on sample information such as tables‚ graph‚ the mean‚ median‚ mode and etc. c) A researcher will use the F distribution to make an inference on the ratio between two population variances. d) To construct a 90% confidence interval for u‚ if a small sample was selected randomly from normal population with unknown variance‚ the t distribution is used. e) The significance level a is the probability of rejecting the null hypothesis when it is false. f) Non-parametric test is used when the data are not
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INVESTMENT & PORTFOLIO MANAGEMENT FIN3IPM TUTORIAL ANSWERS TUTORIAL 1: INTRODUCTION CHAPTER 1: QUESTION 1 a The process of investment concerns the purchase of assets which will provide a future return to allow for future consumption or further investment. Individuals have to make choices between current and future consumption and because their pattern of income does not always match their pattern of consumption‚ they are required to make investments. Throughout an individual’s life
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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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