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Unformatted text preview: IE 330 Lecture 5 Chapter 3 contd 1/30/08 The need of Statistical Inference In statistical quality control, the probability distribution is used to model some quality characteristic. The parameters of a probability distribution are unknown. Estimation of Process Parameters The parameters of a process can be time varying, how do we identify a process change? Hypothesis Testing Random Samples Random Sample: Sampling from an infinite population or finite population with replacement: A sample is selected so that the observations are independently and identically distributed. Sampling n samples from a finite population of N items without replacement if each of the possible samples has an equal probability of being chosen n N Terminology Estimate: a particular numerical value of an estimator, computed from sample data. Point estimator: a statistic that produces a single numerical value as the estimate of the unknown parameter Interval estimator: a random interval (or called confidence interval) in which the true value of the parameter falls with some level of probability. Statistic: any function of the sample data that does not contain unknown parameters. Sampling distribution: The probability distribution of a statistic. If x is a random variable with unknown mean and known variance 2 , what is the confidence interval for mean ? Point estimator The approximate distribution of is regardless of the distribution of x per the central limit theorem. Given confidence level , then 100(1 )% twosided confidence interval on is: 100(1 )% upper confidence interval on is: 100(1 )% lower confidence interval on is: C. I. of Population MeanVariance Known = = n i i n x x 1 / ) ( ) / , ( 2 n N n Z x n Z x +  2 / 2 / 2 / } Pr{ 2 / = Z z...
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This note was uploaded on 04/07/2008 for the course IE 330 taught by Professor Tezcan during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 Tezcan

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