unit7_summer_2015 - STA247H1F Unit 7 Central Limit Theorem...

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STA247H1FUnit 7: Central Limit TheoremSummer 2015STA247H1FSummer 20151 / 17
Outline1Sampling Distributions2Sampling Distribution of The Sample MeanSTA247H1FSummer 20152 / 17
Sampling DistributionsSampling DistributionsAstatisticis any quantity that is calculated from sample data; forexample, the mean, the sample variance, the proportion, etc.The statistic varies from sample to sample and hence it is a randomvariable and has a probability distribution called thesampling distribu-tion.The knowledge of the sampling distribution of a statistic helps to makeinference about the correspondingpopulation (true) parameter.The random variablesX1, X2,· · ·, Xnare said to form a random sam-ple of sizenif1TheXi’s are independent random variables.2EveryXihas the same probability distribution.STA247H1FSummer 20153 / 17
Sampling DistributionsDeveloping a Sampling DistributionAssume there is a population as follows:Population sizeN= 4Random variable,X,is age of individualsValues ofX: 18, 20, 22, 24 (years)STA247H1FSummer 20154 / 17
Sampling DistributionsDeveloping a Sampling DistributionSummary Measures for the Population Distribution:Mean:μ=Ni=1xiN=18+20+22+244= 21standard deviation:σ=qNi=1(xi-μ)2N=5 = 2.236STA247H1FSummer 20155 / 17
Sampling DistributionsDeveloping a Sampling DistributionNow consider all possible samples of sizen= 2STA247H1FSummer 20156 / 17
Sampling DistributionsSampling Distribution of All Sample MeansSTA247H1FSummer 20157 / 17
Sampling DistributionsDeveloping a Sampling DistributionSummary Measures of this Sampling Distribution:STA247H1FSummer 20158 / 17
Sampling DistributionsComparing the Population with its Sampling DistributionSTA247H1FSummer 20159 / 17

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