Week6 - Stat231 William Marshall Stat231 William Marshall...

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Unformatted text preview: Stat231 William Marshall Stat231 William Marshall June 7, 2010 Stat231 William Marshall Week 6 Goals: Confidence intervals Introduce students T distribution Stat231 William Marshall Confidence Intervals A way to quantify sample error Provides a range of plausible parameter values Stat231 William Marshall Example 10 To assess long term performance of a process, a engineer randomly samples 100 parts from one shifts production. She then measures a critical diameter for each sampled part. The measurements are recorded in microns as a deviation from 2.000 cm. The target value is 24 microns and the specifications are 18 to 30 microns. (see week6example1.txt) Stat231 William Marshall Ex 10 Model Data: y 1 , y 2 ,..., y 100 Model: Y i = μ + R i , ∼ R i ∼ G (0 ,σ ) Figure: Stat231 William Marshall Ex 10 Analysis Estimators: ˜ μ = ¯ Y , ˜ σ 2 = ∑ ( Y i- ¯ Y ) 2 n- 1 Estimates: ˆ μ = 23 . 33, ˆ σ = 2 . 91 How to quantify sample error? Confidence interval for σ Stat231 William Marshall Confidence Interval for σ What is needed for a confidence interval?...
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This note was uploaded on 11/21/2011 for the course MATH STAT 231 taught by Professor Marsh during the Spring '10 term at Waterloo.

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Week6 - Stat231 William Marshall Stat231 William Marshall...

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