Chapter 7 - Chapter 7.Statistical Intervals based on a...

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Unformatted text preview: Chapter 7.Statistical Intervals based on a single sample Statistical Interval The point estimate is a single number (accurate)- does not provide information about precision and reliability of estimation- report an entire interval of plausible values- an interval estimate Accuracy and Precision A Confidence Interval- first select a confidence level, which is a measure of reliability of the interval Precision of an interval estimate is conveyed by the width of the confidence interval 7.1 Basic Properties of Confidence Intervals 1 2 , , , n X X X L : rs from 2 ( , ) N : unknown, : known 2 : ( , ) X N n 1 : ( 0, 1) / X Z N n - = ( 1. 96 1. 96) 0. 95 P Z- < < = ( 1. 96 1. 96) 0. 95 / X P n -- < < = ( 1. 96 / 1. 96 / ) 0. 95 P X n X n - < < + = Random Interval interval whose end points are rvs ( 1. 96 / , 1. 96 / ) X n X n - + 1. 96 / X n The probability that this random interval will cover the true mean is 95% Def) 95% Confidence Interval for ( 1. 96 / , 1. 96 / ) x n x n - + 1. 96 / x n Ex 7.2 : 2. 0, 31, 80. 0 n x = = = 95% CI : 1. 96 / 80. 0 (1. 96) 2 / 31 80. 0 0. 7 ( 79. 3, 80. 7) x n = = = We are confident at 95% level that 79. 3 80. 7 < < The interval estimate 1. 96 / X n is no longer random interval 2- The probability that the random interval will cover the true mean is 95% and We are confident at 95% level that 79. 3 80. 7 < < are incorrect statements Interpreting a confidence interval...
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This note was uploaded on 01/06/2011 for the course STAT 511 taught by Professor Bud during the Fall '08 term at Purdue University-West Lafayette.

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Chapter 7 - Chapter 7.Statistical Intervals based on a...

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