eChapters

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.

Hypothesis testing is the statistical procedure used in order to accept or reject statistical null hypotheses. One of the major purpose for which we formulate the hypothesis is, to test the statistical significance of the relation, difference or variation etc. among given sample/s at a given point of time or at different time points.

True/False

Q.1.    A hypothesis that sets the fundamental objective of scientific study is called the “Research hypothesis”.
Q.2.     A statistical assumption or statement about the unknown parameters of a population is known as Statistical hypothesis.

8.1 Statistical Hypotheses

in attempting to reach decisions about the populations, it is useful to make assumptions or guesses about the populations involved. When the assumption or statement about a phenomenon occurring under certain conditions is formulated as proposition it is called a scientific hypotesis. We can construct criteria by which a scientific hypothesis may be ‘the  yield of a new paddy variety will be 3500 kg per hectare’. In statistical language it may be stated as ‘the random variable (yield of paddy) is distributed normally with mean 3500 kg/ha’. Such a statement or proposition about the probability distribution of a random variable is called the statistical hypothesis.

10.1. Introduction

Decision-making is a fundamental aspect of human life, influencing choices in both personal and professional settings. Every individual, whether consciously or unconsciously, engages in decision-making daily, ranging from simple tasks like selecting a meal to complex strategic planning in organizations. However, decision-making becomes increasingly challenging when multiple conflicting criteria are involved. The presence of numerous factors, each with varying degrees of importance, often creates ambiguity and uncertainty, making it difficult to arrive at the most suitable option. To address these challenges, structured decision-making methodologies have been developed to provide a systematic and logical framework for evaluating alternatives.

One such widely recognized method is the Analytical Hierarchy Process (AHP), introduced by Thomas L. Saaty in the 1970s. AHP was designed to assist decision-makers in breaking down complex problems into a structured and systematic hierarchy. This approach allows for a step-by-step evaluation of different factors, making it easier to analyze their relative importance. By structuring a problem into different levels - such as goal, criteria, sub-criteria, and alternatives - AHP provides clarity in decision-making and enhances consistency in judgments. The method is particularly beneficial when dealing with decisions that involve both tangible and intangible factors, as it allows subjective preferences to be quantified systematically (Saaty, 2008).

Introduction

In the annals of history, the term “Renaissance” evokes images of a time marked by profound cultural, artistic, and scientific rebirth. The Renaissance of the 14th to the 17th century was characterized by an extraordinary surge in creativity and intellectual achievement, which laid the groundwork for the modern world. Today, we find ourselves at the cusp of a new Renaissance—a Digital Renaissance—propelled by the rapid and relentless advancements in technology. This new era, like its historical counterpart, is marked by a transformative shift that is redefining every aspect of human life, from how we work and communicate to how we learn and govern.

This chapter delves into the essence of this transformative era, exploring the fundamental technological innovations reshaping our world and their far-reaching impacts on society. We will examine the pivotal technologies driving the Digital Renaissance, including artificial intelligence, blockchain, the Internet of Things (IoT), and other emerging technologies such as virtual and augmented reality and 5G networks. By understanding these technologies and their applications, we can appreciate how they collectively contribute to a digital transformation that is as revolutionary as the artistic and scientific achievements of the past.

Introduction

Agriculture has always been linked with prosperity, man power and the ability to feed and raise human population. In earlier times, humans as man power were deployed on the fields to do all the necessary operations to cultivate the crops, but during the industrial revolution, with development of different farm machines the uses of human labor on the fields were drastically decreased. Further, with advancement of technologies and more availability of computers, Artificial Technology (AI) has been gaining momentum in recent years.

AI has the potential to transform the agricultural sector through cost reduction and increased crop yields, and minimizing environmental impacts. AI can help farmers better manage their land, improve crop quality, and increase their productivity In addition, AI can be used to monitor and analyze the health of crops, livestocks, and soils to identify issues and assist in their resolution. The primary idea of using artificial intelligence in agriculture is due its adaptability, superiority, and cost-viability. The customary techniques that were utilized by the farmers were not adequate enough to satisfy their necessities. (Khan et al. 2022) With the right implementation and technology, AI can be an invaluable tool to help farmers increase their efficiency and profitability. In today’s rapidly evolving world, where the demand for food continues to escalate amidst concerns over environmental sustainability and resource scarcity, Artificial intelligence (AI) has become a transformative force in agriculture, from optimizing crop production and resource management to enhancing decision-making processes. Globally, AI is changing how we approach farming techniques.

The digital age has revolutionized the way we live, work, and interact with the world around us. Digital transformation has become a crucial imperative for businesses of all sizes and industries, enabling them to not only adapt to the changing landscape but also thrive in it. (De Lucas,2021). The rapid advancement of technologies such as 5G, cloud computing, big data, artificial intelligence, IoT, and blockchain has opened up a plethora of opportunities for enterprises to enhance their operations, improve customer experiences, and gain a competitive edge. (Anjali et al, 2023). Businesses can increase their reach, automate jobs, obtain insights from data, personalize services, and streamline procedures by utilizing these technologies. They must reconsider their business models and implement more flexible and agile strategies in response to these exponential changes. (Bansal et al, 2020, Fenech et al, 2019).

Introduction

Stocks from different firms can be traded and listed on the stock market. In addition, the stock market evaluates listed firms based on their worth, effectiveness, profitability, and capability. Anybody can trade shares on the stock market, which is an open global market. GDP is the total amount of profit produced in a country over a given period. To develop products and services in a country to a plausible degree, it is helpful to measure the monetary policy of completed goods and services that are acquired for a single end consumer. It comprises all earnings generated inside a country’s borders. The GDP of any nation may be used to determine the size and state of that nation’s economy. GDP is a measure of a nation’s total production and performance and is used as a gauge of economic health. Strong GDP growth frequently signals more consumer spending, corporate profitability, and company expansion, all of which are positive indicators of optimistic mood in the stock market. On the other hand, a slow GDP growth rate might undermine investor confidence and cause stock values to decline.

Changing Dynamics in HM

HM has transformed significantly; a lot because of changes in consumer behaviour, technological advancement, economic developments, regulatory changes, and growing consciousness of sustainability (Samaddar & Mondal, 2024). These changing dynamics have pushed customer’s expectations toward better and more personalized service (Law et al., 2024). Initially, the focus was on basic services and manual processes, but since then, the HM industry has embraced smart technologies like mobile apps, AI, IoT, and big data analytics. These developments have revolutionized the way customers interact; from merely checking in with their mobile phones, and controlling their room settings, to house-keeping and service delivery, thanks to AI-powered customization and automation. Using cloud services for managing properties and improving cyber security helps keep operations smooth and keeps data safe. Efforts to use energy and water more wisely show the industry's move towards being more sustainable. As the HM continues to evolve, industry stakeholders eye towards more personalized, efficient, and sustainable guest experiences. This would reflect the ongoing commitment to excellence and adaptation efforts to strive and evolve in the dynamic global landscape.

Introduction

Chemical exposure in the workplace is a prevalent concern across various industries, including manufacturing, agriculture, healthcare, and construction. These exposures can range from acute to chronic and involve many substances, from heavy metals and solvents to pesticides and industrial chemicals. While the physical health effects of chemical exposure are well-documented, the psychological impacts are less understood but equally significant. Psychological stress is a response to perceived threats or challenges characterized by physical, emotional, and cognitive symptoms. Theories such as the Transactional Model of Stress and Coping by Lazarus and Folkman emphasize the role of individual perception and coping mechanisms in stress experiences.

The modern industrial landscape is characterized by ubiquitous chemicals, ranging from benign substances to potentially hazardous compounds. As industries strive for higher productivity and efficiency, the workforce is frequently exposed to various chemicals. This exposure is not without consequences; while the physical health effects of chemical exposure have been extensively studied, the psychological impacts are less understood. Emerging research indicates that chemical exposure can significantly contribute to psychological stress, affecting worker health, productivity, and overall well being.

Maps make it easier to interpret and communicate the results of any GIS analysis. R has a large number of packages for making thematic maps. Static mapping is straightforward with plot()methods provided by core spatial packages sf and raster. The use of plot() function have been discussed in the previous chapters. Another package for mapping isspwithspplot() having enough options for producing good quality thematic maps.It is also possible to create advanced maps using ggplot2. This chapter discusses, separately, preparing thematic maps from vectors and rasters with the above mentioned packages. A dedicated map-making package tmaphas been given special focus in this chapter.

Theoretical Probability Distribution

Many random variables associated with statistical experiments have similar properties, and as such can be described by the same probability functions. The distribution obtained from a theoretical listing of outcomes and probabilities, which can be described by a mathematical formula representing same phenomenon of interest is called a theoretical probability distribution. The distributions of discrete and continuous random variables are accordingly called discrete or continuous probability distributions.

Discrete Probability Distribution: It can be defined as a probability distribution of discrete random variables. Such a distribution will represent data that has a f inite countable number of outcomes. If the random variable X is a discrete random variable, the probability function P(X) is called probability mass function and its distribution is called discrete probability distribution. There are two conditions that a discrete probability distribution must satisfy. These are given as follows:

Types of Discrete Probability Distributions

There are several important discrete probability distributions-

• Uniform distribution

• Binomial distribution

• Negative Binomial distribution

• Geometric distribution

• Poisson distribution

• Hyper-Geometric distribution

True/False

Q.1.    The process of knowing all the relevant information from the known sample to the unknown “Population parameter” is known as “Statistical inference.”
Q.2.    The method of estimating the unknown parameter of the population on the basis of known sample values is known “Estimation method.”
Q.3.    The “Point estimation and Interval estimation” are the two methods of estimating the unknown parameters of the population.

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.

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".

Based on the nature and purpose of the content, there are numerous classes of scientific communications. Theses represent the class of research communications that are of great importance to the students. Thesis is part and parcel of the master’s and doctoral programme in almost every academic institution. In some institutions, even the bachelor students are expected to submit their brief report on project.

Introduction

It is a very important chapter as many questions are asked in competitive examination based on time and work relationship. This topic deals with the simultaneous performance involving the efficiency of an individual or a group and the time taken by them to complete a piece of work. Work is the effort applied to produce a deliverable or accomplish a task. A certain amount of time (T) is taken to complete a certain work (w). The number of units of work done per unit time is called the rate of work (R).

Hence, Work (W) = R x T

Whenever some work is done, the total work itself can be taken as one unit. Hence, we assume the total work done as one unit in the problems we encounter in order to simplify the computations. In these cases, R = 1 / T or T = 1 / R. In other words, R and T are inversely proportional as R T = W, which is a fixed quantity.

Time Series

A series of observations recorded over time is known as a time series. In other words, a time series is a set of observations taken at specified times, usually at equal intervals. For example: Annual retail sales, rainfall measurements, heartbeats per minute, etc. Such studies are to be based on the analysis of time series data collected over time. Thus, the analysis of time series plays an important role in an investigation of economic, social, commercial and even biological phenomenon.

Components of time series

In a long time series, generally, there are following four components:

• Secular trend or long term movements

• Seasonal variations

• Cyclic variations • Random or irregular movements

• Secular trend or long term movements: It is that characteristic of a time series which extends consistently throughout the entire period of time under consideration. It shows a long term tendency of an activity to grow or to decline. The term long period of time in a relative phenomenon and cannot be defined exactly. For some cases a period as small as a weak may be fairly long while in other cases, a period as long as two years may not be assumed long.

Scientific research is always based on observable and measurable facts. This applies to physical as well as humanitarian fields of science. In order to investigate social or psychological phenomenon, most of the times we need quantified information related to the phenomenon under investigation. In order to secure this data, we need one or more method/ means of collecting observable/measurable data.