Premium Essay

Annotated Sampling and Distribution

In: Business and Management

Submitted By pwacannon
Words 2939
Pages 12
Distributions, Sampling and Estimation

Our main objective in this section is to learn how to estimate some important characteristics of random variables using data. We will concentrate on estimating the mean from a normal distribution, and the proportion of success in a binomial distribution. To talk about estimation, we first need to know something about distributions and sampling.

Most data used for decision making exhibit variation. We are interested in drawing conclusions from such data. Probability and statistics give us the necessary tools.

We will again make use of the concept of a random variable. We have reviewed discrete random variables already. Before moving on, we need to review continuous random variables.

Continuous random variables take on continuous or interval values (there are an infinite number of possibilities). If you are measuring, the distribution of the result will almost always be continuous. For example, the width of an extruded bar is a continuous random variable.

The distribution of a continuous random variable is represented by a continuous curve (called the probability density function (pdf) and often denoted f(y)). The height of the curve does not represent probabilities; instead, the area under the curve between two points tells us about the probability. As a result, the probability that a continuous random variable is exactly equal to a single value is 0 (there is no area under a single point).

The Binomial and Normal Distributions

As noted earlier, we will be talking about estimating the mean of a normal distribution and the proportion of success in a binomial distribution. To proceed, therefore, we need to review these two distributions.

The Binomial Distribution

The binomial distribution is a discrete distribution and…...

Similar Documents

Premium Essay

Sampling

...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......

Words: 2468 - Pages: 10

Premium Essay

Sampling

...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......

Words: 1337 - Pages: 6

Premium Essay

Sampling Techniques

...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......

Words: 1536 - Pages: 7

Free Essay

Sampling

...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 ...

Words: 589 - Pages: 3

Premium Essay

Sampling File

... Dissertation, Unpublished 11 Government Document 11 Report From a Private Organization 11 Conference Proceedings 11 Reference List: Electronic Sources (Web Publications) 12 Article From an Online Periodical 12 Online Scholarly Journal Article: Citing DOIs 12 Article From an Online Periodical with DOI Assigned 12 Article From an Online Periodical with no DOI Assigned 12 Article From a Database 13 Abstract 13 Newspaper Article 13 Electronic Books 13 Chapter/Section of a Web document or Online Book Chapter 14 Online Book Reviews 14 Dissertation/Thesis from a Database 14 Online Encyclopedias and Dictionaries 15 Online Bibliographies and Annotated Bibliographies 15 Data Sets 15 Graphic Data (e.g. Interactive Maps and Other Graphic Representations of Data) 15 Qualitative Data and Online Interviews 15 Online Lecture Notes and Presentation Slides 16 Nonperiodical Web Document, Web Page, or Report 16 Computer Software/Downloaded Software 16 E-mail 17 Online Forum or Discussion Board Posting 17 Blog (Weblog) and Video Blog Post 17 Wikis 17 Audio Podcast 17 Video Podcasts 18 Reference List: Other Non-Print Sources 18 Interviews, Email, and Other Personal Communication 18 Motion Picture 18 A Motion Picture or Video Tape with International or National Availability 18 A Motion Picture or......

Words: 6671 - Pages: 27

Premium Essay

Sampling Probability

...Probability Sampling Cultural Studies Essay 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......

Words: 3261 - Pages: 14

Premium Essay

Survey Sampling

...Review – Survey Sampling Matthew King Liberty University BUSI 600-B13 LUO Dr. Shawna Wentlandt September 27, 2014 Abstract Conducting a survey is an incredibly fruitful method in gathering informational data related to a particular field or idea. When conducting that survey, one of the first questions to answer is who will partake in the survey. The methodology employed to determine how many, and the parameters of who will be surveyed is known as sampling. This literature review will summarize and synthesize many articles on the topic of sampling. Introduction Literature Review Purpose This literature review will summarize and synthesize over twenty-four articles related to the science and art of survey sampling. Sampling for a survey is paramount to the research as it ensures accuracy of polling a population. An understanding of sampling will not be necessary to the comprehension of this review. It serves to introduce the reader to survey sampling in general, while acting as a quick handbook to sampling. Those with a beginning interest should be able to use this review as a first step into sampling science. Each section should provide a further understanding of sampling from the various articles reviewed. Literature Review Outline The literature review will begin with an introduction section to survey sampling. The history of survey sampling will be shown by the articles reviewed. Following an introduction to sampling, methodologies used in sampling will......

Words: 6113 - Pages: 25

Premium Essay

Sampling

...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......

Words: 10191 - Pages: 41

Premium Essay

Sampling Tech

...org/OurWork/Schools/Fieldwork+and+local+learning/Fieldwork+techniques/Sampling+techniques.htm Two categories of sampling techniques, and variety of sampling techniques within each category Sampling techniques What is sampling? • A shortcut method for investigating a whole population • Data is gathered on a small part of the whole parent population or sampling frame, and used to inform what the whole picture is like Why sample? In reality there is simply not enough; time, energy, money, labour/man power, equipment, access to suitable sites to measure every single item or site within the parent population or whole sampling frame. Therefore an appropriate sampling strategy is adopted to obtain a representative, and statistically valid sample of the whole. Sampling considerations • Larger sample sizes are more accurate representations of the whole • The sample size chosen is a balance between obtaining a statistically valid representation, and the time, energy, money, labour, equipment and access available • A sampling strategy made with the minimum of bias is the most statistically valid • Most approaches assume that the parent population has a normal distribution where most items or individuals clustered close to the mean, with few extremes • A 95% probability or confidence level is usually assumed, for example 95% of items or individuals will be within plus or minus two standard deviations from the mean • This also means that up to five per cent may lie......

Words: 1366 - Pages: 6

Premium Essay

Distribution

...week 4 Distribution Randy Weatherford University of Phoenix week 4 Distribution Channels of distribution of sales for designer jeans for Starbucks new Starbutts. The key for distribution is to align the manufacture to the sales, shortest point where the manufacturer to the customer purchasing the product. First, Starbucks will assess the competitors line of product to identify all channels of categories so Starbucks can identify their where they can be successful. Competitors' distribution channels. As a starting point, make a list of any competitors that could compete directly with you for the same customers. Then divide these competitors into categories based on the distribution channels they currently use. The result will be a picture of which channels are being successfully used in your type of business and location. (2015, p. 1) The lines of distribution are as follows, first of all direct lines to currently own retail outlets, wholesale outlets, Direct mail through flyers or catalogs, telemarketing, Cyber marketing, and cable or TV advertisement. Each of these avenues provide value to the sale of the product. The wholesale and retail outlets provide a direct link between the customer and the manufacture but this can be the more expensive direction because the products provided are manufactured and shipped to the retail stores without orders in place. Direct mail through catalog or flyers provide the customers the options and saves Starbucks the capitol......

Words: 512 - Pages: 3

Premium Essay

Qnt351 Week3 Learning Team Sampling Distributions Real Estate Part 2

...QNT351 Week3 Learning Team Sampling Distributions Real Estate Part 2 Click Link Below To Buy: http://hwaid.com/shop/qnt351-week3-learning-team-sampling-distributions-real-estate-part-2/ Sampling Distributions – Real Estate Part 2 Directions: Use the real estate data you used for your Week 2 learning team assignment. Analyze the data and explain your answers. 1. Review the data and for the purpose of this project please consider the 100 listing prices as a population. • Explain what your computed population mean and population standard deviation were. 2. Divide the 100 listing prices into 10 samples of n=10 each. Each of your 10 samples will tend to be random if the first sample includes houses 1 through 10 on your spreadsheet, the second sample consists of houses 11 through 20, and so on. • Compute the mean of each of the 10 samples and list them: 3. Compute the mean of those 10 means. • Explain how the mean of the means is equal, or not, to the population mean of the 100 listing prices from above. 4. Compute the standard deviation of those 10 means and compare the standard deviation of the 10 means to the population standard deviation of all 100 listing prices. • Explain why it is significantly higher, or lower, than the population standard deviation. 5. Explain how much more or less the standard deviation of sample means was than the population standard deviation. According to......

Words: 383 - Pages: 2

Premium Essay

Audit Sampling

...Summary Audit sampling is necessary and helps improve an audit engagement because examining all items are rather very timely, requires more effort, and of course, at higher cost. Audit risks such as inherent, control and detection risk are first assessed when doing audit sampling. Low control risk means auditors rely extensively on the entity's internal control, and vice versa. The process for determining risks and gathering evidences to provide reasonable assurance are done through other audit procedures such as tests of controls and tests of details. These procedures are done by sampling. Using sampling, when auditors do not obtain sufficient and appropriate evidences, there is a risk of not identifying material errors and therefore result in a wrong conclusion. The use of either non-statistical sampling techniques or statistical ones does not directly affect application of audit procedures, appropriateness of audit evidences or courses of actions that could be taken. Even though the procedures in non-statistical sampling is less formal, they are still rigorous. Non-statistical sampling method involves eight steps namely establish objective test, defining the population, determining distortions, determining the appropriate sample size, determination of the right method for the sample selection, proper testing of the selected sample, extrapolating results, risk assessment. Firms include in their policies the techniques which they use to implement auditing procedures....

Words: 1449 - Pages: 6

Premium Essay

Sampling

...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,......

Words: 4006 - Pages: 17

Free Essay

Sampling

...Unit 3 – Sampling Teri Isbell American InterContinental University Abstract Three different types of surveys will be discussed for sample size and how they compare to each other. A personal survey’s information is provided and the breakdown of the answers is shown in charts for review. A personal opinion regarding how survey information can be used with a business or other service is discussed. Introduction An entertainment, political, and general survey will be examined for sample size and discussed in this paper. A personal survey will also be reviewed and additional information will be discussed as to how they relate to each other and how the information could be used in a business or other setting. Part 1: Survey Analysis: Entertainment Social gaming is taking the desktop and console gaming world to new heights by attracting gamers that might not have every touched a video game before according to Shaer, (2010). He reports that 56.8 million American consumers over the age of 6 had participated in social game playing over the past three months. According to the U.S. Census Bureau, the 2010 population was 281,421,906, and Shaer’s 56.8 million consumers represent approximately 20% of the overall population. I was surprised to find the accuracy in Shaer’s numbers representing one-fifth of the U.S. population in 2010. That is a staggering number of people doing nothing more than playing games! To further understand the impact these numbers have on social......

Words: 2203 - Pages: 9

Premium Essay

Sampling

...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......

Words: 1788 - Pages: 8