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# Lecture16 - lecture 16 Condence Intervals II lecture 16...

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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

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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?

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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 Number of a Category in a Finite Population lecture 16, Confidence Intervals II Sample Size Determination
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Lecture16 - lecture 16 Condence Intervals II lecture 16...

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