class07-1-handouts

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

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ) ....
View Full Document

## 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.

### Page1 / 16

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online