ch_8_Notes-1

# ch_8_Notes-1 - Chapter 8 Interval Estimation Outline •...

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Unformatted text preview: 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. 1 For the case of a sample mean estimating a population mean, the sampling error = μ- x Margin of Error: 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 x 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., ± x Margin of Error. From last chapter, we know how to compute => 2 ) ( k X k P ≤- ≤- μ Intervals and Level of Confidence: Interval extend from x z x σ α 2 /- to x z x σ α 2 / + We are 100(1- α )% confident that the interval constructed from x z x σ α 2 /- to x z x σ α 2 / + 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 x z x σ α 2 / ± is called a 100(1- α )% confidence interval (CI). What are the factors affecting intervals? 3 μ 2 / α 2 / α Sampling Distribution 1- α of all values x x 100(1 - α ) % of intervals contain μ . 100α % do not. 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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ch_8_Notes-1 - Chapter 8 Interval Estimation Outline •...

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