Quantitative methods Time value of money Effective annual rate (EAR) Effective annual rate (EAR) = (1+stated annual rate/frequency‚ m) ^ m-1 Annuities Ordinary annuities: cash flow at the end of each period‚ normal one; Annuities due: cash flow at the beginning of each period‚ first payment =t0; Calculator setting: [2nd][BGN]-[2ND][SET]; same procedure for setback to END; Payment at beginning of next three years‚ N=4‚ always +1 using annuities due It is a BGN question‚ if first payment is today
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2A 1. A variable X has a distribution which is described by the density curve shown below: What proportion of values of X fall between 1 and 6? (A) 0.550 (B) 0.575 (C) 0.600 (D) 0.625 (E) 0.650 2. Which of the following statements about a normal distribution is true? (A) The value of µ must always be positive. (B) The value of σ must always be positive. (C) The shape of a normal distribution depends on the value of µ. (D) The possible values of a standard normal variable range from −3.49 to
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Math 221 Quiz Review for Weeks 5 and 6 1. Find the area under the standard normal curve between z = 1.6 and z = 2.6. First we look for the area of both by doing “2nd ‚Vars‚ NORMALCDF” and inputting “-1000‚ “Z‚” 0‚ 1 then find the difference between both. 2. A business wants to estimate the true mean annual income of its customers. It randomly samples 220 of its customers. The mean annual income was $61‚400 with a standard deviation of $2‚200. Find a 95% confidence interval for the true mean
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Preference of type I error Preference of type II error Determine appropriate distribution for the test of Mean 9.4 Two–tailed Tests and One–tailed Tests for Mean Case study on Two–tailed and One-tailed tests 9.5 Classification of Test Statistics Statistics used for testing of hypothesis Test procedure How to identify the right statistics for the test 9.6 Testing of Hypothesis in the Case of Small Samples 9.7 ‘t’ Distribution Uses of ‘t’ test 9.8 Summary 9.9 Glossary 9.10 Terminal Questions
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is not always the case. Some examples of distributions that aren’t normal are incomes in a region that are skewed to one side and if you need to are looking at people’s ages but need to break them down to for men and women. We need a way to look at the frequency distributions of these examples. We can find them by using the Central Limit Theorem. The Central Limit Theorem states that random samples taken from a population will have a normal distribution as long as the sample size is sufficiently
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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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28903 Getafe (Spain) Fax (34) 91 624-98-49 BAYESIAN INFERENCE FOR THE HALF-NORMAL AND HALF-T DISTRIBUTIONS M.P. Wiper‚ F.J. Girón‚ A. Pewsey* Abstract In this article we consider approaches to Bayesian inference for the half-normal and half-t distributions. We show that a generalized version of the normal- gamma distribution is conjugate to the half-normal likelihood and give the moments of this new distribution. The bias and coverage of the Bayesian posterior mean estimator of the halfnormal
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Statistics for Managers using Microsoft Excel 6th Edition Module 4 Sampling & Confidence Interval Estimation Copyright ©2012 Pearson Education Chap 8-1 Chapter Outline Confidence Intervals for the Population Mean‚ μ when Population Standard Deviation σ is Known when Population Standard Deviation σ is Unknown Confidence Intervals for the Population Proportion‚ p Determining the Required Sample Size Copyright ©2012 Pearson Education Chap 8-2 Introduction Copyright ©2012 Pearson
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sample of 64 students is taken. a. What are the expected value‚ standard deviation‚ and shape of the sampling distribution of the sample mean? b. What is the probability that these 64 students will spend a combined total of more than $715.21? c. What is the probability that these 64 students will spend a combined total between $703.59 and $728.45? ANS: a. 10.5 0.363 normal b. 0.0314 c. 0.0794 2. The life expectancy in the United States is 75 with a standard deviation of 7 years
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Rho 4 Probability 4 Binomial Distribution 4 Assumptions: 5 Subjective Probability 5 Normal Distribution 5 Standard Normal Distribution 5 Sampling Distribution 5 Standard Error of Statistic 5 Central Limit Theorem 5 Area under the Sampling Distribution of the Mean 6 Sampling Distribution‚ Difference between Independent means 6 Sampling Distribution of a Linear Combination of Means 6 Sampling Distribution of Pearson’s R 7 Sampling Distribution of Difference between Independent
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