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ELEMENTARY STATISTICAL METHODS

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The purpose of this book is to acquaint the reader with the increasing number of applications of statistics in engineering and the applied sciences. It can be used as a textbook for a first course in statistical methods in Universities and Polytechnics. The book can also be used by decision makers and researchers to either gain basic understanding or to extend their knowledge of some of the most commonly used statistical methods. Our goal is to introduce the basic theory without getting too involved in mathematical detail, and thus to enable a larger proportion of the book to be devoted to practical applications. Because of this, some results are stated without proof, where this is unlikely to affect the reader’s comprehension. However, we have tried to avoid the cook-book approach to statistics by carefully explaining the basic concepts of the subject, such as probability and sampling distributions; these the reader must understand. The worst abuses of statistics occur when scientists try to analyze their data by substituting measurements into statistical formulae which they do not understand.
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... If p is the proportion of observations in a random sample of size n that belongs to a class of interest, then an approximate 100(1 -)% confidence interval of the proportion p of the population that belongs to this class is (see Ofosu & Hesse, 2011) Exercise 2(b) 1. A researcher found that 66% of a sample of 14 infants had completed the hepatitis B vaccine series. ...
... In many situations we want to know whether we can conclude that a set of observations constitute a random sample from an infinite population. Test for randomness is of major importance because the assumption of randomness underlies statistical inference (see Ofosu & Hesse, 2011 ...
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A statistical method is called non-parametric if it makes no assumption on the population distribution or sample size. This is in contrast with most parametric methods in elementary statistics that assume that the data set used is quantitative, the population has a normal distribution and the sample size is sufficiently large. In general, conclusions drawn from non-parametric methods are not as powerful as the parametric ones. However, as non-parametric methods make fewer assumptions, they are more flexible, more robust, and applicable to non-quantitative data. This book is designed for students to acquire basic skills needed for solving real life problems where data meet minimal assumption and secondly to beef up their reading list as well as provide them with a “one shop stop” textbook on Nonparametric.
... They also take charge of quality control issues in manufacturing and ensuring quality and dependability of product. In the health sector, they are responsible for studying and improving the efficiency of delivery systems and practices (Ofosu and Hesse, 2011). Statistical knowledge is required in many areas of life to enable one to understand the world around and also to make accurate decisions in life (Cimpoeru and Roman, 2018). ...
... The test statistic is given by (see Cramér (1946) and Birch (1964) It can also be shown that, for large n, the statistic H has an approximate chi-square distribution with (r -1)(c -1) degrees of freedom if 0 H is true (see Ofosu and Hesse (2011)). Therefore, we would reject the hypothesis of independence if the observed value of the test statistic H is greater than the critical value 2 ...
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