# Lec19 - Short Version of Chapter 8 Version of Chapter...

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IOE/Stat 265, Fall 2009 Lecture #19: Hypothesis Tests for One Mean 8-1 Hypotheses & Test Procedures 8-2 Tests about a Population Mean Tests about a Population Proportion 8-3 8-4 P - Values 8-5 Comments on Selection of Tests 1 hort Version of Chapter 8 Short Version of Chapter 8 ± Fundamentally there is no difference between Interval Estimation (Chapter 7) and Hypothesis Testing (Chapter 8). “ ll hypotheses that lie within confidence ± All hypotheses that lie within confidence intervals are not rejectable. All hypotheses that lie outside confidence intervals are rejectable”. ± All essential formulas for Chapters 7 and 8 are 2 summarized on following pages. Overv iew 8-1 Overview I. Statistical Hypothesis ± Null and Alternative Hypothesis yp ± Test Statistics and Rejection Regions II. Errors in Hypothesis Testing ype I and II errors ± Type I and II errors 3 Statistical Hypothesis 8-1 Statistical Hypothesis tatistical Hypothesis - laim bout the value of a ± Statistical Hypothesis claim about the value of a single population parameter/characteristic (e.g. mean, variance, proportion), or relationship between several population characteristics. ± Examples of Claims: ± Mean diameter of an engine cylinder is 81 mm. ± Mean exceeds the mileage standard 30 MPG. ± Variance is within the standard, 20 microns 2 . ± % Defective is less than 5%. ± In hypothesis testing, we collect a random sample of data from a population and test the claim. 4

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ull and Alternative Hypothesis Null and Alternative Hypothesis ± To evaluate a claim, you identify a null and alternative ,y y hypothesis. ± Null Hypothesis, H 0 laim that is initially assumed to be true ± Claim that is initially assumed to be true. ± Default Hypothesis (Status Quo) ± Alternative Hypothesis, H yp , 1 ± Assertion that is contradictory to H 0 . (implies the need for change) ± Null Hypothesis “is rejected” if sample evidence suggests at it is false If not we “ ail to reject H ” that it is false. If not, we fail to reject H 0 . ± So, possible outcomes of test are: ± Reject H or Fail to Reject H 5 0 ± NOTE: failure to reject H 0 is not to say that we have proven H 0 is true. xamples: Null Hypotheses (H Examples: Null Hypotheses (H 0 ) ± Identify a null and alternative hypothesis for each of the prior examples. ± Mean diameter of an engine cylinder is 81 mm. ± Mean exceeds the mileage standard 30 MPG. ± Variance is within the standard, 20 microns 2 . Defective is less than 5% 6 ± % Defective is less than 5%. “ avored Claim” Favored Claim setting up a test we typically have a favored claim ± In setting up a test, we typically have a favored claim (default) which is the H 0 .
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## This note was uploaded on 03/17/2010 for the course IOE 265 taught by Professor Garyherrin during the Fall '09 term at University of Michigan-Dearborn.

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Lec19 - Short Version of Chapter 8 Version of Chapter...

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