eChapters

Coconut is the most beautiful and useful of palms known to mankind. Coconut is unique, producing a host of products and by products with distinctive applications at home and in industry. It is essentially an oil seed crop providing all amenities for human life, which include food, energetic beverage, medicine, fibre, wood, shell and a variety of raw materials for production of array of products of commercial importance. In view of its versatile uses and affinity to Indian culture, it is rightly called the “tree of heaven” or “Kalpavriksha”.

Cocoa (Theobroma cacao L.) is the third important beverage crop grown for its seeds known as beans, used mainly in chocolate industry. It is the source of cocoa butter and cocoa mass.

Cashew (Anacardium occidentale L.) is an export-oriented crop grown for its nuts, a true drupe. Often referred as ‘wonder nut’, it is highly delicious and nutritive. Its nutritional composition compares well with almond, hazel nut and walnut. It is a zero-cholesterol nut with high content of unsaturated fatty acids, proteins and carbohydrates with a right combination of amino acids, vitamins and minerals. Kernels extracted from nuts are often consumed as such or used in confectionery items and various kinds of dishes. Kernel oil of pale yellow colour is used in pharmaceutical and cosmetic industries. Cashew nut shell liquid (CNSL) extracted from its shell has many industrial applications - for making paints, resins, flame-retardants, etc. Testa covering the kernel, rich in tannin, can be an acceptable substitute for wattle bark tannin in leather industry. Cashew apple, the pseudo-fruit, is rich in vitamin C. It is used to cure scurvy, diarrhea, uterine complaints and dropsy.

Arecanut palm (Areca catechu L.) is the source of common masticatory nut, popularly known as arecanut, betelnut, or supari. It is used extensively in India by all sections of people as masticatory, and is an essential requisite for several religious and social ceremonies.

Commercial crops include a variety of high value plantation crops, which play a vital role in the agricultural economy and export trade of many developing and developed countries (Table 1). Tea, coffee, cocoa, rubber, coconut, arecanut, oil palm, cashew, palmyra and cardamom are the major crops grown on a plantation scale. These crops are perennial in nature and the cultivation is labour intensive, generating considerable employment opportunity during on farm operations and off farm processing activities. The most obvious characteristic is that plantations are monocultures; the same species occupying large contiguous area usually in even aged stands. Exceptions are coconut, arecanut, cocoa and coffee, which are grown either as mono crop or as multiple crops. These crops are grown in humid tropics, mainly between 20°N and 20°S of equator in an area of 35.7 million ha yielding about 74.4 million tonnes of produce and contributing US $ 11 billion to global trade during 2002.

13.1 Introduction
In the previous chapters, we have considered different tests of significance based on normal distribution, F distribution, student’s t distribution and Chi-square (χ2) distribution which are frequently applied by the users of different disciplines of applied sciences and social sciences. In this chapter some more tests of significance are considered which have not been covered in those chapters. These tests are also based on t, F, Fisher’s z transformation, χ2 and some other test statistics are also discussed one by one in the following sections.

12.1 Chi-Square Variate
The square of a standard normal variate is known as a chi – square variate or chi square statistic with one degree of freedom.

11.1 Introduction
In the preceding chapter 10, we have discussed in detail, the test procedures for which it has been assumed that the sample size n is large, (i.e n >,30). Those tests are also known as approximate tests or z tests. But in case when sample size n is small i.e. n<30, the approximate test fails to deal with such problem and we apply the theory of exact sample, for small sample tests. The exact sample tests however can be applied to large samples also though the converse is not plausible. In all the exact sample tests, the basic assumption is that the parent population is normally distributed.
In this part we will discusse in details the exact sample tests (based on exact sampling distributions namely snedekor’s F, student’s t and chi square (χ2) distributions. These distributions will be simply introduced in short because main emphasis has to be given only on the test procedures based on them.

10.1 Normal Distribution
The normal distribution is the most widely used distribution in statistics. Almost all biological data including the agricultural data eg. crop yield, plant height, seed weight, seed size, protein percent in pulse, oil content in an oil seed etc are assumed to be normally distributed. In practice their distribution is rarely verified. In distribution theory, for large values of n, the number of trial (or sample size), almost all the distributions e.g. Binomial, poission, Negative binomial, chi square, student’s t, and Snedenor’s F distributions etc. are very closely approximated by normal distribution. It is a continuous distribution with mean and variance as its two parameters.

9.1 Introduction
In the preceeding chapter, we have studied the estimation part of statistical decision (inference) infered about the parameters of the population on the basis of information available in the sample observations drawn from the parent population under study. In the present chapter we discuss the problems related with the tests of statistical hypothesis and its significance about the population parameters under study. For understanding of the subject matter considered in this chapter, very clearly and easily, one must be familier with the statistical terminologies used in the subject matter. Hence we discuss the various notable terminologies with some suitable examples in a simple way for better understanding.

8.1 Introduction
We have already discussed in details how different sampling schemes can be employed to draw the representative samples suitable to many kinds of population whose sampling units differ in nature. From practical view points, however, it is often more important to be able to make decision about certain unknown characteristics of the population on the basis of informations available in the representative samples which are drawn from the parent populations. Such decisions taken, are known as the “Statistical decisions”. For example, we may wish to decide on the basis of sample data whether (i) One educational system is better than the other or not, (ii) A given six faced die is unbiased (balanced) or not, (iii) A new insecticide is really effective to control the attack of insects or not? etc. Such problems are dealt with in the theory of statistical decisions which uses the principles of sampling theory.

7.1 Introduction
In chapter 5, the cluster sampling has been discussed in which clusters were considered as sampling units and all the elements in the selected clusters were enumerated completely. It has been stated there that the cluster sampling is economical under certain circumstance but the method restricts the spread of sample over the population which results generally in increased sampling variance of the estimator under consideration. It is, therefore, logical to expect that the efficiency of the estimator will be increased by distributing the elements over a large numbers of clusters. Hence instead of observing all the units in the selected clusters, one may like to observe only few elements of the selected clusters. This will involve the sampling work to be done also within the selected clusters. If we do so, the process of selection will involve sampling work to be done at two stage, one for selecting the clusters where sampling units are the clusters and the second for selecting the units (elements) within the selected clusters where sampling units are the elements.
The process of sampling can be done at more than two stages. In this case the first stage unit will be larger than the second stage units and the second stage units will be larger than the third stage units and so on. Due to process of sampling in stages, such sampling is called “Multistage sampling.”

6.1 Introduction
So far we have considered the methods of sampling in which the successive units (elements or clusters) were selected with the help of random numbers. Now, we shall consider a new method of sample selection in which only the first unit of the sample is selected with the help of random number, the rest being selected automatically according to a predetermined pattern. The method is known as systematic sampling. It is operationally more convenient than simple random sampling and which at the same time ensures for each unit, equal probability of inclusion in the sample. The systematic sampling can also be termed as systematic random sampling because of the first unit of the sample being chosen randomly. The pattern usually followed in selecting a systematic sample is a simple pattern involving regular spacing of units.
Thus, suppose a population consists of N units and is serially numbered from 1 to N. Suppose further that N is expressable as the product of two integers k and n so that N=nk. Draw a random number i such that 1 < i < k and select the unit with the corresponding serial number and every kth unit in the population there after i.e. the sample consists the units bearing the serial numbers as

5.1 Introduction
In random sampling it is assumed in prior that the population is divisible into a finite number of distinct and identifiable units and these units are known as sampling units. The smallest unit into which the population can be divide, is called an elementary unit (element) of the population. A group of such units is known as cluster. When such cluster is treated as sampling unit, then the sampling procedure adopted is known as cluster sampling. If the entire area containing the population under study is divided into smaller area segments and each element in the population belongs to one and only one such area segment, the sampling is sometimes known as area sampling.
Generally, identification and location of an element requires considerable time. However, once an element is located, the time taken for surveying a few neighbouring elements is small. Thus, the main function in cluster sampling is to specify clusters or to divide the population into appropriate number of clusters. Clusters are generally made up of neighbouring elements and hence elements within a cluster happen to be of similar nature. As a matter of fact, the number of elements in a cluster should be small and the number of clusters should be large. The required number of clusters can be selected either by equal or unequal probabilities of selection. All the units in the selected clusters are enumerated completely i.e. complete enumeration is made in all the selected clusters.

4.1 Introduction
In many surveys, information on an auxiliary (supplementary, ancillary or apriori) variable x, which is highly (positively or negatively)correlated with the variable y under study, is readily available and can be used for improving the sampling design. Stratified sampling and probability proportional to size (p.p.s) schemes are two examples of improved sampling designs, in which the use of data on auxiliary variable has been made. However in both the schemes, it implies that the information on auxiliary variable on individual sampling units is available prior to presentation of sampling design. In case, data on auxiliary variable for individual sampling units are not available but only the aggregate value for all units of auxiliary variable is available, the two schemes can not be used. In such a situation, the aggregate data on auxiliary variable can still be used at the time of estimation of parameters under consideration, provided the data on auxiliary variable for the sampled units can be easily obtained at the time of recording the values of the study variable. Such types of estimation are based on ratio, product, difference and regression methods of estimation.

3.1 Introduction
Out of all methods of sampling, the most commonly used procedure in surveys is the stratified random sampling. When population units are of heterogeneous nature and if we select a sample using SRSWOR scheme then the sample selected may not be the representative sample and the estimate worked out from that sample will not be the reliable estimate of the population parameter. The estimate of sampling variance of the sample estimator obtained from that sampling scheme may happen to be very high leading to get a less precise estimate of the parameter. In such type of population, to overcome these draw backs, we use another sampling scheme known as stratified random sampling which is defined as follows.

2.1 Simple Random Sampling
The simplest and common most method of sampling is simple random sampling. In this procedure, the sample is drawn unit by unit with equal probability of selection for each unit at each draw. It is sometimes referred to as unrestricted random sampling.

The use of sampling in making decisions about an aggregate (or population) is possibly as old as civilization itself. Sampling is first broadly classified into two categories known as subjective and objective. Any type of sampling which depends upon the personal judgement or discretion of the sampler himself, is called subjective sampling. But the sampling method which is governed by a sampling rule or is independent of the sampler’s own judgement is known as objective sampling. The main difficulty with subjective sampling is that the sampler is ignorant of the degree of representativeness of his sample or the accuracy of the final estimates of the population values obtained.

Objective sampling is further subdivided as non-probabilistic, probabilistic and mixed. In non-probabilistic objective sampling, there is a fixed sampling rule but there is no selection probability attached to the sampling unit e.g. selection of every 10th individual from a list, starting with the first, or selecting every 10th line in a paddy field. If however, the selection of the first individual is made in such a manner that each of the first 10 gets an equal chance of being selected, it becomes a case of mixed sampling, partly probabilistic and partly non-probabilistic). On the other hand, if for each individual unit there is a definite pre-assigned probability of being selected, the sampling is said to be probabilistic sampling.

22.1 Introduction

Nanotechnology has proved to have infinite potential in increasing the quality of life of the human population. There is however, a growing realization regarding the potential health and safety risks of associated with development, production and application of these nanoparticles. Nanoscale particles are produced from a variety of different processes. Nanoparticles are the end product of a wide variety of physical, chemical and biological processes, some of which are novel and radically different, others of which are quite commonplace. Nanometer sized particles are also found in the atmosphere where they originate from combustion sources (traffic, forest fires), volcanic activity, and from atmospheric gas to particle conversion processes such as photochemically driven nucleation. A large quantity of nanoscale particles are also produced during the various human activities, Welding can generate large quantities of nanoparticles usually in the form of a well defined plume of aggregated nanoparticles.

21.1 Introduction

Nanotechnology is an emerging field of science which is being highly exploited in the sphere of medicine where “nano” plays a vital role in delivery of drugs or chemical molecules to the point it is required in précised quantities in right proportions. Nanoscience infuses intelligence to the truck load of chemical constituents that are to be delivered at appropriate locations and cleave from the site after the task is complete. Such process will likely to reduce the cost besides ensuring environmental safety. Nanoscale devices with its unique properties make the agricultural system more smart and effective; such devices are capable of responding to different situations by themselves, thus taking appropriate remedial action with the need of external directions from humans. In short, these devices act as a detectors and if need arises serve as a solution/remedy for the particular issue. These smart delivery systems of chemicals in controlled and targeted manner can be considered synonymous to the proposed nano-drug delivery system in human (Patolsky et al., 2006).