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Unformatted text preview: Part IV Inference: From Samples to Population (Our Ultimate Destination) Fall 2008 1 Chapter 8 Sampling Distributions Fall 2008 2 Overview ● A new sample mean can be calculated each time a new sample is taken from the same population ● In this way, the sample mean can be analyzed as a random variable ● Being able to calculate (approximately) the distribution of the sample mean is a critical tool for inference Fall 2008 3 Chapter 8 Section 1 Distributions of the Sample Mean Fall 2008 4 Chapter 8 – Section 1 ● Learning objectives Understand the concept of a sampling distribution Describe the distribution of the sample mean for samples obtained from normal populations Describe the distribution of the sample mean for samples obtained from a population that is not normal Fall 2008 5 Distribution of the Sample Mean ● Often the population is too large to perform a census … so we take a sample ● Often the population is too large to perform a census … so we take a sample ● How do the results of the sample apply to the population? What’s the relationship between the sample mean and the population mean What’s the relationship between the sample standard deviation and the population standard deviation? ● Often the population is too large to perform a census … so we take a sample ● How do the results of the sample apply to the population? What’s the relationship between the sample mean and the population mean? What’s the relationship between the sample standard deviation and the population standard deviation? ● This is statistical inference Fall 2008 6 Distribution of the Sample Mean ● We want to use the sample mean x to estimate the population mean μ ● If we want to estimate the heights of eight year old girls, we can proceed as follows Randomly select 100 eightyearold girls Compute the sample mean of the 100 heights Use that as our estimate ● This is using the sample mean to estimate the population mean Fall 2008 7 Distribution of the Sample Mean ● However, if we take a series of different random samples Sample 1 – we compute sample mean x 1 Sample 2 – we compute sample mean x 2 Sample 3 – we compute sample mean x 3 Etc. ● However, if we take a series of different random samples Sample 1 – we compute sample mean x 1 Sample 2 – we compute sample mean x 2 Sample 3 – we compute sample mean x 3 Etc. ● Each time we sample, we may get a different result ● The sample mean x is a random variable! Fall 2008 8 Distribution of the Sample Mean ● Because the sample mean is a random variable The sample mean has a mean The sample mean has a standard deviation The sample mean has a probability distribution ● This is called the sampling distribution of the sample mean Helpful Hint: Look over Example 1 on p.376 of your textbook....
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This note was uploaded on 02/14/2011 for the course STAT 250 taught by Professor Sims during the Spring '08 term at George Mason.
 Spring '08
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