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Chapter 8 Notes - 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) Sampling Error (II) Probability Statement about the Sampling Error (III) Constructing an Interval Estimate: Large-Sample Case with σ Known (IV) Calculating an Interval Estimate: Large-Sample Case with σ Unknown (I). Sampling Error: Sampling error: The absolute value of the difference between an unbiased point estimate and the population parameter. For the case of a sample mean estimating a population mean, the sampling error = Margin of Error:
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The upper limit on the sampling error. Motivation for Interval Estimation: Population mean ( µ ) is usually unknown. In practice, the value of the sampling error cannot be determined exactly because the population mean µ is unknown. Therefore, the sampling distribution of can be used to make probability statements about 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 =>
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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?
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Example: A simple random sample of 50 items resulted in a sample mean of 32 and a sample standard deviation of 6.
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