Preface The book entitled “Agricultural Statistics” has been designed for all U.G. and P.G. Students of “Pure Statistics, Agricultural Statistics, Biological & Social Sciences” and those who have to appear in competitive examinations of I.S.S., S.S.S., State’s P.S.C.’ and I.A.S. Tis book is also useful for faculties of “Department of Statistics” of Indian Universities. The book is the outcome of 28 years of teaching experience of U.G., P.G. and Ph. D. students of different disciplines of Agriculture, Agil. Engg. and Agril. Statistics. in J.N.K.V.V. Jabalpur. The content of the book covers the syllabus on the topic “Statistical Methods.” The book contains 15 chapters, out of which the chapters (1-4) deal with Discriptive Statistics, (5) Probability Theory, (6-10) Random variables and Distribution Functions, (11-14) Theory of Tests of Significance based on small and large samples and (15) Simple & Multiple Correction - Regression Analysis. In each chapter, three types of question” True/ False, Fill in the Blanks and Multiple Choice Questions & Answers” alongwith the “Key Answers” have been provided. During the preparation 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. Khara, 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. The author is very much thankful and extends his honourable honour of higher order to Prof. Kalloo Gautam, The Vice -chancellor (J.N.K.V.V Jabalpur) for his kind permission to hand the manuscript to “New India Publishing Agency” New Delhi to publish it in the present shape of a book. The author is thankful to Sh. Harishchand Maurya; Smt. Sangeeta Maurya and their lovely children (Mr. Rohit & Ku. Richa) Maurya for providing moral support during the preparation of the manuscript.

Preliminaries Section-A : Write True / False Q.1 Statistics in singular is used to denote a subject (branch) of science. Q.2 Statistics in plular is used to denote data or methods. Q.3 The data first time collected is known as primary data. Q.4 Primary data is collected from published report. Q.5 Editing of data is not necessary. Q.6 Consistency must be maintained in data. Q.7 Baised and unbiased errors are known as statistical error. Q.8 Arrangement of data in different, rows & columns is known as classification.

Section-A : Write True / False Q.1 A better and more beautiful way to present the data in a more visual form can be done by means of diagram. Q.2 Description of data through diagrams and graphs is better for layman. Q.3 Diagram does not register a meaningful impression almost before we start to think about it. Q.4 Diagrams are never used by the business man and government agencies for advertisement and educating people. Q.5 Diagrams do not give visual presentation of data. Q.6 The diagrams put a rememberance for a longer time in mind of human being. Q.7 Diagrams facilitate comparison and reveal pattern of data. Q.8 Diagrams show approximate values of items in data. Q.9 Diagrams are more attractive, appealing and impressive than tables. Q.10 Diagrams can be more easily compared and interpreted than the tables. Q.11 Tables contain precise figures while diagrams indicate approximate figures.

Section-A : Write True / False Q.1 Dispersion of a given set of values, gives an idea about the homogeneity or heterogeneity of the distribution of values. Q.2 The measure of scatteredness of a set of values about an average is known as the “measure of variation or dispersion”. Q.3 The measure of dispersion must be based on all the observations. Q.4 Measure of dispersion should be amenable to further mathematical treatment. Q.5 Measure of dispersion should be affected as little as possible by fluctuation of sampling. Q.6 The measures which express the spread of observations in terms of distance between the values of two selected observations, are known as “distance measures” e.g. range and interquartile range (or quartile deviation).

Section-A : Write True / False Q.1 If an experiment is repeated under an identical conditions, we generally come to a result (i.e. outcome) which is unique or certain. Q.2 In an experiment, the result (outcome) may not be unique but it is one of the several possible outcomes. Q.3 The phenomena described in Ql, are known as “deterministic or predictable”. Q.4 In deterministic phenomena, the results can be predicted with certainity Q.5 A deterministic model stipulates that the conditions under which an experiment is performed, determine the ouctome of the experiment Q.6 The phenomena which do not lead themselves to deterministic approach, are known as “Unpredictable or probabilistic” phenomena. Q.7 The phenomena frequently occured in business, economic and social science or even in our day to day life, are known as “deterministic phenomena”. Q.8 A manufacturer can ascertain the future demand of his product with certainity. Q.9 A sales manager can not predict with certainity about the sales target next year.

Section-A : Write True / False Q.1 A random variable (r.v) is a real number x connected with the outcomes of a random experiment. Q.2 In tossing of a balanced die at one time, the number coming on the upper most face of the die is a random variable x which takes any one out of 6 values taken as 1, 2, 3, 4, 5, 6. Q.3 Let s be the sample space associated with a given random experiment. A real valued function defned on s and taking values in R (-∞,∞) is called one dimensional random variable. Q.4 In general a n dimensional random variable is simply a function whose domain is S and whose range is a collection of n-tuples of real members (vectors in n-space).

Section-A : Write True / False Q.1 The average value of a random fenamenon is termed as “Mathematical Expectation” or “Expected value” of random fenamenon. Q.2 The mathematical expression to compute the expected value of a discrete random variable X with its p.m.f. f(x) is def ned as

Section-A : Write True / False Q.1 The moment generating function (m.g.f) of a random variable X (about origin having the probability function f (x) is defned as

9.1 Section-A : Write True / False Q.1 The probabilistic laws for dif erent values of a random variable are made on the basis of given conditions. T ese conditions are known as "prior considerations". Q.2 If the probabilistic laws are made for dif erent values of a random variable on the basis of results obtained from an experiment, then such results are known as "a posterior inferences".9.1.1 Discrete Uniform Distribution Q.3 A random variable X is said to have a discrete uniform distribution over the range [1, n] if its p.m.f is written as

Section-A : Write True / False 10.1.1 Normal Distribution Q.1 A r.v. X is said to have a normal distribution with parameters (μ, σ2) if its p.d.f. is given by the probability law

11.1 Section-A : Write True / False Q.1 Some assumptions or guesses made about the unknown population parameters, is know as "Statistical hypothesis". Q.2 For the normal distribution N(μ, σ2), the statement (1) μ = 25.0 and (ii) σ2 = 37.0, are known as statistical hypotheses. Q.3 Let p = 0.5 is the probability of getting a head in single throw of a coin. Ten, this statement is not a statistical hypothesis. Q.4 The statistical hypothesis under consideration (under test), is known as "Null hypothesis". Q.5 The null hypothesis is denoted by "Ho".

12.1 Section-A : Write True / False Q.1 Almost all biological data e.g. crop yield, plant height, seed weight, seed size, protein content in pulse, oil content in oil seed etc. are assumed to be normaly distributed. Q.2 Let X be a normal variable with N(μ, σ2). The random variable Z def ned as Z = (x - μ)/σ, is known as standard normal variable. Q.3 The standard normal variable Z is denoted as Z ~ N (0, 1). Q.4 The p.d.f. of random variable Z is given as

13.1 Section-A : Write True / False Q.1 The square of a standard normal variate is known as Chi-square variate with one d.f. Q.2 If X ~ N(μ, σ2) and Z = (x - μ)/σ then Z2 is known as Chi-square variate with 1.d.f. Q.3 If Xi ~ N(μi, σi), i = 1,2,...., n are n independent normal variates then

14.1 Section-A : Write True / False Q.1 If sample size n is small ie n < 30, then the small sample test is applicable. Q.2 The exact sample test (small sample test) can be applied to large sample test but the converse is not plaussible. Q.3 If (x21 , x22 ) are two independent chi-square variates with (V1, V2) degree of freedom then F statistic is def ned as

15.1 Section-A : Write True / False Q.1 In bivariate distribution if the change in one variable afects a change in the other variable, the variables are said to be correlated. Q.2 If the change in both the variables takes place in the same direction then the variables are said to have a positive or direct correlation. Q.3 The pair of variables say, Income and expenditure in house hold or the height and weight of a group of children possess the direct correlation between them. Q.4 If the change in both the variables takes place in oposite directions, then the variables are said to have "Negative or inverse" correlation. Q.5 The pairs of variables say (i) Price and demand of a commodities or (ii) Volume and pressure of a perfect gas" have a negative correlation. Q.6 The two variables are said to have a perfect positive correlation if the deviation in one variable is followed by a corresponding and proportionate deviation in the other variable. Q.7 There are some funny combinations of variables between which the correlation are said to be "spurious or nonsense".

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