Lecture16 - lecture 16, Confidence Intervals II 1 / 24...

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Unformatted text preview: lecture 16, Confidence Intervals II 1 / 24 Review Sample Size Determina- tion Confidence Intervals for a Population Proportion Determining the Sample Size Confidence Intervals for Parameters of Finite Populations Confidence Intervals for Population Mean and Total for a Finite Population Confidence Intervals for the Proportion/ Total Number of a Category in a Finite Population lecture 16, Confidence Intervals II Outline 1 Review 2 Sample Size Determination 3 Confidence Intervals for a Population Proportion Determining the Sample Size 4 Confidence Intervals for Parameters of Finite Populations Confidence Intervals for Population Mean and Total for a Finite Population Confidence Intervals for the Proportion/ Total Number of a Category in a Finite Population lecture 16, Confidence Intervals II 2 / 24 Review Sample Size Determina- tion Confidence Intervals for a Population Proportion Determining the Sample Size Confidence Intervals for Parameters of Finite Populations Confidence Intervals for Population Mean and Total for a Finite Population Confidence Intervals for the Proportion/ Total Number of a Category in a Finite Population lecture 16, Confidence Intervals II Review Review A ( 1- α ) 100 % confidence interval for μ : • when σ is known: ¯ x ± z α/ 2 · σ √ n , where ¯ x is a sample mean, z α/ 2 σ √ n is called the margin of error at ( 1- α ) 100 % confidence • when σ is unknown: ¯ x ± t α/ 2 · s √ n , t α/ 2 s √ n is the margin of error at ( 1- α ) 100 % confidence General formula: Point Estimate ± (Critical Value)(Standard Error) Interpretation: We are ( 1- α ) 100 % confident that the interval covers μ lecture 16, Confidence Intervals II 3 / 24 Review Sample Size Determina- tion Confidence Intervals for a Population Proportion Determining the Sample Size Confidence Intervals for Parameters of Finite Populations Confidence Intervals for Population Mean and Total for a Finite Population Confidence Intervals for the Proportion/ Total Number of a Category in a Finite Population lecture 16, Confidence Intervals II Sample Size Determination Sample Size Determination • Margin of error is affected by 1. confidence level, 2. variation in the data, and 3. number of observations • Sometimes we want a small margin of error (high precision) while maintaining a high confidence level. How to achieve such a goal? • Increase the sample size! The margin of error ( z α/ 2 σ √ n when σ known or t α/ 2 s √ n when σ unknown) decreases as the sample size n increases. • Suppose we want the margin of error at ( 1- α ) 100 % confidence to be at most a number ε . How big must the sample size n be? lecture 16, Confidence Intervals II 4 / 24 Review Sample Size Determina- tion Confidence Intervals for a Population Proportion Determining the Sample Size Confidence Intervals for Parameters of Finite Populations Confidence Intervals for Population Mean and Total for a Finite Population Confidence Intervals for the Proportion/ Total...
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This note was uploaded on 12/28/2010 for the course BUSINESS A ISOM 111 taught by Professor Yingyingli during the Fall '10 term at HKUST.

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Lecture16 - lecture 16, Confidence Intervals II 1 / 24...

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