This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Stat231 William Marshall Stat231 William Marshall June 20, 2010 Stat231 William Marshall Week 8 Goals: More Confidence intervals CI Summary Intro to hypothesis testing Stat231 William Marshall Relative Likelihood The likelihood function L ( ) = f ( y 1 , y 2 ,..., y n ) The Maximum likelihood estimate, is the value of which maximizes L ( ) The relative likelihood function, a normalized version of the likelihood R ( ) = L ( ) L ( ) The relative likelihood gives context to the value of the likelihood and allows us to determine plausible values of Stat231 William Marshall Example 14 In an incoming inspection, a sample of 50 parts is randomly selected from a large batch and tested to see if all specifications are met. A total of 7 of the selected parts fail to meet the specifications. Find a 95% confidence interval for the proportion of parts in the batch that fail to meet specifications. Model: Y Bino (50 , ) Data: y = 7 What is the relative likelihood function for ? Stat231 William Marshall Distribution Can replace estimate with estimator in relative likelihood R ( ) = L ( ) L ( ) What is the distribution of R ( )? Unproven result: For large values of n, 2 log R ( ) 2 1 Stat231 William Marshall Likelihood based CI Find an approximate 95% CI for Using the tables P ( 2 1 < 3 . 84) = 0 . 95 Substitute 2...
View
Full
Document
 Spring '10
 Marsh

Click to edit the document details