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A probability sampling method is any method of sampling that utilizes some form of random selection. In order to have a random selection method, you must set up some process or procedure that assures that the different units in your population have equal probabilities of being chosen. Humans have long practiced various forms of random selection, such as picking a name out of a hat, or choosing the short straw. These days, we tend to use computers as the mechanism for generating random numbers as the basis for random selection.

Probability sampling methods are those in which every item in the universe has a known chance, or probability of being chosen for sample. This implies that the selection of the sample items is independent of the person making the study that is the sampling operation is controlled so objectively that the items will be chosen strictly at random.

Types of probability sampling

Simple Random Sampling: The simplest form of random sampling is called simple random sampling. Neither of these mechanical procedures is very feasible and, with the development of inexpensive computers there is a much easier way. Simple random sampling is simple to accomplish and is easy to explain to others. Because simple random sampling is a fair way to select a sample, it is reasonable to generalize the results from the sample back to the population. Simple random sampling is not the most statistically efficient method of sampling and you may, just because of the luck of the draw, not get good representation of subgroups in a population. To deal with these issues, we have to turn to other sampling methods.

Systematic Sampling: Stratified Random Sampling, also sometimes called proportional or quota random sampling, involves dividing your population into homogeneous subgroups and then taking a simple…...

...Variables Sampling 689 I have edited a portion of Module G from your textbook so that it more closely follows my lecture. I need to acknowledge that this is not my original work and much of it is taken word for word from the 2nd edition of Auditing & Assurance Services by Louwers, Ramsay, Sinason and Strawser. Tad Miller Classical Variables Sampling LEARNING OBJECTIVE Understand the basic process underlying classical variables sampling in an audit examination. When performing substantive procedures, one approach is classical variables sampling. Classical variables sampling methods use normal distribution theory and the Central Limit Theorem to provide a range estimate of the account balance. The auditor uses the sample estimates to determine whether the account balance is fairly stated. The Central Limit Theorem indicates larger sample sizes provide a sampling distribution that more closely reflects a normal distribution. Therefore, larger sample sizes will yield a lower level of sampling risk. In this section, we briefly illustrate mean-per-unit classical variables sampling. We illustrate the manual calculations necessary to determine sample size and evaluate sample results. However, if clients maintain records in electronic format, auditors typically use computer software to perform these tasks. Classical Variables Sampling: Planning In the planning stages of classical variables sampling, the auditor determines the objective of sampling, defines the......

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... Probability – the chance that an uncertain event will occur (always between 0 and 1) Impossible Event – an event that has no chance of occurring (probability = 0) Certain Event – an event that is sure to occur (probability = 1) Assessing Probability probability of occurrence= probability of occurrence based on a combination of an individual’s past experience, personal opinion, and analysis of a particular situation Events Simple event An event described by a single characteristic Joint event An event described by two or more characteristics Complement of an event A , All events that are not part of event A The Sample Space is the collection of all possible events Simple Probability refers to the probability of a simple event. Joint Probability refers to the probability of an occurrence of two or more events. ex. P(Jan. and Wed.) Mutually exclusive events is the Events that cannot occur simultaneously Example: Randomly choosing a day from 2010 A = day in January; B = day in February Events A and B are mutually exclusive Collectively exhaustive events One of the events must occur the set of events covers the entire sample space Computing Joint and Marginal Probabilities The probability of a joint event, A and B: Computing a marginal (or simple) probability: Probability is the numerical measure of the likelihood that an event will occur The probability of any event must be between 0 and 1,...

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...Statistics 100A Homework 5 Solutions Ryan Rosario Chapter 5 1. Let X be a random variable with probability density function c(1 − x2 ) −1 < x < 1 0 otherwise ∞ f (x) = (a) What is the value of c? We know that for f (x) to be a probability distribution −∞ f (x)dx = 1. We integrate f (x) with respect to x, set the result equal to 1 and solve for c. 1 1 = −1 c(1 − x2 )dx cx − c x3 3 1 −1 = = = = c = Thus, c = 3 4 c c − −c + c− 3 3 2c −2c − 3 3 4c 3 3 4 . (b) What is the cumulative distribution function of X? We want to ﬁnd F (x). To do that, integrate f (x) from the lower bound of the domain on which f (x) = 0 to x so we will get an expression in terms of x. x F (x) = −1 c(1 − x2 )dx cx − cx3 3 x −1 = But recall that c = 3 . 4 3 1 3 1 = x− x + 4 4 2 = 3 4 x− x3 3 + 2 3 −1 < x < 1 elsewhere 0 1 4. The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by, 10 x2 f (x) = (a) Find P (X > 20). 0 x > 10 x ≤ 10 There are two ways to solve this problem, and other problems like it. We note that the area we are interested in is bounded below by 20 and unbounded above. Thus, ∞ P (X > c) = c f (x)dx Unlike in the discrete case, there is not really an advantage to using the complement, but you can of course do so. We could consider P (X > c) = 1 − P (X < c), c P (X > c) = 1 − P (X < c) = 1 − −∞ f (x)dx P (X > 20) = 10 dx......

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...Probability & Statistics for Engineers & Scientists This page intentionally left blank Probability & Statistics for Engineers & Scientists NINTH EDITION Ronald E. Walpole Roanoke College Raymond H. Myers Virginia Tech Sharon L. Myers Radford University Keying Ye University of Texas at San Antonio Prentice Hall Editor in Chief: Deirdre Lynch Acquisitions Editor: Christopher Cummings Executive Content Editor: Christine O’Brien Associate Editor: Christina Lepre Senior Managing Editor: Karen Wernholm Senior Production Project Manager: Tracy Patruno Design Manager: Andrea Nix Cover Designer: Heather Scott Digital Assets Manager: Marianne Groth Associate Media Producer: Vicki Dreyfus Marketing Manager: Alex Gay Marketing Assistant: Kathleen DeChavez Senior Author Support/Technology Specialist: Joe Vetere Rights and Permissions Advisor: Michael Joyce Senior Manufacturing Buyer: Carol Melville Production Coordination: Liﬂand et al. Bookmakers Composition: Keying Ye Cover photo: Marjory Dressler/Dressler Photo-Graphics Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and Pearson was aware of a trademark claim, the designations have been printed in initial caps or all caps. Library of Congress Cataloging-in-Publication Data Probability & statistics for engineers & scientists/Ronald E. Walpole . . . [et al.] — 9th ed. p. cm. ISBN......

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...SAMPLING Definition: the act, process, or technique of selecting a representative part of a population for the purpose of determining parameters or characteristics of the whole population. TYPES OF SAMPLING TECHNIQUES: Cluster sampling Cluster sampling is a sampling technique where the entire population is divided into groups, or clusters and a random sample of these clusters are selected. All observations in the selected clusters are included in the sample. Cluster sampling is typically used when the researcher cannot get a complete list of the members of a population they wish to study but can get a complete list of groups or 'clusters' of the population. It is also used when a random sample would produce a list of subjects so widely scattered that surveying them would prove to be far too expensive, for example, people who live in different counties in the Country. Advantages One advantage of cluster sampling is that it is cheap, quick, and easy. Instead of sampling the entire country when using simple random sampling, the research can instead allocate resources to the few randomly selected clusters when using cluster sampling. A second advantage to cluster sampling is that the researcher can have a larger sample size than if he or she was using simple random sampling. Because the researcher will only have to take the sample from a number of clusters, he or she can select more subjects since they are more accessible. Disadvantages One main disadvantage of......

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...Sampling Techniques Psychology 341 August 11, 2013 ABSTRACT The present research paper was designed to discuss the different types of sampling methods used to conduct research in the field of Psychology. The sampling techniques included in this paper are probability sampling, non probability sampling, surveys and questionnaires. The use of examples for each type of technique is given to further the understanding of each specific type. Furthermore, some the most important aspects that should considered before selecting a method are outlined in detail. Sampling Techniques When conducting research, it is almost impossible to study the entire population that we are interested in looking at more in depth. For example, if we were interested in comparing the level of romantic satisfaction among college students in the United States, it would be practically impossible to survey every single person who is attending college in the country. Not only would it take an extremely long time to do so, but it would also be very expensive. That is why researchers will use small samples from the population to gather their data instead. A sample is particularly useful because it allows the researcher to make inferences about a specific population without having to actually survey the entire population (Trochim, 2006). There are several sampling techniques used to gather information about a sample. Some of these include probability sampling, non probability sampling, surveys, and......

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...Sampling Douglas P. Shumski April 27, 2014 MATH301-1402A-01 Susan Lee 1. In your own words, discuss the differences between discrete and continuous random variables because the statistical analysis of each type of variable is different. Discrete Variable – This type of variable is only in the form of a particular value, and does not consider any values that may fall in between each particular value. The example that I would provide here would be that I have two children. I do not have 2.8 children. Continuous Random Variable - This type of variable can take on any value that is available on a range. My example of this type of variable would be the measure of temperature. The temperature can be measured in tenths, such as 86.9 degrees, and not the whole number of 87 degrees. A person’s individual height or weight could also be considered as a continuous random variable. 2. Roll a die 20 times and record the event in Excel |Roll 1 |1 |Roll 11 |6 | |Roll 2 |5 |Roll 12 |5 | |Roll 3 |3 |Roll 13 |2 | |Roll 4 |6 |Roll 14 |4 | |Roll 5 |6 |Roll 15 |6 | |Roll 6 |3 |Roll 16 |3 | |Roll 7 |5 |Roll 17 |4 | |Roll 8 |4 |Roll 18 |6 | |Roll 9 |2 |Roll 19 |5 | |Roll 10 |1 ...

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...| 2108 | Nonprobability sampling in management research ESS has made a survey created to measure attitudes cross-nationally in Europe, using probability sampling. Measuring an attitude across countries is a tough job, but to successfully apply the methods of probability sampling too, seems close to impossible. This essay will look at the sample-problems that this survey faces, and how a non-probability sample can be successfully integrated. Before starting to analyse the survey, I would like to briefly explain what a sample is, and the main differences between the two sampling techniques. First of all the objective of most surveys or research projects is to obtain information about the parameters of a population. To do this a sample is collected representing a subgroup of the population selected for participation in the project. The sample characteristics are used to “make inferences about the population parameters”. (Malhotra, 2010: 370) Meaning that you by selecting a small representation of the population can tell something about the whole population. Non-probability sampling can be defined briefly as “Sampling techniques that do not use chance selection procedures, but rather rely on personal judgement of the researcher” (Malhotra and Birks, 2000, 358) An example of this would be a person who choices people on the street to take part in a survey by using his personal judgement. There are different types of non-probability sampling, the most common are:......

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...Sampling Sampling Third Edition STEVEN K. THOMPSON Simon Fraser University A JOHN WILEY & SONS, INC., PUBLICATION Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and speciﬁcally disclaim any implied warranties of merchantability or ﬁtness for a particular purpose. No warranty may be created or extended by sales representatives......

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...Odd-Numbered End-of-Chapter Exercises * Chapter 2 Review of Probability 2.1. (a) Probability distribution function for Y Outcome (number of heads) | Y 0 | Y 1 | Y 2 | Probability | 0.25 | 0.50 | 0.25 | (b) Cumulative probability distribution function for Y Outcome (number of heads) | Y 0 | 0 Y 1 | 1 Y 2 | Y 2 | Probability | 0 | 0.25 | 0.75 | 1.0 | (c) . Using Key Concept 2.3: and so that 2.3. For the two new random variables and we have: (a) (b) (c) 2.5. Let X denote temperature in F and Y denote temperature in C. Recall that Y 0 when X 32 and Y 100 when X 212; this implies Using Key Concept 2.3, X 70oF implies that and X 7oF implies 2.7. Using obvious notation, thus and This implies (a) per year. (b) , so that Thus where the units are squared thousands of dollars per year. (c) so that and thousand dollars per year. (d) First you need to look up the current Euro/dollar exchange rate in the Wall Street Journal, the Federal Reserve web page, or other financial data outlet. Suppose that this exchange rate is e (say e 0.80 Euros per dollar); each 1 dollar is therefore with e Euros. The mean is therefore e C (in units of thousands of Euros per year), and the standard deviation is e C (in units of thousands of Euros per year). The correlation is unit-free, and is unchanged. 2.9. | | Value of Y | Probability Distribution of X | | | 14 | 22 | 30 | 40 | 65 | | | Value......

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...PROBABILITY ASSIGNMENT 1. The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the US are using their seat belts. Sample data consistent with the NHTSA survey are as follows. (Data as on May, 2015) Driver using Seat Belt? | Region | Yes | No | Northeast | 148 | 52 | Midwest | 162 | 54 | South | 296 | 74 | West | 252 | 48 | Total | 858 | 228 | a. For the U.S., what is the probability that the driver is using a seat belt? b. The seat belt usage probability for a U.S. driver a year earlier was .75. NHTSA Chief had hoped for a 0.78 probability in 2015. Would he have been pleased with the 2003 survey results? c. What is the probability of seat belt usage by region of the Country? What region has the highest seat belt usage? d. What proportion of the drivers in the sample came from each region of the country? What region had the most drivers selected? 2. A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In an actual experiment, 100 consumers were asked to pick the design they preferred. The following data were obtained. Do the data confirm the belief that one design is just as likely to be selected as other? Explain. Design | Number of Times Preferred | 1 | 5 | 2 |......

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...merits of alternative sampling frames. Suggest most appropriate one and justify your selection. Research population is the target population on which a study or research is conducted through various different methods inorder to reach a conclusion from the data generated. It is for the benefit of the population directly or indirectly. But, due to very large size of research population, it is not feasible to test all the individuals of the population since it will take too much time and will be expensive as well. So the researchers take few individuals from the research population ( a subset of the set of target population) using sampling techniques. These techniques helps to take out sample as per the requirements of the type of research that is to be conducted. A research population is also known as a well-defined collection of individuals or objects known to have similar characteristics. All individuals or objects within a certain population usually have a common, binding characteristic or trait. Usually, the description of the population and the common binding characteristic of its members are the same. "Government officials" is a well-defined group of individuals which can be considered as a population and all the members of this population are indeed officials of the government. There are various sources from which a sample is created. A set of all these sources is called a Sampling frame from which the sample is selected. With the help of sampling frames,......

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... CASE 01: Sintex Industries Limited: Grooming with Increased Demand of Plastic 1. Discuss various stages of the research to launch this research programme 2. Define the research problem 3. Discuss the type of the research design used for this research programme 4. What will be the nature of data for ascertaining consumer attitude? 5. Discuss the scaling techniques used to measure the consumer attitude, and justify your selection of a particular scaling technique. CASE 02: Air Conditioner Industry in India: Systematic Replacement of the Unorganized Sector by the Organized Sector. 1. What will be your sampling frame, appropriate sampling techniques, sample size, and sampling process? 2. Will you be using probability sampling technique or nonprobability sampling technique and why? 3. What will be your plans to control sampling and non -sampling errors to obtain an accurate result? CASE 03: Centre for Monitoring Indian Economy Pvt. Ltd: An Independent Economic Think Tank. Let us consider you as an owner of a marketing research firm and assume that a multinational company firm has contacted you to prepare a detailed report on the consumer electronics market in India. The report must be prepared in light of the market share for various companies of consumer electronics, future demand for different products of consumer electronics, profit after tax, and various other financial parameters of different companies, compete industry analysis, demographics...

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...PROBABILITY SEDA YILDIRIM 2009421051 DOKUZ EYLUL UNIVERSITY MARITIME BUSINESS ADMINISTRATION CONTENTS Rules of Probability 1 Rule of Multiplication 3 Rule of Addition 3 Classical theory of probability 5 Continuous Probability Distributions 9 Discrete vs. Continuous Variables 11 Binomial Distribution 11 Binomial Probability 12 Poisson Distribution 13 PROBABILITY Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common usage, the word "probability" is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics. There are several competing interpretations of the actual "meaning" of probabilities. Frequentists view probability simply as a measure of the frequency of outcomes (the more conventional interpretation), while Bayesians treat probability more subjectively as a statistical procedure that endeavors to estimate parameters of an underlying distribution based on the observed distribution. The conditional probability of an event A assuming that B has occurred, denoted ,equals The two faces of probability introduces a central ambiguity which has been around for 350 years and still leads to disagreements about...

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...SAMPLING: In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population. The three main advantages of sampling are that the cost is lower, data collection is faster, and since the data set is smaller it is possible to ensure homogeneity and to improve the accuracy and quality of the data. The sampling process comprises several stages: * Defining the population of concern * Specifying a sampling frame, a set of items or events possible to measure * Specifying a sampling method for selecting items or events from the frame * Determining the sample size * Implementing the sampling plan * Sampling and data collecting PROBABILITY AND NON-PROBABILITY SAMPLING: A probability sampling scheme is one in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined. The combination of these traits makes it possible to produce unbiased estimates of population totals, by weighting sampled units according to their probability of selection. Non-probability sampling is any sampling method where some elements of the population have no chance of selection (these are sometimes referred to as 'out of coverage'/'under covered'), or where the probability of selection can't be accurately determined. It involves the selection of elements based on assumptions......

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