Lect17_L6_L7_handout

Lect17_L6_L7_handout - lecture 17 Confidence Intervals I...

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Unformatted text preview: lecture 17, Confidence Intervals I Confidence Intervals z-Based Confidence Intervals for a Population Mean: σ Known Example lecture 17, Confidence Intervals I Outline 1 Confidence Intervals 2 z-Based Confidence Intervals for a Population Mean: σ Known Example lecture 17, Confidence Intervals I Confidence Intervals z-Based Confidence Intervals for a Population Mean: σ Known Example lecture 17, Confidence Intervals I Confidence Intervals Background • interested in population characteristics (parameters) • too expensive or impossible to obtain complete data of the population • samples are taken; sample provides useful information about the population • but the information is imperfect • e.g. (previous chapter), using sample mean as a point estimate of population mean • point estimate doesn’t provide information about its distance from the population parameter • e.g. (this chapter), confidence intervals for a population mean • interval estimates lecture 17, Confidence Intervals I Confidence Intervals z-Based Confidence Intervals for a Population Mean: σ Known Example lecture 17, Confidence Intervals I Confidence Intervals Recall, Sampling Distribution of Sample Mean • Recall that if a population is normally distributed with mean μ and standard deviation σ , then the sampling distribution of ¯ X is normal with mean μ ¯ X = μ and standard deviation σ ¯ X = σ √ n . • the standard deviation of the sampling distribution of sample means is also called the standard error of the sample mean (or “SE") • Use a normal curve as a model of the sampling distribution of the sample mean • exactly, if the population is normal • approximately, by the Central Limit Theorem for large samples, if the population is not normal lecture 17, Confidence Intervals I Confidence Intervals z-Based Confidence Intervals for a Population Mean: σ Known Example lecture 17, Confidence Intervals I Confidence Intervals Confidence Intervals, Example • Suppose David is in the business of estimating the mean of populations that are • normally distributed with standard deviation σ • Each time he makes a survey, he: • takes a random sample of size n • computes the sample mean • claims that the population mean lies in the range of sample mean ± σ √ n (Or, equivalently, sample mean ± 1 SE ) • How much confidence can you place in his claims? lecture 17,...
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This note was uploaded on 12/30/2009 for the course ISOM ISOM111 taught by Professor Anthonychan during the Fall '09 term at HKUST.

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Lect17_L6_L7_handout - lecture 17 Confidence Intervals I...

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