Preface The book entitled “Inferential Statistics” has been designed for all P.G. and Ph.D. students of “Pure Statistics” and Agricultural Statistics and for those who have to appear in competitive examinations of I.S.S., I.E.S., state’s PS.C and IAS. This book is also useful for faculties of “Department of Statistics” of Indian Universities. The book is the outcome of 30 years of teaching experience of U.G., P.G. and Ph.D. students of different disciplines of Agriculture, Agril. Engg. and Agril Statistics in J.N.K.V.V., Jabalpur. The content of the book covers the syllabus on the topic “Statistical Inference.” The book contains 9 chapters out of which Chapters (1-2) deals with the “Point Estimation”, (3) Interval estimation, (4-5) Test of hypothesis, (6) Sequential statistics, (7) Decision theory, (8) Linear estimation and (9) Theory of ordered statistics. In each chapter three type of questions. “True/False, Fill in the Blanks and Multiple Choice Questions & Answers” alongwith “Key Answers” have been provided. During the preperation of this manuscript, the author has incorporated the fruitful academic advices provided by Dr. H.P. Singh, Prof & Head, School of Studies in Statistics, Vikram University, Ujjain and Dr. B.B. Khare, Prof. (Statistics), Department of Statistics, B.H.U., Varanasi. It is expected to have a good popularity due to its usefulness amongst students and its users.

1.1 Write True/False Q.1    The process of knowing all the relevant information from the known sample to the unknown population, is known as “Statistical Inference.” Q.2    An enquier may be completely unknown to some feature of the population but he may want to guess completely about that feature based on a random sample drawn from the population. This type of problem is known as the “Problem of Estimation.”

2.1  Write True/False Q.1    From theoretical point of view, the most general method of estimation is the “Maximum Likelihood Estimation Method.” Q.2    The method of “maximum Likelihood Estimation” was initially formulated by the statistician named as “C.F. Gauss.”

3.1  Write True/False Q.1    The estimates obtained though various methods of point estimation, in general, do not concide with the true values of the parameters. Q.2    The statistician is interested in finding an ‘interval’ within which the true value of the parameter θ is expected to lie with certain ‘confidence coefficient’, say (1 – α).

4.1 Write True/False 4.1.1 Preliminaries Q.1    In selection of a test, one should try to keep the probabilities of both types of error small. Q.2    Under a non-sequential sampling scheme (i.e. fixed sample size n), it is not possible to minimise both the errors at the same time.

5.1  Write True/False Q.1    The null hypothesis H0 is said to be composite if it does not specify the joint probability of x1, x2, ......, xn completely. Q.2    We may write null hypothesis as :     H0 : θΣ Ωθ0-

6.1  Write True/False Q.1    A procedure to make an inference about the unknown values of parameters of one or more than one distribution in which the sample size say n is a ramdom variable, is known as “Sequential procedure.” Q.2    The principal feature of sequential procedure is a ‘Sampling Scheme’ which provides a rule under which one decides at each stage of sampling whether to stop or continue the sampling work.

7.1  Write True/False Q.1    All the problem of statistical inference may be considered as the problem of “Decision making in the face of uncertainty.” Q.2    The problem of point estimation is the problem if deciding which value in the “parameter space” Wq is the true value of the parameter.

8.1 Write True/False Q.1    Any linear function of sample observations which is used to estimate the population parameter or parametric function,is called the “Linear estimator.”

9.1  Write True/False Q.1    In the subject matter of order statistic, the useful beta distribution is written as :

Bibliography 1.    Alexander M. Mood, Franklin A. Gryabill and Duane C. Bose : (1974) Introduction to the Theory of Statistics. McGraw. - Hill. 2.    Agarwal, B.L. (1999) : Basic Statistics. Wiley Eastern Ltd., New Delhi. 3.    Fisher, R.A. (1925) : Theory of Statistical Estimation, Proceedings of Combridge Philosophical Society. 4.    Gupta, S.C. and Kapoor, V.K. (1983) : Fundamental of Mathematical Statistics. Kushwaha, K.S. Sultan Chand and Sons, New Delhi. 5.    Goon, A.M., Gupta, M.K. and Dasgupta, B. (1980) : An Outlines of Statistical Theory. The World Press Pvt. Ltd., Kolkata. 6.    Kushwaha, K.S. and Kumar, Rajesh (2009) : The Theory of Sample Survey and Statistical Decisions, New India Publishing Agency, New Delhi. 7.    Kushwaha, K.S. and Kumar, Rajesh (2009) : Basic Concept in Statistics. New India Publishing Agency, New Delhi. 8.    Kendall, M.G. and Stuart, A. (1961) : The Advance Theory of Statistics, Vol.-2. Charles Griffin and Company, Ltd. London. 9.    Murray, R. Spiegel (1961) : Schaum’s Outline of Theory and Problems of Statistics. Schaum Publishing Company, New Yark. 10.    Raw, C.R. (1973) : Linear Statistical Inference. John Wiley. 11.    Steel, R.G.D. and Torrie, J.H. (1980) : Principles and Procedures of Statistics, A Biometrical Approach. McGraw Hill Kogakusha, Ltd. International Student Edition. 12.    Searle, S.R. (1971) : Linear Models. John Wiley.