ch8_notes_V2011

# ch8_notes_V2011 - Chapter 8 Interval Estimation Outline:...

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Chapter 8 Interval Estimation Outline: Interval Estimation of a Population Mean –Large Sample Case –Small Sample Case Determining the Sample Size Interval Estimation of Population Proportion Interval Estimation of a Population Mean: Large-Sample Case (I) Probability Statement about the Sampling Error (II) Constructing an Interval Estimate: Large-Sample Case with σ Known (IV) Calculating an Interval Estimate: Large-Sample Case with Unknown Margin of Error and the Interval Estimate: A point estimator cannot be expected to provide the exact value of the population parameter. An interval estimate can be computed by adding and subtracting a margin of error to the point estimate. 1

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2 I Point Estimate + Margin of Error I Motivation for Interval Estimation: The purpose of an interval estimate is to provide information about how close the point estimate is to the value of the parameter (which is unknown). Slide The upper limit on the sampling error. Interval Estimation: An interval estimate of a population parameter is constructed by subtracting and adding a value, called the margin of error , to a point estimate, i.e., Margin of Error. From last chapter, we know how to compute => 2
Intervals and Level of Confidence: Interval extend from to We are 100(1- α )% confident that the interval constructed from to will include the population mean µ . 1. This interval is established at the 100(1- α )% confidence level . 2. The value (1- α ) is referred to as the confidence coefficient . 3. The interval estimate is called a 100(1- α )% confidence interval (CI). What are the factors affecting intervals? 3

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4 Example: A simple random sample of 50 items resulted in a sample mean of 32 and a sample standard deviation of 6. a. Provide a 90% confidence interval for the population mean. b. Provide a 95% confidence interval for the population mean. (II). Precision Statement--Probability Statement about Sampling Error : 4
α ) probability that the value of a sample mean will provide a sampling error of or less. e.g. Suppose a sample size n =100 and a population standard deviation σ=20, there is a 0.95 probability that the value of a sample mean will provide a sampling error of or less. 5

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## This note was uploaded on 03/03/2012 for the course MGMT 305 taught by Professor Priya during the Spring '08 term at Purdue.

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ch8_notes_V2011 - Chapter 8 Interval Estimation Outline:...

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