...Case 1: Century National Bank The Century National Bank has offices in several cities in the Midwest and the southeastern part of the United States. Mr. Dan Selig, president and CEO, would like to know the characteristics of his checking account customers. What is the balance of a typical customer? How many other bank services do the checking account customers use? Do the customers use the ATM service and, if so, how often? What about debt cards? Who uses them, and how are they used? To better understanding the customers, Mr. Selig asked Mrs. Wendy Lamberg, Director of planning, to select a sample of customers and prepare a report. To begin, she has appointed a team of us. Then, we started by selecting a random sample of 60 customers. In addition to the balance in each account at the end of last month, we determined: * The number of ATM (automatic teller machine) transactions in the last month. * The number of other bank services (a saving account, a certificate of deposit, etc) the customer uses. * Whether the customer has a debt card (this is a relatively new bank service in which charges are made directly to the customer's account). * Whether or not interest is paid on the checking account. * The sample includes customers from the branches in Cincinnati, Ohio; Atlanta, Georgia; Louisville, Kentucky; and Erie, Pennsylvania. Banking Data Set-case: X1 = Account balance in $ X2 = Number of ATM transactions in the month X3 = Number of other bank services...
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...A point estimation is a sample statistic that gives a good guess about a population parameter. In the same way, a point estimate of the mean overpayment is simply a good guess about what the average overpayment for the population is. Investigating all 1,000 claims and obtaining the overpayment amount for each would either be impractical, unfeasible or both. Thus, the auditor deems a sample size of 50 claims to be adequate and sufficiently representative of the entire population. The mean overpayment amount of this sample is then calculated in order to obtain a point estimate of the mean overpayment. The estimated mean is then extrapolated to the overpayment amount to the population of all 1,000 claims. http://pages.wustl.edu/montgomery/lecture-7 Point Estimate vs. Interval Estimate To estimate population parameters, statisticians use sample statistics. For example, we use sample means to estimate population means and we use sample proportions to estimate population proportions. An estimate of a population parameter can be expressed in one of two ways: * Point estimate. A point estimate of a population parameter is a single value of a statistic. For example, the sample mean x is a point estimate of the population mean μ. In the same way, a sample proportion p is a point estimate of the population proportion P. * Interval estimate. An interval estimate is defined by two numbers, and the population parameter is said to lie between those two numbers. For example...
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...Goethe University Frankfurt Advanced Econometrics 2, Part 2 Sommersemester 2016 Prof. Michael Binder, Ph.D. I. Vector Autoregressions and Vector Error Correction Models 3. Estimation and Inference with and without Parameter Restrictions Cointegrated VAR – Case of a Single Cointegrating Relationship Special Case of One Cointegrating Relationship: Weak Exogeneity and ARDL Models When the cointegration rank of a cointegrated VAR is one, then under certain conditions it is feasible to work with a notably more parsimonious model, namely the so-called Autoregressive Distributed Lag (ARDL) model of the form: p q 1 − ∑ φ j Lj yt =∑ θ j ' xt − j + ε t , = 1= 0 j j iid ( (76) ) with ε t ~ 0, σ 2 . Note: For simplicity of notation only, in (76) model deterministic components are irgnored and it is assumed that all elements of x enter with the same lag order, namely q. 68 Goethe University Frankfurt Advanced Econometrics 2, Part 2 Sommersemester 2016 Prof. Michael Binder, Ph.D. I. Vector Autoregressions and Vector Error Correction Models 3. Estimation and Inference with and without Parameter Restrictions Cointegrated VAR – Case of a Single Cointegrating Relationship To understand when we can reduce a cointegrated VAR to an ARDL model, let us carefully derive the ARDL model in (76) from a system of equations in zt = ( yt xt )′ . Suppose zt is generated by { } p j εt , I − ∑ Φ j L zt = j =1 (77) iid t = 1, 2,..., T , with ε t ~ ( 0, Ω ) . We assume that...
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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 or...
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...Managerial Economics Sat. 11:00 – 14:00 Demand Estimation and Forecasting Facilitators : Mr. John Michael G. Favila Mr. Jose Miguel G. Catan Learning Objectives * Identify a wide range of Demand Estimation and Forecast Methods. * Understand the nature of Demand Function * Understand that the Demand Estimation and Forecasting is all about minimizing risk. Demand Estimation and Demand Forecasting; distinguished. * Demand Estimation attempts to quantify the link between the level of for a product and the variables which determines it whereas the Demand Forecasting simply attempts to predict the level of sales at some particular future date. 7 stages of Demand Estimation 1. Statement of a Theory or Hypothesis : This usually comes from a mixture of economic Theory and previous empherical studies. 2. Model Specification : This means determining what variables should be included in the demand model and what mathematical form or forms such a relationship should take. 3. Data Collection : Gathering necessary information. a. Cross-sectional data : Provide information on a group opf entities at a given time. b. Time-serie data: Provide information on the entity over time. i. Quantitative: Data that are expressed in nominal in either ordinal or cardinal. ii. Qualitative: Expressed in categories. 4. Estimation of Parameters : This means computing the value of the coefficient...
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...Uniform Crime Reporting Statistics - UCR Data Online http://www.ucrdatatool.gov/ National or state crime in 2009 State Population Violent Crime rate Murder and nonnegligent manslaughter rate Forcible rape rate Robbery rate Aggravated assault rate Property crime rate Burglary rate Larceny-theft rate Motor vehicle theft rate Alabama 4708708 449.8 6.9 31.9 132.9 278.1 3772.4 1037.2 2499.9 235.3 Alaska 698473 633 3.1 73.3 93.8 462.7 2946 515 2189.2 241.8 Arizona 6595778 408.3 5.4 32 122.8 248.1 3556.5 809.8 2352.8 394 Arkansas 2889450 517.7 6.2 47.3 89.4 374.8 3773.7 1203.1 2359.3 211.2 California 36961664 472 5.3 23.6 173.4 269.7 2731.5 622.6 1665.1 443.8 Colorado 5024748 337.8 3.5 44.6 67.4 222.3 2666.2 530.4 1887.9 247.9 Connecticut 3518288 298.7 3 18.5 113.4 163.7 2335.8 428.4 1694.9 212.5 Delaware 885122 636.6 4.6 38.2 188.8 405 3349.6 783.2 2351 215.5 Florida 18537969 612.5 5.5 29.7 166.7 410.6 3840.8 981.1 2588.6 271.1 Georgia 9829211 426.1 5.8 23.4 148.6 248.3 3666.6 1000.7 2328.7 337.2 Hawaii 1295178 274.8 1.7 30.3 79.8 163 3661.2 708.6 2580.5 372.1 Idaho 1545801 228.4 1.4 35.7 15.8 175.4 1988.7 424.2 1471.1 93.3 Illinois 12910409 497.2 6 30.2 177.6 283.4 2736.9 603 1927.3 206.6 Indiana 6423113 333.2 4.8 25.5 114.5 188.4 3116.2 761.5 2138.7 216.1 Iowa 3007856 279.2 1.1 28.4 39.7 210 2308.7 539.4 1640 129.3 Kansas 2818747 400.1 4.2 38.9 63.4 293.6 3207.8 690.7 2305.9 211.2 Kentucky 4314113...
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...territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. Dotted lines on maps represent approximate border lines of which there may not yet be full agreement. The mention of specific companies or of certain manufacturers’ products does not imply that they are endorsed or recommended by the NACP in preference to others of a similar nature that are not mentioned. National HIV Prevalence & AIDS Estimates Report Contents Page II III IV 1-2 3-7 8- 16 18-27 28-30 Acknowledgments List of Tables Introduction Background of Estimation and Projection Process Estimation Process and Method Results Appendices Notes National HIV Prevalence & AIDS Estimates Report I Acknowledgment T he Technical Report was produced by the National AIDS/STI Control Programme (NACP), Ghana Health Service. The Tools for generating the estimates and projections; Estimation and Projection Package (EPP) and SPECTRUM were developed by UNAIDS and the Futures Institute. Data from both 2003 and 2008 DHS, Ghana Statistical Service Census Data, HIV Sentinel Survey (HSS) and NACP HIV/AIDS programme data were used to derive the...
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...PERCENTAGES: THE MOST USEFUL STATISTICS EVER INVENTED Thomas R. Knapp © 2010 "Eighty percent of success is showing up." - Woody Allen “Baseball is ninety percent mental and the other half is physical.” - Yogi Berra "Genius is one percent inspiration and ninety-nine percent perspiration." - Thomas Edison Preface You know what a percentage is. 2 out of 4 is 50%. 3 is 25% of 12. Etc. But do you know enough about percentages? Is a percentage the same thing as a fraction or a proportion? Should we take the difference between two percentages or their ratio? If their ratio, which percentage goes in the numerator and which goes in the denominator? Does it matter? What do we mean by something being statistically significant at the 5% level? What is a 95% confidence interval? Those questions, and much more, are what this book is all about. In his fine article regarding nominal and ordinal bivariate statistics, Buchanan (1974) provided several criteria for a good statistic, and concluded: “The percentage is the most useful statistic ever invented…” (p. 629). I agree, and thus my choice for the title of this book. In the ten chapters that follow, I hope to convince you of the defensibility of that claim. The first chapter is on basic concepts (what a percentage is, how it differs from a fraction and a proportion, what sorts of percentage calculations are useful in statistics...
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...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). ...
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...Statistical quality control relates heavily on the goodness of control chart limits. The more accurate those limits are, the more likely are to detect whether a process is in control. Various procedures have been developed to compute good control limits. This paper proposes construction of Range chart by considering a Pareto distribution of IV kind. The cumulative distribution function of sample range from their distribution is derived. The percentiles of the distribution of range are worked out and are used to construct the control limits. The performance of the control chart is compared with that of gamma based control chart. Interval estimation for the scale parameter is also worked out. Received Nov 11, 2012 Revised Mar 17, 2013 Accepted Mar 28, 2013 Keyword: Order Statistics Distribution of Range Interval estimation Percentiles Control limits Copyright © 2013 Institute of Advanced Engineering and Science. All rights reserved. Corresponding Author: R. Subba Rao, Shri Vishnu Engineering College for Women, Bhimavaram - 534202, A.P., India. Email: rsr_vishnu@rediffmail.com 1. INTRODUCTION Industrial statisticians are accustomed to monitoring the stability of the process output through the maintenance of control charts. Use of these control charts assumes that the process output is normally distributed or that appeal to the central limit theorem is...
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...| |UNIVERSITI TUNKU ABDUL RAHMAN (UTAR) | | | | | |FACULTY OF BUSINESS AND FINANCE (FBF) | Teaching Plan | |Unit Code & |UBEQ1123 QUANTITATIVE TECHNIQUES II | | |Unit Title: | | | |Course of Study: |Bachelor of Commerce (Hons) Accounting | | | |Bachelor of Business Administration (Hons) | | | |Bachelor of Business Administration (Hons) Banking and Finance | | | |Bachelor of Business Administration (Hons) Entrepreneurship ...
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...MANAGEMENT KOZHIKODE Extension of Downing Effect to estimate A population to mean: technique optimize cost and accuracy BUSINESS RESEARCH METHODS PROJECT REPORT Submitted By Satyapriya Ojha Roll No. PGP/17/165 Section – C Contents Abstract ................................................................................................................................................. 3 Problem Area ....................................................................................................................................... 4 1. 2. Error and sampling .................................................................................................................. 4 Cost of Sampling ..................................................................................................................... 5 Introduction and Hypothesis ............................................................................................................. 6 Causal Relations ................................................................................................................................... 8 Literature Review .............................................................................................................................. 10 Illusory Superiority ........................................................................................................................ 10 Sampling Error and Estimation .............................................................
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...file named SHOPPING that you downloaded from the Premium Web Site in module 1. Write a short report that includes an introduction, a conclusion paragraph and a body which answers fully the two questions posed in the problem. Please include any tables of calculations and graphs associated with this problem in the body. It should be double-spaced and in APA style format. The case in Chapter 2 listed 30 questions asked of 150 respondents in the community of Springdale. The coding key for the responses was also provided in that earlier exercise. The data are in file SHOPPING. In this exercise, some of the estimation techniques presented in the chapter will be applied to the survey results. You may assume that these respondents represent a simple random sample of all potential respondents within the community and that the population is large enough that application of the finite population correction would not make an appreciable difference in the results. Managers associated with shopping areas like these find it useful to have point estimates regarding variables describing the characteristics and behaviors of their customers. In addition, it is helpful for them to have some idea as to the likely accuracy of these estimates. Therein lies the benefit of the techniques presented in this chapter and applied here. 1. Item C in the description of the data collection instrument lists variables 7, 8, and 9, which represent the respondent’s general attitude toward each of the three shopping...
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...Disadvantages Simple random Random sample from whole population • Highly representative if all subjects participate; the ideal • There is no scope of personal bias • Each item has an equal chance of being selected • It provides more accurate and reliable data • It becomes possible to have an idea about the errors of estimation • Not possible without complete list of population members; potentially uneconomical to achieve; • Can be disruptive to isolate members from a group; • Time-scale may be too long, data/sample could change • It is not suitable if the field of enquiry is small Stratified random Random sample from identifiable groups (strata), subgroups, etc. • Can ensure that specific groups are represented, even proportionally, in the sample(s) (e.g., by gender), by selecting individuals from strata list • It eliminates the difference between strata and thereby reduces the sampling error • It brings about a gain in the precision of the sample estimate when the strata variability is the least • Independent estimates for the different strata can be prepared • . More complex, requires greater effort than simple random. • Strata must be carefully defined • The result maybe misleading if the basis of stratification in not properly decided Cluster/block Random samples of successive clusters of subjects (e.g., by institution) until small groups are chosen as units • Possible to select randomly when no single list of population members exists, but local lists can do. ...
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...Statistical Concepts 1.3 Data Measurement Nominal Level Ordinal Level Interval Level Ratio Level Comparison of the Four Levels of Data Statistical Analysis Using the Computer: Excel and MINITAB KEY TERMS census ordinal level data descriptive statistics parameter inferential statistics parametric statistics interval level data population metric data ratio level data nominal level data sample nonmetric data statistic nonparametric statistics statistics STUDY QUESTIONS 1. A science dealing with the collection, analysis, interpretation, and presentation of numerical data is called _______________. 2. One way to subdivide the field of statistics is into the two branches of ______________ statistics and _____________ statistics. 3. A collection of persons, objects or items of interest is a _______________. 4. Data gathered from a whole population is called a _______________. 5. If a population consists of all the radios produced today in the Akron facility and if a quality...
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