Chap_9 - Chapter 9 Estimation and Confidence Intervals...

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Chapter 9 Estimation and Confidence Intervals
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Chapter Goals After completing this chapter, you should be able to: Distinguish between a point estimate and a confidence interval estimate Construct and interpret a confidence interval estimate for a single population mean using both the z and t distributions Determine the required sample size to estimate a single population mean within a specified margin of error Form and interpret a confidence interval estimate for a single population proportion
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Confidence Intervals Content of this chapter Confidence Intervals for the Population Mean, when Population Standard Deviation is Known when Population Standard Deviation is Unknown Determining the Required Sample Size Confidence Intervals for the Population Proportion, p
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Point and Interval Estimates A point estimate is a single number, a confidence interval provides additional information about variability Point Estimate Lower Confidence Limit Upper Confidence Limit Width of confidence interval
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Point Estimates We can estimate a Population Parameter … with a Sample Statistic (a Point Estimate) Mean Proportion p x μ p
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Confidence Intervals How much uncertainty is associated with a point estimate of a population parameter? An interval estimate provides more information about a population characteristic than does a point estimate Such interval estimates are called confidence intervals
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Confidence Interval Estimate An interval gives a range of values: Takes into consideration variation in sample statistics from sample to sample Based on observation from 1 sample Gives information about closeness to unknown population parameters Stated in terms of level of confidence Never 100% sure
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Estimation Process (mean, μ, is unknown) Population Random Sample Mean x = 50 Sample I am 95% confident that μ is between 40 & 60.
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General Formula The general formula for all confidence intervals is: Point Estimate (Critical Value) (Standard Error)
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Confidence Level Confidence Level Confidence in which the interval will contain the unknown population parameter A percentage (less than 100%)
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Confidence Level, (1- ) Suppose confidence level = 95% Also written (1 - ) = .95 A relative frequency interpretation: In the long run, 95% of all the confidence intervals that can be constructed will contain the unknown true parameter A specific interval either will contain or will not contain the true parameter No probability involved in a specific interval (continued)
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Confidence Intervals Population Mean σ Unknown Confidence Intervals Population Proportion σ Known
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This note was uploaded on 03/22/2012 for the course FINA 210 taught by Professor Dakroub during the Spring '12 term at American University in Cairo.

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Chap_9 - Chapter 9 Estimation and Confidence Intervals...

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