Chapter 13: Chi-Square Applications SHORT ANSWER 1. When samples of size n are drawn from a normal population‚ the chi-square distribution is the sampling distribution of = ____________________‚ where s2 and are the sample and population variances‚ respectively. ANS: PTS: 1 OBJ: Section 13.2 2. Find the chi-square value for each of the right-tail areas below‚ given that the degrees of freedom are 7: A) 0.95 ____________________ B) 0.01 ____________________ C) 0.025 ____________________
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information in your discussion. What recommendations do you have if the 40-week completion time is required? 2. Suppose that management requests that activity times be shortened to provide an 80% chance of meeting the 40-week completion time. If the variance in the project completion time is the same as you found in part (1)‚ how much should the expected project completion time be shortened to achieve the goal of an 80% chance of completion within 40 weeks? 3. Using the expected activity times as the
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(RA ‚ RB ) −0.0322 = = −1. σ (RA )σ (RB ) 0.14 × 0.23 The assets are perfectly negatively correlated. Consider portfolio P formed from assets A and B such that you invest α fraction of your wealth into A and (1 − α) fraction into B. The variance of such portfolio is σ (RP )2 = = = = α2 σ (RA )2 + (1 − α)2 σ (RB )2 + 2α(1 − α)Cov (RA ‚ RB ) α2 σ (RA )2 + (1 − α)2 σ (RB )2 + 2α(1 − α)σ (RA )σ (RB )ρ(RA ‚ RB ) α2 σ (RA )2 + (1 − α)2 σ (RB )2 − 2α(1 − α)σ (RA )σ (RB ) [ασ (RA ) − (1
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Theory of Errors and Least Squares Adjustment Huaan Fan ISBN 91-7170-200-8 Royal Institute of Technology (KTH) Division of Geodesy and Geoinformatics 100 44 Stockholm Sweden August 2010 Theory of Errors and Least Squares Adjustment Huaan Fan‚ PhD Royal Institute of Technology (KTH) Division of Geodesy and Geoinformatics Teknikringen 72‚ 100 44 Stockholm‚ Sweden Phone: +46 8 7907340 Fax: +46 8 7907343 E-mail: hfan@kth.se URL: http://www.infra.kth.se/impgg With 22 illustrations and 49
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Bivariate analysis Contingency table In this case‚ we use contingency table to analyze the relationship between 2 qualitative variables. And this test works by comparing expected and observed frequencies with x2 distribution. Correlation coefficient When we need to test the relationship between 2 quantitative variables‚ we use correlation coefficient and it measured by standardized covariance measure and investigates linear dependence. Before doing this‚ it is better to first make a scatterplot
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A statistical theory that states that given a sufficiently large sample size from a population with a finite level of variance‚ the mean of all samples from the same population will be approximately equal to the mean of the population. Furthermore‚ all of the samples will follow an approximate normal distribution pattern‚ with all variances being approximately equal to the variance of the population divided by each sample’s size. Using the central limit theorem allows you to find probabilities for
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Error 0.022666 Median 0.0607 Median 0.0511 Median 0.0108 Mode -0.5085 Mode -0.8652 Mode -0.3641 Standard Deviation 0.305747 Standard Deviation 0.489717 Standard Deviation 0.22552 Sample Variance 0.093481 Sample Variance 0.239822 Sample Variance 0.050859
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8%)] = – 4.4% 18% – 8% = 10% αC = 17% – [8% + 0.7 × (16% – 8%)] = 3.4% 17% – 8% = 9% αD = 12% – [8% + 1.0 × (16% – 8%)] = – 4.0% 12% – 8% = 4% Stocks A and C have positive alphas‚ whereas stocks B and D have negative alphas. The residual variances are: 2(eA ) = 582 = 3‚364 2(eB) = 712 = 5‚041 2(eC) = 602 = 3‚600 2(eD) = 552 = 3‚025 b. To construct the optimal risky portfolio‚ we first determine the optimal active portfolio. Using the Treynor-Black technique‚ we construct the active
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Remington’s Steakhouse Project Brian Jones Research Methods & Applications Dr. Jones August 25‚ 2011 Table of Contents Table of Contents 2 List of Tables 3 Introduction 4 The Research Objectives 4 The Research Questions 5 Literature Review 6 Answers to Research Questions 8 Recommendations to Remington’s 15 References 18 Annotated Bibliography 19 Appendix(ces) 22 List of Tables Table 1 Demographic Description of the Average Remington’s Patron9 Table 2 Reported Income by Remington’s
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Skewness‚ Kurtosis‚ and the Normal Curve Skewness In everyday language‚ the terms “skewed” and “askew” are used to refer to something that is out of line or distorted on one side. When referring to the shape of frequency or probability distributions‚ “skewness” refers to asymmetry of the distribution. A distribution with an asymmetric tail extending out to the right is referred to as “positively skewed” or “skewed to the right‚” while a distribution with an asymmetric tail extending out to
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