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Unformatted text preview: PSTAT 120B  Probability & Statistics Class # 071 Confidence interval review Jarad Niemi University of California, Santa Barbara 10 May 2010 Jarad Niemi (UCSB) Confidence interval review 10 May 2010 1 / 16 Class overview Announcements Announcements Homework Homework 5 due today by 4pm in SH 5521 If Tony is late, turn homework into my office. Midterm II This Friday Covers 8.5–8.8,9.1–9.5 Jarad Niemi (UCSB) Confidence interval review 10 May 2010 2 / 16 Class overview Goals Review confidence intervals Important definitions, theorems, and concepts Example questions Jarad Niemi (UCSB) Confidence interval review 10 May 2010 3 / 16 Confidence interval review Definitions Definition A 100(1 α )% confidence interval (CI) for θ is an interval estimator ( ˆ θ L , ˆ θ U ) whose probability of containing θ over repeated sampling is the confidence coefficient (1 α ), i.e. P ( ˆ θ L ≤ θ ≤ ˆ θ U ) = 1 α where ˆ θ L is the lower confidence limit and ˆ θ U is the upper confidence limit. Definition A onesided confidence interval sets either ˆ θ L =∞ or ˆ θ U = ∞ : an upper onesided confidence interval is (∞ , ˆ θ U ) and a lower onesided confidence interval is ( ˆ θ L , ∞ ). Jarad Niemi (UCSB) Confidence interval review 10 May 2010 4 / 16 Confidence interval review Definitions Definition A pivotal quantity for θ has the following characteristics: It is a function of the data, θ , and known constants. Its probability distribution is known and does not depend on the parameter θ . Finding a confidence interval Suppose U = f ( θ ) is a pivotal quantity. To obtain a twosided 100(1 α )% confidence interval, find a and b such that α 2 = P ( U ≤ a ) = P ( U ≥ b ) ....
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This note was uploaded on 11/23/2010 for the course MATH 104b taught by Professor Ceniceros,h during the Spring '08 term at UCSB.
 Spring '08
 Ceniceros,H
 Statistics, Numerical Analysis, Probability

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