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Unformatted text preview: 71 Introduction•The field of statistical inference consists of those methods used to make decisions or to draw conclusions about a population. •These methods utilize the information contained in a samplefrom the population in drawing conclusions.•Statistical inference may be divided into two major areas:•Parameter estimation•Hypothesis testing71 Introduction¡Suppose that we want to obtain a point estimation of a population parameter.¡The observations are random variables, say X1, X2, …, Xn.¡Therefore, any function of the observations, or any statistic, is also a random variable.¡For example, the sample meanX, and the samplevariance S2are statisticsand they are also random variables.¡Since a statistic is RV, it has a probability distribution.¡We call the probability distribution of a statistic a samplingdistribution.Definition71 IntroductionΘis the uppercase of θ71 Introduction71 Introduction7.2 Sampling Distributions and the Central Limit TheoremStatistical inferenceis concerned with making decisionsabout a population based on the information contained in a random sample from that population.Definitions:7.2 Sampling Distributions and the Central Limit Theorem¡If we are sampling from a population that has an unknownprobability distribution, the sampling distribution of the sample meanwill still be approximately normalwith mean μand variance σ2/n, if the sample size is large.¡This is one of the most useful theorems in statistics, and it is called central limit theorem.7.2 Sampling Distributions and the Central Limit TheoremXis N(μ, σ2/n)•If the population is continuous, unimodal and symmetric, n=5 is enough....
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This note was uploaded on 10/12/2011 for the course STATISTICS 101 taught by Professor Nazim during the Spring '10 term at Qatar University.
 Spring '10
 nazim
 Probability

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