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class07-1-handouts - PSTAT 120B - Probability &...

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Unformatted text preview: PSTAT 120B - Probability & Statistics Class # 07-1- 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. Mid-term 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 one-sided confidence interval sets either ˆ θ L =-∞ or ˆ θ U = ∞ : an upper one-sided confidence interval is (-∞ , ˆ θ U ) and a lower one-sided 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 two-sided 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.

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class07-1-handouts - PSTAT 120B - Probability &...

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