# 7.1 - STAT3000 Chapter 7: Inference for Distributions...

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STAT3000 Chapter 7: Inference for Distributions Substitute standard deviation to “s” Here we no longer assume that population standard deviations are known. The t procedures for inference about means are among the most common statistical methods. STAT3000 Section 7.1: Inference for the Mean of a Population Estimating μ When σ is Unknown We will use t* rather than z*. ________________________________ ____ 149

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The main difference between the sampling distributions of t and z is that the t statistic is more variable than z, which follows from the fact that t contains two random quantities ( X and s) but z contains only one ( X ). The actual amount of variability in the sampling distribution of t depends on n. The smaller n is, the more variable the sampling distribution of t is. As the sample size grows large, s becomes closer to σ and thus t becomes closer to z in distribution. 150
Just as normal distributions are characterized by μ and σ , t distributions are characterized by degrees of freedom. df = n-1, where n-1 is the divisor that appears in the formula for s 2 . CI for

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## This note was uploaded on 06/05/2011 for the course STAT 3000 taught by Professor Staff during the Spring '08 term at UGA.

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7.1 - STAT3000 Chapter 7: Inference for Distributions...

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