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Lecture 5 - IE 330 Lecture 5 Chapter 3 cont’d The need of...

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Unformatted text preview: IE 330 Lecture 5 Chapter 3 cont’d 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 μ and known variance σ 2 , what is the confidence interval for mean μ ? Point estimator The approximate distribution of is regardless of the distribution of x per the central limit theorem. Given confidence level α , then 100(1- α )% two-sided confidence interval on μ is: 100(1- α )% upper confidence interval on μ is: 100(1- α )% lower confidence interval on μ is: C. I. of Population Mean—Variance Known ∑ = = n i i n x x 1 / ) ( ) / , ( 2 n N σ μ n Z x n Z x σ + ≤ μ ≤ σ- α α 2 / 2 / 2 / } Pr{ 2 / α = ≥ α Z z...
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Lecture 5 - IE 330 Lecture 5 Chapter 3 cont’d The need of...

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