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Unformatted text preview: Chapter 7 Sampling Distributions Sampling Distribution of the Sample Mean x : is the distribution of all possible sample means that can be obtained by taking random samples of size n from a population. Properties of the Sampling Distribution of x : Consider a population that is normally distributed with mean μ and standard deviation σ . If we take random samples of size n from this population, then the sampling distribution of the sample mean x : 1. Has a normal distribution 2. Has mean x μ = μ population mean mean of all possible averages 3. Has standard deviation Population standard deviation x σ = n σ Sample size Interpretations: 1. The averages in the sampling distribution are clustered more closely together than the individual measurements in the population. If n > 1, then n σ < σ 2. If the sample size is increased, then the averages become more closely clustered together. x σ = n σ implies that if n then n σ See the summary box on page 283. Conditions for x σ formula Example: See Figure 7.3 on pages 283284 Individual Mileages Distribution of averages for n = 5 Distribution of averages for n = 50 Process Monitoring A process is a sequence of operations that takes inputs ( labor, raw materials, capital, machines, etc ) and turns them into outputs (product and services). A process operates and produces output over time . We wish to study one or more quality characteristics of the output. Examples: Diameter of an auto part Time it takes to admit a patient to an emergency room Number of errors on an invoice As the process operates, the quality characteristic exhibits variation . Too much variation bad quality Statistical Process Control (SPC): SPC is a systematic method for analyzing process data (quality characteristics) in which we monitor and study this process variation. The goal is to stabilize and reduce the amount of process variation. We collect data from the process by sampling at equally spaced time points (say, every 5 min., hourly, daily, etc) This is called periodic sampling . We then plot the data versus time to see if the process is in statistical control . A process is in statistical control if it does not exhibit any unusual process variations. Often, this means that the process exhibits a constant amount of variation around a constant mean (or level). This can be checked by using a runs plot (or a more sophisticated version called a control chart ). This process is in control . Runs plots that indicate that the process is out of control ....
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 Fall '11
 Dr.Weese
 Control Chart, Process capability, LCL

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