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ams572_notes_2 - AMS 572 Lecture Notes#2 Sept 13 2010...

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AMS 572 Lecture Notes #2 Sept. 1 3 , 2010. Chapter 7: Inference on one population mean h 1. Motivation & simple random sample Eg) We wish to estimate the average height of adult US males Take a random sample. - “Simple” random sample: every subject in the population has the same chance to be selected. 2. Introduction to statistical inference on one population mean For a “ random sample” of size n: <i> Point estimatior sample mean () Other estimators: median, mode, trimmed mean, … <ii> Confidence Interval (C.I.) Eg) 95% C.I. for μ 99.9999% C.I. (‘6-9’ in the manufacture industry) <iii> Hypothesis Test Eg) : μ : μ 1
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Point Estimator, C.I., Test Statistical Inference - Draw some conclusion on the population (parameters of interest) based on a random sample. 3. Normal Distribution <i> Probability Density Function (p.d.f.) (X follows normal distribution of mean and variance ) , = area under the pdf curve bounded by a and b <ii> Cumulative Density Function (c.d.f.) <iii> Z-score Standard Normal Distribution 2
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Proof) 1> Use c.d.f.
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