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In this chapter some preliminary terminologies have been provided which are very much useful and frequently used in dealing with the theory of sample surveys and its application.

Important Definitions

• Sampling method or sampling technique is the process of studying the population by gathering information (on basis of samples) and analyzing that data.

• Population: The whole group we are interested in census.

• Census: A collection of data from the whole population

• Sample: A collection of data from part of the population

• Parameter Vs Statistics: Parameter is statistical measure pertaining to population whereas statistics is measure pertaining to sample.

• Estimate-Value of population parameter obtained from sample.

• Livestock census carried every 5 years (2019-20th livestock census)

7.1 Meaning of Sampling
    
Before we consider sampling theory, we first define the terms population and sample.
 
The word ‘population’ or ‘universe’ in statistics is used to refer to any collection of individuals or of their attributes or of results of operations which can be numerically specified. For example the assemblage of heights of all the individuals in the population is called a population of heights.  Similarly we may consider the population of weights, wages, yields of grain; prices of wheat, mileages of automobile tyres, etc. a population containing a finite number of individuals or members is called a finite population.  For instance the population f ages of the workers in a factory constitute a finite population of ages. A population with infinite number of members is known as infinite population.  For example the population of pressures of temperatures at various points in the atmosphere is an infinite population. 

True/False

Q.1.    Collectivity (totality) of all sampling units is known as the “Population” and population size is denoted by “N”.
Q.2.    A list of all sampling units with their identification is known as “Sampling frame”. For example a list of all newly-born children in maternity home during a period of three months with specification of their sex, weight, name of their parents, their permanent address, etc. is known as sampling frame.
Q.3.    A function of all sampling units in the population is known as population parameter or population constant.

A sample is just a part of a population selected according to some rule or plan. Following are some of the methods of sampling.

1. Simple Random Sampling

The simplest and the most commonly used type of probability sampling is simple random sampling. In this kind of sampling, each member of the population has the same probability of being included in the sample. Simple random sampling may be with or without replacement.

Population: The word population or universe in statistics means a set of observations relating to a phenomenon under investigation.

Sample: It is a fraction or a subset of population drawn through a valid statistical procedure so that it can be regarded as representative of the entire population.

Sampling: The statistical procedure of drawing a sample from the population is called Sampling.

Census enquiry or complete enumeration: When each and every unit of the population is investigated for the characteristic under study, known as census enquiry or complete enquiry.

Sample enquiry or sample enumeration: It is a part of the population is investigated for the characteristic under study, known as sample enquiry or sample enumeration.

Necessity of sampling: Since, the process of collecting information from all the elements of a large population may be, in general, expensive, time consuming and difficult. We help to sampling and generalise the properties of the sample to the entire population. The statistical procedures which are used for drawing inferences or conclusions about the population from sample data are covered under Inferential Statistics or Statistical inference. Thus, sampling theory is the basis of statistical inference in which we wish to obtain maximum information about the population with minimum effort and maximum precision.

Sampling is the process of drawing a part of population supposed to be the representative of that population.

Types: Sampling process can be either random or non-random. Most frequently we use random sampling method in our studies. But sometimes the purpose of the study demands for non-random sampling in one or other phase of sampling (Example: When we want to study the impact of life skills development programme on the disabled female beneficiaries)

Rationally selected and contextually defined research problem is the foundation to the successful research project. If the selected research problem is not in line with the interests of the researcher, available time, resources, infrastructure & knowledge base then achieving success in research process remains highly uncertain. Consequently, in addition to hindering of professional growth of the researcher, it also results in wastage of time, money and human effort. Most importantly, it may sometimes add up incorrect knowledge into scientific base, hindering the process of scientific progress. Hence the identification of the research problem and designing the problem statement is the most important step in the research process.

One of the objectives of experiments in cultivators’ field is to test technology for adoption in a targeted area i.e. NARP Zone, or a district. In that case interaction between district x treatment within a zone or between blocks x treatment within a district should not be significant. If the targeted area is a district, an experiment in cultivators’ fields must occur in at least two blocks. Also, if the targeted area is a zone, an experiment should occur in at least two districts in order to estimate interaction.

Analysis of cultivators’ field experiment

The on-farm trials were conducted in 25 villages on kharif rice during 1992-93. The treatments viz. T1-Farmers’ practice with local variety, T2-Farmers’ practice with improved variety, T3-Farmers’ practice with improved variety +recommended fertilizer and T4-Improved practice with improved variety +recommended fertilizer. Farmers level of NPK fertilizer was 40:0:0 and local variety was Suzata while recommended NPK fertilizer was 80:40:20.

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.

In many experimental situations, it becomes necessary to repeat an experiment over time ( for a number of seasons or years ) and / or over space ( a number of places). This repetition ( or replication ) of the experiment broadens the scope of the experiment in the sense that our recommendations will be applicable for a number of seasons /or a number of places . A single experiment performed in one place for only one season will provide recommendations for that place and for that season . It may not be applicable to other places or for other seasons . In the case of agricultural experiments , for example , there may be present treatment x place interaction and/ or treatment x season interaction . So the results of a series of experiments , performed over different places for different seasons with the same set of treatments,will have wider applicability .

We shall consider the simplest case of repetition of experiments of identical structure over a number of places ( it is the same for a number of seasons ). Let us consider randomized block experiments with t treatments in r blocks and conducted in p places. The analysis of the experiment in a place is based on the linear model . Before attempting a combined analysis for the p experiments ,it is necessary to perform the analysis for the p places separately and interpret the results separately .It may be of interest to find out whether differences among the treatments are the same in the different places so that a ‘ best ‘ treatment may be recommended for all the places, or whether different treatments are to be recommended for different places . The model for this combined analysis may be written as

The questions related to different series like perfect squares, perfect cubes, geometric, arithmetic, two stage types etc. are given to quantify the aptitude of the students. These series have a definite pattern and require to stressed upon the basic knowledge and aptitude of the candidates to find out the proper answer. The series may follow different pattern either additive, deductive or multiple based on earlier values given in the series. Some of the tips are given below for better understanding of the students and also these tips will help you to solve some of the ticklish questions.

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".

True/False

Q.1.    Two independent random variables (X,Y) are always uncorrelated but reverse may not be true

A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected.

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. An example of a simple random sample would be the names of 25 employees being chosen out of a hat from a company of 250 employees. In this case, the population is all 250 employees, and the sample is random because each employee has an equal chance of being chosen.

The numerical based on simple mathematics like divide, multiply, sum, deduction, under root, percentage etc are given below to sharpen the inherent ability of the students. This simplication is a very good exercise to aqcquaint the students about basic mathmetics so that they can solve tough questions quickly. Therefore some tips are given below for solving the questions.

Introduction

The 21st century has witnessed unprecedented changes in the global job mar ket, driven by technological innovation, globalization, and evolving industry needs. As traditional job roles become obsolete and new ones emerge, skill development has become paramount for both individuals and organizations. This paper explores the concept, importance, key elements, methodologied and challenges in skill development.

Objectives of the study

This study carried on the basis of following objectives

1. To study the concept of Skill Development.

2. To know the Importance of Skill Development.

3. To know Key elements of Skill Development.

4. To know Methodologies of Skill Development.

5. To know Challenges in Skill Development.

A sample is said to be small sample if the sample size(n) is less than 30. Various small sample tests are: (i) t-test (ii) F-test

t-test performs the following tests for small sample(s).

1. To test the equality between a single sample mean and the assumed population mean.
2. To test the equality of two independent sample means.
3. To test the equality of two paired sample means.
4. To test the equality between sample correlation coefficient and the assumed population correlation coefficient

Introduction

Industry 4.0 is essentially the digital revolution of artificial intelligence and subsequent production processes utilizing contemporary smart technology. Cyber-physical systems, or intelligent machines, are the cornerstone of this revolution (Scoop, 2018). The key features of Industry 4.0 include the integration of IoT, increasing automation technology, and enhanced communication and self-counseling techniques (Tay et al., 2018). According to Schwab (2017), new developments in artificial intelligence (AI), robotics, nanotechnology, biotechnology, the Internet of Things (IoT), decentralized systems, 3D printing, fifth-generation communication technologies, quantum computing, and autonomous cars will all be part of this revolution. Early in the 2010s, Germany saw the emergence of Industry 4.0 as a result of government initiatives to advance manufacturing computerization as part of its high-tech strategy project. The concept of Industry 4.0 has been implemented in a variety of contexts and rebranded by various industries or businesses as needed.

Introduction

Financial inclusion has become a global agenda because it is now well recoganised that a nation can prosper only if it ensures inclusive growth. Financial access and use of formal financial system, the means of financial inclusion, have positive association with inclusive growth (Levine and Demirguc-Kunt, 2008). The financial systems which are more inclusive have provided broader access to appropriate financial services to ensure that the benefit can be availed by poor and disadvantaged sections of the society (Akter, 2016). Since, financial inclusion is the process of ensuring availability of f inancial services and well-timed and sufficient credit as required by vulnerable groups such as low income segment and weaker segment of the society at an affordable cost (Rangarajan Committee on financial inclusion, 2005). Thus, the study of financial inclusion on the basis of socio economic factors is the key to investigate individual characteristics associated with financial inclusion (Allen, Kunt, Klapper, Peria, 2012). Understanding financial usage on the basis of socio economic factors enables framing appropriate financial inclusion strategies to achieve financial inclusion in real sense. Many international agencies like International Monetary Fund, Asian Development Bank, World Bank release data on financial inclusion around the world. Global findex report is published by World Bank after the interval of every three years to present the picture of financial inclusion on various socio economic parameters. Around the world, 74% adults, 72% female, 70% income poorest population, 63% out of labour force population and 66% rural population report to have account at formal financial system (World Bank Global findex report, 2021).