Lecture15 - lecture 15, Confidence Intervals I 1 / 26...

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Unformatted text preview: lecture 15, Confidence Intervals I 1 / 26 Confidence Intervals z-Based Confidence Intervals for a Population Mean: σ Known t-Based Confidence Intervals for a Population Mean: σ unknown t Distribution t-Based Confidence Intervals A Brief Summary lecture 15, Confidence Intervals I Outline 1 Confidence Intervals 2 z-Based Confidence Intervals for a Population Mean: σ Known 3 t-Based Confidence Intervals for a Population Mean: σ unknown t Distribution t-Based Confidence Intervals 4 A Brief Summary lecture 15, Confidence Intervals I 2 / 26 Confidence Intervals z-Based Confidence Intervals for a Population Mean: σ Known t-Based Confidence Intervals for a Population Mean: σ unknown t Distribution t-Based Confidence Intervals A Brief Summary lecture 15, Confidence Intervals I Sampling Distribution of Sample Mean ( review) • When the population size N is infinity or large, if the population is normally distributed, or if the population is not normally distributed but the sample size n is large, then the sampling distribution of ¯ X is (exactly or approximately) normal with mean μ and standard deviation σ ¯ X ≈ σ √ n . • The standard deviation of the sampling distribution of sample means is also called the standard error (for short, SE) of the sample mean lecture 15, Confidence Intervals I 3 / 26 Confidence Intervals z-Based Confidence Intervals for a Population Mean: σ Known t-Based Confidence Intervals for a Population Mean: σ unknown t Distribution t-Based Confidence Intervals A Brief Summary lecture 15, Confidence Intervals I Empirical rule for the sample mean I Empirical rule for the sample mean: (a) about 68% of all possible sample means are within one standard deviation σ ¯ X of μ (b) about 95% of all possible sample means are within two σ ¯ X of μ (c) about 99.7% of all possible sample means are within three σ ¯ X of μ • Typically, • firstly, μ is unknown, and • secondly, there’s only one sample • How to make use of this rule? Can we say something about μ based on the sample? lecture 15, Confidence Intervals I 4 / 26 Confidence Intervals z-Based Confidence Intervals for a Population Mean: σ Known t-Based Confidence Intervals for a Population Mean: σ unknown t Distribution t-Based Confidence Intervals A Brief Summary lecture 15, Confidence Intervals I Confidence Intervals Interval Estimates • Interested in population characteristics (parameters) • Too expensive or impossible to obtain complete data of the population • A sample is taken; sample provides useful information about the population: • e.g., sample mean is a point estimate of population mean • but the information is imperfect • e.g., sample mean is unlikely to be exactly equal to the population mean • Point estimate doesn’t provide information about the size of the estimation error • In this chapter, we will study confidence intervals for a population mean • interval estimates lecture 15, Confidence Intervals I 5 / 26 Confidence...
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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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Lecture15 - lecture 15, Confidence Intervals I 1 / 26...

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