standard deviation
D) Range
Ans: 2
25) Z score criteria applicable to :
A) Normal distribution
B) Skewed deviation
C) Chi square test
D) Paired t test
Ans: 1
26) For a Negative skewed data mean will be;
A) Less than median
B) More than median
C) Equal to median
D) One
Ans: 1
27) Qtest is used for detecting:
A) Outliers
B) Interquartile range
C) Difference of means
D) Difference of proportions
Ans: 1
28) About standard Normal curve all is true except:
A) Area = 1
B) S.D = 1
C) Bell shaped
D) Mean and Median = 1
Ans: 4
29) For calculation of sample size for a prevalence study all of the following are necessary except:
A) Prevalence of disease in population
B) Power of the study
C) Significance level
D) Desired precision
Ans: 4
30) True about cluster sampling are all except :
A) Sample size same as simple random
B) It is two stage sampling
C) Cheaper than other methods
D) It is a method for rapid assessment
Ans: 1
31) In a study, variation in cholesterol was seen before and after giving a drug. The test which would give its significance is :
A) Unpaired t test
B) Fischer test
C) Paired t test
D) Chi square test
Ans: 3
32) Appropriate statistical method to compare two proportion is :
A) Chi square test
B) Student’s t test
C) Odds ratio
D) Correlation Coefficient
Ans: 1
33) For testing the statistical significance of the difference in heights of school children:
A) Student’s test
B) Chi square test
C) Paired t test
D) One way analysis of variance (One way ANOV)
Ans: 4
34) Pearson or Spearman coefficient is used for evaluation of :
A) Differences in proportion
B) Comparison of more than 2 means
C) Comparison of variance
D) Correlation
Ans: 4
35) Receiver Operator Characterstic (RO) curve is usually drawn between:
A) Sensitivity & Specificity
B) (1Sensitivity) & Specificity
C) Sensitivity & (1Specificity)
D) (1Sensitivity) & (1Specificity)
Ans: 3
1) Probability
2) Correlation
3) Measures of Dispersion
4) Harmonic Mean
Answer: 2
2. The word Regression was used for the first time by
1) Sir Francis Galtom in 1877
2) Sir Francis Galton in 1787
3) Fredrick C. Mills in 1877
4) A.L. Bowley 1877
Answer: 1
3. If Mode and Median of a series are 22 and 21.4 respectively, what will be the value of Arithmetic Mean?
1) 15.99
2) 34.30
3) 21.10
4) 19.33
Answer: 3
4. Statistical averages are of how many types?
1) 2
2) 3
3) 4
4) 5
Answer: 2
5. Karl Pearson coefficient of Correlation is calculated on the basis of measure of
1) Arithmetic mean
2) Standard deviation
3) Arithmetic mean and standard deviation
4) Median and standard deviation
Answer: 3
6. The coefficient of variation of a series is 30% and standard deviation is 15, then its arithmetic mean is
1) 0.5
2) 5.0
3) 2.0
4) 50.00
Answer: 4
7. Statistics diagrams are the instruments of
1) Analysis
2) Interpretation
3) Presentation
4) Collection of data
Answer: 3
8. Method of analysis of variance was proposed by_
1) Sir Ronald A. Fisher(1923)
2) Sir Francis Galton(1877)
3) Wallis and Roberts(1911)
4) Karl Pearson(1932)
Answer: 1
9. Which one of the following is the correct sequence of steps of research ?
1) Problem identification, data analysis, hypothesis, conclusion
2) Hypothesis, data collection, sampling, conclusion, data analysis
3) Thinking about solution, selection of tools, hypothesis, data collection, data analysis
4) Problem identification, hypothesis, data collection, data analysis, conclusion
Ans: 4
10. In the identification of problem the researcher should decide
1) The title and the variables
2) The objectives
3) The variables, title and objectives
4) The title
Ans: 3
11. Probability is known as
1) Deliberate sampling
2) Systematic sampling
3) Stratified sampling
4) Simple random sampling
Ans: 4
12. Which aspect is not related with significance of research ?
1) Research inculcates scientific thinking.
2) Solutions suggested in research are universal
3) Research promotes the habit of logical thinking
4) Spatial and temporal aspects are basis of geographical research
Ans: 2
13. Which of the following is not a quality of good research ?
1) Systematic
2) Methods of data analysis should be appropriate
3) Based on preconceived ideas.
4) Logical
Ans: 3
14. Which is not a method of hypothesis testing ?
1) Chisquire Test
2) Circular Test
3) Student's T. Test
4) Parametric Test
Ans: 2
15. Which type of sampling is done if a population from which a sample drawn does not constitute a homogenous group ?
1) Systematic
2) Random
3) Stratified
4) Area
Ans: 3
16. Which is not a type of the measurement of scale ?
1) Simple Scale
2) Nominal Scale
3) Ordinal Scale
4) Ratio Scale
Ans: 1
17. In report writting, select the correct sequence of the following heads using codes given below : (A) Objectives
(B) Cartographic representation (C) Conclusions (D) Data Collection
1) A, B, C and D
2) A, D, B and C
3) D, A, B and C
4) A, B, D and C
Ans: 2
18. Which is not a characteristic of a research problem ?
1) Relationship between variables
2) Research problem should be in question form
3) Protection of moral judgements
4) Test ability
Ans: 3
19. Which of the following is the correct sequence of increased emphasis on practical action related to research ?
1) Applied  Pure Policy Action
2) Pure  Applied Policy Action
3) Action Applied Policy Pure
4) Policy  Pure  Applied  Action
Ans: 2
20. The sqaure of standard deviation is called :
1) Variance
2) Precision
3) Regression
4) Relative Standard Deviation
Ans: 1
21. Which of the following is not considered as determinate error ?
1) Operational Error
2) Additive Error
3) Proportional Error
4) Random Error
Ans: 4
22) Which of the following is used to denote a continuous variables?
A) Simple bar
B) Histogram
C) Pie diagram
D) Multiple bar
Ans: 2
23) Likert scale is:
A) Ordinal scale
B) Nominal scale
C) Variance scale
D) Categorical scale
Ans: 1
24) Measuring variation between two different units is done through :
A) Variance
B) Coefficient of variance
C) Standard deviation
D) Range
Ans: 2
25) Z score criteria applicable to :
A) Normal distribution
B) Skewed deviation
C) Chi square test
D) Paired t test
Ans: 1
26) For a Negative skewed data mean will be;
A) Less than median
B) More than median
C) Equal to median
D) One
Ans: 1
27) Qtest is used for detecting:
A) Outliers
B) Interquartile range
C) Difference of means
D) Difference of proportions
Ans: 1
28) About standard Normal curve all is true except:
A) Area = 1
B) S.D = 1
C) Bell shaped
D) Mean and Median = 1
Ans: 4
29) For calculation of sample size for a prevalence study all of the following are necessary except:
A) Prevalence of disease in population
B) Power of the study
C) Significance level
D) Desired precision
Ans: 4
30) True about cluster sampling are all except :
A) Sample size same as simple random
B) It is two stage sampling
C) Cheaper than other methods
D) It is a method for rapid assessment
Ans: 1
31) In a study, variation in cholesterol was seen before and after giving a drug. The test which would give its significance is :
A) Unpaired t test
B) Fischer test
C) Paired t test
D) Chi square test
Ans: 3
32) Appropriate statistical method to compare two proportion is :
A) Chi square test
B) Student’s t test
C) Odds ratio
D) Correlation Coefficient
Ans: 1
33) For testing the statistical significance of the difference in heights of school children:
A) Student’s test
B) Chi square test
C) Paired t test
D) One way analysis of variance (One way ANOV)
Ans: 4
34) Pearson or Spearman coefficient is used for evaluation of :
A) Differences in proportion
B) Comparison of more than 2 means
C) Comparison of variance
D) Correlation
Ans: 4
35) Receiver Operator Characterstic (RO) curve is usually drawn between:
A) Sensitivity & Specificity
B) (1Sensitivity) & Specificity
C) Sensitivity & (1Specificity)
D) (1Sensitivity) & (1Specificity)
Ans: 3
36. “The systematic and controlled handling of variables to see if treatments will create expected result” is an essential step in
A:Ex Post facto Research
B:Scientific Method
C:Diagnostic method
D:Exploratory research
Correct Answer: OptionB
37. In a sponsored research which of the following action of the sponsor is in compliance with ethical considerations
A: Instructions on How to do research
B: Instructions on what is to be reported and not
C:Instructions on purposes of research
D: Instructions on not to conceal the sponsor
Correct Answer: OptionD
38. Reliability in research stands for
A:Replicability
B:Validity
C:Measureability
D:Comparability
Correct Answer: OptionA
39. Insufficient evidence in research leads to
A:Faulty analysis
B:Over generalization
C:Poor sampling
D: Wrong methodology
Correct Answer: OptionB
40. Citation index is directly related to
A:Periodicity of a journal
B:Popularity of a journal
C:Impact factor of a journal
D: Publication of a journal
Correct Answer: OptionC
41. For two random variables X and Y, the relation E(XY)=E(X)E(Y) holds good
A:if X and Y are statistically independent.
B:for all X and Y.
C:if X and Y are identical.
D:none of these.
Correct Answer: OptionA
A:Ex Post facto Research
B:Scientific Method
C:Diagnostic method
D:Exploratory research
Correct Answer: OptionB
37. In a sponsored research which of the following action of the sponsor is in compliance with ethical considerations
A: Instructions on How to do research
B: Instructions on what is to be reported and not
C:Instructions on purposes of research
D: Instructions on not to conceal the sponsor
Correct Answer: OptionD
38. Reliability in research stands for
A:Replicability
B:Validity
C:Measureability
D:Comparability
Correct Answer: OptionA
39. Insufficient evidence in research leads to
A:Faulty analysis
B:Over generalization
C:Poor sampling
D: Wrong methodology
Correct Answer: OptionB
40. Citation index is directly related to
A:Periodicity of a journal
B:Popularity of a journal
C:Impact factor of a journal
D: Publication of a journal
Correct Answer: OptionC
41. For two random variables X and Y, the relation E(XY)=E(X)E(Y) holds good
A:if X and Y are statistically independent.
B:for all X and Y.
C:if X and Y are identical.
D:none of these.
Correct Answer: OptionA
42. In the simultaneous tossing of two perfect coins, the probability of having atleast one head is
A:12
B:14
C:34
D:1
Correct Answer: OptionC
43. If P1 (x) and P2 (x) be the marginal probability functions of two independent discrete random variables X and Y, then their joint probability function P(x,y)=
A:P1(x)/P2(y)
B:P1(x)P2(y)
C:P2(y)/P1(x)
D:None of these
Correct Answer: OptionB
44. Var(2X± 3) if Var(X)=1 is
A:5
B:13
C:4
D:none of these.
Correct Answer: OptionC
45. The height of persons in a country is a random variable of the type
A:continuous random variable
B:discrete random variable
C:neither discrete nor continuous random variable
D:continuou as well as discrete random variable
Correct Answer: OptionA
46. A probability distribution in which mean is equal to variance is
A:Binomial
B:Gamma
C:Normal
D:Poisson
Correct Answer: OptionD
47. The skewness in a binomial distribution will be zero, if
A:p<1/2
B:p>1/2
C:p<q
D:p=1/2
Correct Answer: OptionD
48. The coefficient of variation of Poisson distribution with mean 4 is
A:1/4
B:2/4
C:4
D:2
Correct Answer: OptionB
49. If X is a normal variate representing the income in Rs. per day with mean=50 and S.D=10. If the number of workers in a factory is 1200, then the number of workers having income more than Rs. 62.00 per =0.3849 where Z is a standard normal variate)
A:462
B:738
C:138
D:none of the above.
Correct Answer: OptionC
50. The distribution for which mode does not exist is
A:normal
B:tdistribution
C:continuous rectangular distribution
D:F distribution
Correct Answer: OptionC
51. A box contains 12 items out of which 4 are defective. A person selects 6 items from the box. The expected number of defective items out of his selected items is
A:2
B:3
C:3/2
D:none of the above.
Correct Answer: OptionA
52. If Z is a standard normal variate, the proportion of items lying between z=0.5 and z=3.0 is
A:0.4987
B:0.1915
C:0.3072
D:0.3098
Correct Answer: OptionC
53. Factorization theorem for sufficiency is known as
A:RaoBlackwell theorem
B:CramerRao theorem
C:ChapmanRobins theorem
D:FisherNeyman theorem
Correct Answer: OptionD
54. If the expected value of an estimator is not equal to its parametric function τ(Θ) , it is said to be a
A:unbiased estimator
B:biased estimator
C:consistent estimator
D:none of the above.
Correct Answer: OptionB
55. The sample median is _______________ estimate for the mean of normal population.
A:unbiased
B:consistent
C:unbiased and consistent
D:none of the above.
Correct Answer: OptionC
56. If a sufficient estimator exists it is a function of the _______ estimator.
A:moment estimator
B:minimum chisquare estimator
C:maximum likelihood estimator
D:none of the above
Correct Answer: OptionC
57. The credit of inventing the method of moments for estimating the parameter goes to
A:R. A. Fisher
B:J. Neyman
C:Laplace
D:Karl Pearson
Correct Answer: OptionD
58. CramerRao inequality with regard to the variance of an estimator provides
A:upper bound on the variance
B:lower bound on the variance
C:asymptotic variance of an estimator
D:none of the above
Correct Answer: OptionB
59. Estimate and Estimator are
A:synonyms
B:related to population
C:different
D:none of the above
Correct Answer: OptionC
60. The idea of testing of hypothesis was first set forth by
A:R.A.Fisher
B:J.Neyman
C:E.L.Lehman
D:A.Wald
Correct Answer: OptionB
61. A wrong decision about H0 leads to
A:one kind of error
B:two kinds of errors
C:three kinds of errors
D:four kinds of errors
Correct Answer: OptionB
62. In terms of type II error β and θ , the true parameter, the function 1β(θ) is called
A:power of the test
B:power function
C:OC function
D:none of the above
Correct Answer: OptionB
63. Testing H0:µ =1500 against µ<1500 leads to
A:onesided lower tailed test
B:onesided upper tailed test
C:twotailed test
D:all the above
Correct Answer: OptionA
64. The mean difference between 9 paired observations is 15.0 and the standard deviation of differences is 5.0. The value of statistic t is
A:27
B:9
C:3
D:zero
Correct Answer: OptionB
65. Range of statistic t is
A:1 to 1
B:−∞ to ∞
C:0 to ∞
D:0 to 1
Correct Answer: OptionB
66. Given the following eight sample values 4, 3, 3, 0, 3, 3, 4, 4 the value of student's tstatistc to test H0 : µ =0 is
A:2.73
B:0.97
C:3.30
D:0.41
Correct Answer: OptionD
67. In a contingency table, the expected frequencies are computed under
A:null hypothesis H0
B:alternative hypothesis H1
C:H0 and H1 both
D:no consideration of hypothesis
Correct Answer: OptionA
68. The term regression was introduced by
A:R.A.Fisher
B:Sir Francis Galton
C:Karl Pearson
D:none of the above
Correct Answer: OptionB
69. If βYX and βXY are two regression coefficients they have
A:same sign
B:opposite sign
C:either same or opposite signs
D:nothing can be said
Correct Answer: OptionA
70. If a constant 50 is subtracted from each of the value of X and Y, the regression coefficient is
A:reduced by 50
B:150 th of the original regression coefficient
C:increased by 50
D:not changed
Correct Answer: OptionD
71. If ρ is the simple correlation coefficient, the quantity ρ2 is known as
A:coefficient of determination
B:coefficient of nondetermination
C:coefficient of alienation
D:none of the above
Correct Answer: OptionA
72. The range of simple correlation coefficient is
A:0 to ∞
B:∞ to ∞
C:0 to 1
D:1 to 1
Correct Answer: OptionD
73. The hypothesis for a specific known value of ρ can be tested by
A:ttest
B:Ztest
C:χ2 test
D:Ftest
Correct Answer: OptionB
74. A measure of linear association of a variable with a number of other variables is known as
A:partial correlation
B:simple correlation
C:autocorrelation
D:multiple correlation
Correct Answer: OptionD
75. Given the regression lines X+2Y5=0, 2X+3Y8=0 and Var(X)=12, the value of Var(Y) is
A:16
B:34
C:43
D:4
Correct Answer: OptionD
76. The sales of a departmental store on Dushera and Diwali are associated with the component of a time series
A:secular trend
B:irregular variation
C:seasonal variation
D:all the above
Correct Answer: OptionC
77. Which index satisfies factor reversal test?
A:Paasche's index
B:Laspeyer's index
C:Walsch price index
D:Fisher's ideal index
Correct Answer: OptionD
78. Control chart consists of
A:three control lines
B:upper and lower control lines
C:the level of the process
D:all the above
Correct Answer: OptionA
79. Replication in an experiment means
A:the number of blocks
B:the number of times a treatment occurs in an experiment
C:total number of treatments
D:none of the above
Correct Answer: OptionB
80. Local control in experimental designs is meant to
A:increase the efficiency of the design
B:reduce experimental error
C:to form homogeneous blocks
D:all the above
Correct Answer: OptionD
81. Moving average method of fitting trend in a time series data removes the effect of
A:long term movements
B:seasonal variation
C:cyclic variations
D:shortterm movements
Correct Answer: OptionD
A:12
B:14
C:34
D:1
Correct Answer: OptionC
43. If P1 (x) and P2 (x) be the marginal probability functions of two independent discrete random variables X and Y, then their joint probability function P(x,y)=
A:P1(x)/P2(y)
B:P1(x)P2(y)
C:P2(y)/P1(x)
D:None of these
Correct Answer: OptionB
44. Var(2X± 3) if Var(X)=1 is
A:5
B:13
C:4
D:none of these.
Correct Answer: OptionC
45. The height of persons in a country is a random variable of the type
A:continuous random variable
B:discrete random variable
C:neither discrete nor continuous random variable
D:continuou as well as discrete random variable
Correct Answer: OptionA
46. A probability distribution in which mean is equal to variance is
A:Binomial
B:Gamma
C:Normal
D:Poisson
Correct Answer: OptionD
47. The skewness in a binomial distribution will be zero, if
A:p<1/2
B:p>1/2
C:p<q
D:p=1/2
Correct Answer: OptionD
48. The coefficient of variation of Poisson distribution with mean 4 is
A:1/4
B:2/4
C:4
D:2
Correct Answer: OptionB
49. If X is a normal variate representing the income in Rs. per day with mean=50 and S.D=10. If the number of workers in a factory is 1200, then the number of workers having income more than Rs. 62.00 per =0.3849 where Z is a standard normal variate)
A:462
B:738
C:138
D:none of the above.
Correct Answer: OptionC
50. The distribution for which mode does not exist is
A:normal
B:tdistribution
C:continuous rectangular distribution
D:F distribution
Correct Answer: OptionC
51. A box contains 12 items out of which 4 are defective. A person selects 6 items from the box. The expected number of defective items out of his selected items is
A:2
B:3
C:3/2
D:none of the above.
Correct Answer: OptionA
52. If Z is a standard normal variate, the proportion of items lying between z=0.5 and z=3.0 is
A:0.4987
B:0.1915
C:0.3072
D:0.3098
Correct Answer: OptionC
53. Factorization theorem for sufficiency is known as
A:RaoBlackwell theorem
B:CramerRao theorem
C:ChapmanRobins theorem
D:FisherNeyman theorem
Correct Answer: OptionD
54. If the expected value of an estimator is not equal to its parametric function τ(Θ) , it is said to be a
A:unbiased estimator
B:biased estimator
C:consistent estimator
D:none of the above.
Correct Answer: OptionB
55. The sample median is _______________ estimate for the mean of normal population.
A:unbiased
B:consistent
C:unbiased and consistent
D:none of the above.
Correct Answer: OptionC
56. If a sufficient estimator exists it is a function of the _______ estimator.
A:moment estimator
B:minimum chisquare estimator
C:maximum likelihood estimator
D:none of the above
Correct Answer: OptionC
57. The credit of inventing the method of moments for estimating the parameter goes to
A:R. A. Fisher
B:J. Neyman
C:Laplace
D:Karl Pearson
Correct Answer: OptionD
58. CramerRao inequality with regard to the variance of an estimator provides
A:upper bound on the variance
B:lower bound on the variance
C:asymptotic variance of an estimator
D:none of the above
Correct Answer: OptionB
59. Estimate and Estimator are
A:synonyms
B:related to population
C:different
D:none of the above
Correct Answer: OptionC
60. The idea of testing of hypothesis was first set forth by
A:R.A.Fisher
B:J.Neyman
C:E.L.Lehman
D:A.Wald
Correct Answer: OptionB
61. A wrong decision about H0 leads to
A:one kind of error
B:two kinds of errors
C:three kinds of errors
D:four kinds of errors
Correct Answer: OptionB
62. In terms of type II error β and θ , the true parameter, the function 1β(θ) is called
A:power of the test
B:power function
C:OC function
D:none of the above
Correct Answer: OptionB
63. Testing H0:µ =1500 against µ<1500 leads to
A:onesided lower tailed test
B:onesided upper tailed test
C:twotailed test
D:all the above
Correct Answer: OptionA
64. The mean difference between 9 paired observations is 15.0 and the standard deviation of differences is 5.0. The value of statistic t is
A:27
B:9
C:3
D:zero
Correct Answer: OptionB
65. Range of statistic t is
A:1 to 1
B:−∞ to ∞
C:0 to ∞
D:0 to 1
Correct Answer: OptionB
66. Given the following eight sample values 4, 3, 3, 0, 3, 3, 4, 4 the value of student's tstatistc to test H0 : µ =0 is
A:2.73
B:0.97
C:3.30
D:0.41
Correct Answer: OptionD
67. In a contingency table, the expected frequencies are computed under
A:null hypothesis H0
B:alternative hypothesis H1
C:H0 and H1 both
D:no consideration of hypothesis
Correct Answer: OptionA
68. The term regression was introduced by
A:R.A.Fisher
B:Sir Francis Galton
C:Karl Pearson
D:none of the above
Correct Answer: OptionB
69. If βYX and βXY are two regression coefficients they have
A:same sign
B:opposite sign
C:either same or opposite signs
D:nothing can be said
Correct Answer: OptionA
70. If a constant 50 is subtracted from each of the value of X and Y, the regression coefficient is
A:reduced by 50
B:150 th of the original regression coefficient
C:increased by 50
D:not changed
Correct Answer: OptionD
71. If ρ is the simple correlation coefficient, the quantity ρ2 is known as
A:coefficient of determination
B:coefficient of nondetermination
C:coefficient of alienation
D:none of the above
Correct Answer: OptionA
72. The range of simple correlation coefficient is
A:0 to ∞
B:∞ to ∞
C:0 to 1
D:1 to 1
Correct Answer: OptionD
73. The hypothesis for a specific known value of ρ can be tested by
A:ttest
B:Ztest
C:χ2 test
D:Ftest
Correct Answer: OptionB
74. A measure of linear association of a variable with a number of other variables is known as
A:partial correlation
B:simple correlation
C:autocorrelation
D:multiple correlation
Correct Answer: OptionD
75. Given the regression lines X+2Y5=0, 2X+3Y8=0 and Var(X)=12, the value of Var(Y) is
A:16
B:34
C:43
D:4
Correct Answer: OptionD
76. The sales of a departmental store on Dushera and Diwali are associated with the component of a time series
A:secular trend
B:irregular variation
C:seasonal variation
D:all the above
Correct Answer: OptionC
77. Which index satisfies factor reversal test?
A:Paasche's index
B:Laspeyer's index
C:Walsch price index
D:Fisher's ideal index
Correct Answer: OptionD
78. Control chart consists of
A:three control lines
B:upper and lower control lines
C:the level of the process
D:all the above
Correct Answer: OptionA
79. Replication in an experiment means
A:the number of blocks
B:the number of times a treatment occurs in an experiment
C:total number of treatments
D:none of the above
Correct Answer: OptionB
80. Local control in experimental designs is meant to
A:increase the efficiency of the design
B:reduce experimental error
C:to form homogeneous blocks
D:all the above
Correct Answer: OptionD
81. Moving average method of fitting trend in a time series data removes the effect of
A:long term movements
B:seasonal variation
C:cyclic variations
D:shortterm movements
Correct Answer: OptionD
82. Which measure of location will be suitable to compare heights of students in two classes?
A:Mean
B:Median
C:Mode
D:None of these
Correct Answer: OptionA
83. The geometric mean of 2, 4, 16 and 32 is
A:6
B:7
C:8
D:9
Correct Answer: OptionC
84. The strength of seven colleges in a city are 385,1748,1343,1935,786,2874 and 2108. Then the median strength is
A:1935
B:1748
C:1343
D:2874
Correct Answer: OptionB
85. The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is actually 110. Therefore, the true mean is ___ and the true median is _____ .
A:50.1, 52
B:50.9, 53
C:51.1, 52
D:50, 53
Correct Answer: OptionA
86. 10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations. The mean of a combined set is given by
A:15
B:10
C:8.5
D:7.5
Correct Answer: OptionC
87. A distribution with more than two modes is called
A:unimodal
B:bimodal
C:multimodal
D:none of these
Correct Answer: OptionC
88. The algebraic sum of the deviations of a set of n values from their arithmetic mean is
A:n
B:0
C:1
D:none of these
Correct Answer: OptionB
89. The mean of 20 observations is 15. On checking it was found that two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 4, then the correct mean is
A:15.15
B:16.15
C:17.15
D:14.15
Correct Answer: OptionA
90. Sum of absolute deviations about median is
A:least
B:greatest
C:zero
D:equal
Correct Answer: OptionA
91. If each of a set of observations of a variable is multiplied by a constant (nonzero) value, the variance of the resultant variable
A:is unaltered
B:increases
C:decreases
D:is unknown
Correct Answer: OptionB
92. The standard deviation of a distribution is 5. The value of the fourth central moment µ4 in order that the distribution be mesokurtic should be
A:equal to 3
B:greater than 1875
C:equal to 1875
D:less than 1875
Correct Answer: OptionC
93. In a frequency curve of scores the mode was found to be higher than the mean. This shows that the distribution is
A:symmetric
B:negatively skewed
C:positively skewed
D:normal
Correct Answer: OptionB
94. A coin is tossed three times in succession, the number of sample points in sample space is
A:6
B:8
C:3
D:4
Correct Answer: OptionB
95. If A and B are two independent events, the probability that both A and B occur is 1/8 and the probability that neither of them occurs is 3/8 . The probability of the occurrence of A is
A:1/2
B:1/3
C:1/4
D:1/5
Correct Answer: OptionA
96:In a Time series data, the two main components which cause lack of stationarity are
A:Seasonal and irregular variations
B:Cyclic and irregular variations
C:Trend and cyclic variations
D:Trend and seasonal variations
Ans: D
97:In the ARMA (1, 1) model `Z_t = ``phi Z_{t1} + epsilon _t  theta epsilon_{t1}` the condition for stationarity
and invertilibility are respectively
A:`  phi  <= 1 and  theta  < 1` with `phi != theta`
B:`  phi  <= 1 and  theta  < 1` with `phi = theta`
C:`  phi  > 1 and  theta  > 1` with `phi!= theta`
D:`  phi  > 1 and  theta  > 1` with `phi = theta`
Ans: A
98:In a Linear programming Problem with `n + m` variables and `m` constraints the number of basic solutions is
A:` ((n+m),(m))`
B:`((n),(m))`
C:`((m),(n))`
D:`((n+m),(nm))`
Ans: A
99:If the demand curve is of the form `p = ae^{bx}` , where `p` is the price and `x` is the demand, then the
price elasticity of demand is
A:`eta_p = bx`
B:`eta_p =  bx`
C:`eta_p = 1//bx`
D:`eta_p =  1 // bx`
Ans: C
100:The Engel's curves for constant prices and those for constant incomes are respectively
A:Concave and Convex
B:Convex and Concave
C:Both Concave
D:Both Convex
Ans: B
A:Mean
B:Median
C:Mode
D:None of these
Correct Answer: OptionA
83. The geometric mean of 2, 4, 16 and 32 is
A:6
B:7
C:8
D:9
Correct Answer: OptionC
84. The strength of seven colleges in a city are 385,1748,1343,1935,786,2874 and 2108. Then the median strength is
A:1935
B:1748
C:1343
D:2874
Correct Answer: OptionB
85. The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is actually 110. Therefore, the true mean is ___ and the true median is _____ .
A:50.1, 52
B:50.9, 53
C:51.1, 52
D:50, 53
Correct Answer: OptionA
86. 10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations. The mean of a combined set is given by
A:15
B:10
C:8.5
D:7.5
Correct Answer: OptionC
87. A distribution with more than two modes is called
A:unimodal
B:bimodal
C:multimodal
D:none of these
Correct Answer: OptionC
88. The algebraic sum of the deviations of a set of n values from their arithmetic mean is
A:n
B:0
C:1
D:none of these
Correct Answer: OptionB
89. The mean of 20 observations is 15. On checking it was found that two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 4, then the correct mean is
A:15.15
B:16.15
C:17.15
D:14.15
Correct Answer: OptionA
90. Sum of absolute deviations about median is
A:least
B:greatest
C:zero
D:equal
Correct Answer: OptionA
91. If each of a set of observations of a variable is multiplied by a constant (nonzero) value, the variance of the resultant variable
A:is unaltered
B:increases
C:decreases
D:is unknown
Correct Answer: OptionB
92. The standard deviation of a distribution is 5. The value of the fourth central moment µ4 in order that the distribution be mesokurtic should be
A:equal to 3
B:greater than 1875
C:equal to 1875
D:less than 1875
Correct Answer: OptionC
93. In a frequency curve of scores the mode was found to be higher than the mean. This shows that the distribution is
A:symmetric
B:negatively skewed
C:positively skewed
D:normal
Correct Answer: OptionB
94. A coin is tossed three times in succession, the number of sample points in sample space is
A:6
B:8
C:3
D:4
Correct Answer: OptionB
95. If A and B are two independent events, the probability that both A and B occur is 1/8 and the probability that neither of them occurs is 3/8 . The probability of the occurrence of A is
A:1/2
B:1/3
C:1/4
D:1/5
Correct Answer: OptionA
96:In a Time series data, the two main components which cause lack of stationarity are
A:Seasonal and irregular variations
B:Cyclic and irregular variations
C:Trend and cyclic variations
D:Trend and seasonal variations
Ans: D
97:In the ARMA (1, 1) model `Z_t = ``phi Z_{t1} + epsilon _t  theta epsilon_{t1}` the condition for stationarity
and invertilibility are respectively
A:`  phi  <= 1 and  theta  < 1` with `phi != theta`
B:`  phi  <= 1 and  theta  < 1` with `phi = theta`
C:`  phi  > 1 and  theta  > 1` with `phi!= theta`
D:`  phi  > 1 and  theta  > 1` with `phi = theta`
Ans: A
98:In a Linear programming Problem with `n + m` variables and `m` constraints the number of basic solutions is
A:` ((n+m),(m))`
B:`((n),(m))`
C:`((m),(n))`
D:`((n+m),(nm))`
Ans: A
99:If the demand curve is of the form `p = ae^{bx}` , where `p` is the price and `x` is the demand, then the
price elasticity of demand is
A:`eta_p = bx`
B:`eta_p =  bx`
C:`eta_p = 1//bx`
D:`eta_p =  1 // bx`
Ans: C
100:The Engel's curves for constant prices and those for constant incomes are respectively
A:Concave and Convex
B:Convex and Concave
C:Both Concave
D:Both Convex
Ans: B