ENMA 420-520 Lecture 7 Slides

# ENMA 420-520 Lecture 7 Slides - Click to edit Master...

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Unformatted text preview: Click to edit Master subtitle style 10/17/09 Statistical Concepts for Engineering Management ENMA 420 / 520 Lecture #7 Tests of Hypothesis 11 10/17/09 Statistical Tests Null Hypothesis H0 About one (or more) population parameters Alternative Hypothesis Ha Accepted if the null hypothesis is rejected Test Statistic Computed from the sample data 22 10/17/09 Types of Errors Type I: Falsely reject the null hypothesis False positive or & Type II: Falsely accept the null hypothesis False negative or & error Also: Type III error (Mitroff): wrong question Type IV error (Keating): wrong philosophical perspective 33 Is there a worst kind of error? 10/17/09 Criticisms of Null Hypothesis Significance Testing (NHST) Highly sensitive to framing Rejecting the negative may not mean accepting the positive A difference can always be found P = 0.05 means 1 out of 20 and more Recommendations: 44 Statistics are never a replacement for critical thought 10/17/09 Exercise 8.4 55 10/17/09 Finding Statistical Tests: One-Tail vs. Two-Tail 66 10/17/09 Statistical Tests: Classical Methods 77 LargeSampleTestBasedontheStandardNormalz- TestStatistic OneTailedTest Two- TailedTest- : - =-- : - =--- : - > --- &-- : - < - l-- : - - & Z & A } v&& :- =-- - l l l & Z & A } v&& :- =-- - l l l & A } v&& &&&&& :- > -- (- &- < -- ) & A } v&& &&&&& : l > -- 2 - Z- -- > --- = - - Z- -- > -- 2 l = - 2 10/17/09 Calculating & 88 For alargesampletestofl : - = - atsignificancelevel : Upper- TailedTest : - = - - - < -- ------ W herel l = - + ----- isthe valueoftheestimator correspondingtotheborder oftherejection . region Lower- TailedTest : - = - -- > -- ------ W herel l = - ----- is thevalueoftheestimator correspondingtotheborder oftherejection . region Two- TailedTest : - = - --- ,- ----- < - < -- ,- ------ W herel l ,- = - + ----- andl l ,- = - ----- are thevalues oftheestimator correspondingtothe . border oftherejectionregion 10/17/09 Choosing Hypotheses Most critical step in analysis Is it the right hypothesis? Is the hypothesis right? One-tail or Two-tailed test? Two-tailed: parameter is above or below a value For example, not equal to a mean One-tailed: parameter is either above or 99 10/17/09 Choosing Hypotheses (Contd) Flat & Absolute Rule: Choose Ha and H0 prior to obtaining and analyzing the sample data. 1010 10/17/09 Exercise 8.10 1111 10/17/09 Exercise 8.12 1212 10/17/09 5 Minute Break Discuss: What are examples of bad hypotheses?...
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## This note was uploaded on 10/17/2009 for the course MET 387 taught by Professor Dean during the Spring '09 term at Old Dominion.

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ENMA 420-520 Lecture 7 Slides - Click to edit Master...

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