UT Knoxville STAT 201 - Chapter 23 (44 pages)

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Chapter 23



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Chapter 23

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Pages:
44
School:
University of Tennessee
Course:
Stat 201 - Introduction to Statistics
Introduction to Statistics Documents

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Chapter 23 Chapter23 Presentation 1213 Inferences About Means Copyright 2009 Pearson Education Inc 1 Sampling Distribution of y Review If we want to estimate a population mean or test a hypothesis about a population mean we start with our understanding of the sampling distribution of y The Central Limit Theorem told us that if the sample size is large enough the sampling distribution model for y is Normal with mean and standard deviation SD y Chapter23 Presentation 1213 Copyright 2009 Pearson Education Inc n 2 A Small Problem So would a 95 confidence interval for the population mean look like this y 1 96 n Unfortunately we don t know How did we deal with a similar issue with proportions Chapter23 Presentation 1213 Copyright 2009 Pearson Education Inc 3 A Small Problem cont So will this produce a 95 confidence interval for the population mean s y 1 96 n Unfortunately no When we substitute s for the sampling distribution of y is no longer normally distributed so we can t use 1 96 Chapter23 Presentation 1213 Copyright 2009 Pearson Education Inc 4 A Small Problem cont In the late 1800 s and early 1900 s the race was on to understand what the sampling distribution of y was when the population standard deviation was not known Until this problem was solved one had to simply assume they knew the population standard deviation an unrealistic assumption in many cases Chapter23 Presentation 1213 Copyright 2009 Pearson Education Inc 5 The Solution William Gosset William S Gosset an employee of the Guinness Brewery in Dublin Ireland worked long and hard to find out what the sampling distribution model was The sampling model that Gosset found has become known as Student s t The Student s t models form a whole family of related distributions that depend on a parameter known as degrees of freedom We often denote degrees of freedom as df and the model as tdf Chapter23 Presentation 1213 Copyright 2009 Pearson Education Inc 6 Student s t vs the Normal Distribution Student s t models



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