1. Stat 418 – Day 3 Maximum Likelihood Estimation (Ch. 1)

2. Last Time Multiple confidence interval procedures for   Main goal: Achieve stated confidence level, e.g., 95% of intervals for all possible random samples capture the value of the parameter  Also nice if narrower

3. Confidence interval for  Exact binomial Wald interval Score interval (Wilson)  Which values of  would not be rejected… Adjusted Wald (Agresti & Coull, 1998)  Approximate is better than "exact" for interval estimation of binomial proportions, American Statistician, 52:119–126.

4. Likelihood function =C(407,248)  248 (1-  ) 209

5. Test of significance? Gives you a point estimate Also allows you to compare to other values  Another value of  will be plausible if the likelihood function at that value isn’t too much smaller

6. Likelihood ratio test Likelihood Ratio compares the unrestricted maximum likelihood to value under null Pearson is z 2 from “score” test (two-sided)

7. To Do Finish reading Ch. 1 Investigation 1 HW 1 solutions posted tonight? HW 2 posted this weekend? Final Exam survey (by Monday?)