# 03 - ENGR 201 Evaluation & Presentation of Experimental...

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1 12 April 2011 ENGR201 Lecture 3 Spring 2011 1 ENGR 201 Evaluation & Presentation of Experimental Data Lecture 3: Statistical Measurement Theory part 2 T. Chmielewski, Electrical & Computer Engineering D. Miller, Mechanical Engineering & Mechanics Drexel University 12 April 2011 ENGR201 Lecture 3 Spring 2011 2 Quiz 1 Performance

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2 12 April 2011 ENGR201 Lecture 3 Spring 2011 3 Announcements • Quiz 2 will be on-line Thursday 4/14 at 5:00 PM thru Friday 4/15 at 5:00 PM – Check BbVista for additional details • Midterm is TBD – Closed book and notes – Calculators are permitted – Scantron and Computational parts – Covers Chapter 1 and 4, labs 1 and 2 12 April 2011 ENGR201 Lecture 3 Spring 2011 4 Homework and Reading Week 3 • Read textbook sections 4.4, 4.5, 4.7,4.8 make sure to pay attention to examples 4.4, 4.5, 4.6, 4.12, 4.13 and Table 4.7 on page 152 • Problems from text: 4.11 (only analyze column 1), 4.12 (only analyze column 1), 4.26, 4.34, 4.42 • Additional information to support lecture concepts – Video: Statistics: Standard Deviation ( cut and paste link ) http://www.youtube.com/watch?v=HvDqbzu0i0E&feature=channel – Compare Student’s t-distribution to normal distribution http://www-stat.stanford.edu/~naras/jsm/TDensity/TDensity.html – Effect of sample size on finite statistics Finite-population.vi in student area of textbook web site
3 12 April 2011 ENGR201 Lecture 3 Spring 2011 5 Recap of Lecture 2 Gaussian or Normal Distribution Infinite statistics Defined by: mean, x’ and variance, σ 2 . • Probability P(x) that a variable x will fall within •x ± δ x is the area under curve Interval with probability •P ( x - σ≤ x x’+ σ ) = 68.27% ( x - 2 σ≤ x x’+ 2 σ ) = 95.45% ( x - 3 σ≤ x x’+ 3 σ ) = 99.73% Px ' δ x x x ' + x () = px ( ) dx x ' x x ' + x 12 April 2011 ENGR201 Lecture 3 Spring 2011 6 Back to original question from Lecture 2 • We measure the diameter of 10 parts (sample) from a population in a crate and find the average, We want to know how well the average diameter of our small sample represents the true average diameter, x’, of the entire crate! Estimate true value x’ as: x ' = x ± u x P % ( ) x ± μ x is the uncertainty interval in the estimate at some probability level

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4 12 April 2011 ENGR201 Lecture 3 Spring 2011 7 Today’s Topics will answer that question and more • Since you can rarely measure every item in a population • If you measure just part of the population (a sample), what can we say about the population as a whole? • Central Tendency {mean and standard deviation} • Confidence Interval • Type of distribution At the conclusion of this lecture we will have the tools to estimate the population mean and population standard deviation albeit with a confidence interval 12 April 2011 ENGR201 Lecture 3 Spring 2011 8 Vocabulary Population and Sample Statistics Population Sample Characteristics Parameters Statistics Mean x’ x Standard Deviation σ S x We say a population has parameters! Sample has statistics.
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## This note was uploaded on 05/18/2011 for the course ENGR 201 taught by Professor Miller during the Spring '08 term at Drexel.

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03 - ENGR 201 Evaluation & Presentation of Experimental...

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