PS_3_and_Solutions

# PS_3_and_Solutions - 16March2011 PS#3 InthisPS, Then we...

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16 March 2011 IE 256 STATISTICS FOR INDUSTRIAL ENGINEERS PS # 3 In this PS, we have discussed the theoretical background of sampling distributions for the mean. Then we considered the first question of PS # 2 to have a practical insight. Lastly, we have concluded the PS with a simulation of these discussions in a statistical package namely R. You are not responsible with the coding procedure in R, I use it just to show you some graphical results. The following figure shows the sampling process from a population. A population is the collection of all possible outcomes of a random variable ܺ . Each individual in the population, represented by , follows a distribution . The mean of the population is and the standard deviation is ߪ . If all outcomes in the population with their probabilities are not given or the distribution of the population with parameters of the distribution is not known we cannot calculate the values of and . Since generally the size of the population is very large, we cannot figure out all outcomes in the population from practical point of view. Hence, we decide to make measurements for a limited number of trials, say ݊ many outcomes, and constitute a sample of the population. ܺ ܦ݅ݏݐ ߤ ߤ ߪ 1

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16 March 2011 Each outcome in a sample, represented with ܺ ,݅ൌ1 ,… , comes from ܦ݅ݏݐ with same parameter values, since they are members of the population. We know all values in a sample, therefore we can calculate sample mean ܺ and sample standard deviation ܵ . Let us repeat this sampling process for ݉ times. This means we take ݉ different samples each of which has ݊ observations. Since we are taking these ݉
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PS_3_and_Solutions - 16March2011 PS#3 InthisPS, Then we...

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