2.1 Interval Estimation - sigma known

2.1 Interval Estimation - sigma known - Dr. Harvey A....

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© 2008 by Harvey A. Singer 1 OM 210:  Statistical Analysis for  Management 2 Confidence Interval Estimation of Means 2.1 σ Known Dr. Harvey A. Singer School of Management George Mason University
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© 2008 by Harvey A. Singer 2 Learning Objectives 1. State what is to be estimated. 2. Explain confidence interval estimates. 1. Compute confidence interval estimates for the population mean. if σ is known. if σ is not known. and must be estimated from s . 4. Compute sample size.
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© 2008 by Harvey A. Singer 3 Statistical Methods Descriptive Statistics Inferential Statistics Estimation Hypothesis Testing Probability Sampling Distributions Statistical Methods
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© 2008 by Harvey A. Singer 4 Estimating Population Parameters “Point” estimation of population parameters from the corresponding sample statistics. The value of the sample statistic is the first and best guess for the value of the corresponding population parameter. A point estimate of a population parameter is the value of the corresponding sample statistic. The calculated mean of a sample, x , is the first and best guess for μ . So x is the point estimate of μ .
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© 2008 by Harvey A. Singer 5 Estimating Population Parameters Quantity Population Parameter Sample Statistic Mean μ x Median population median sample median Variance σ 2 s 2 Standard deviation σ s Proportion π p Difference between means μ 1 μ 2 x 1 x 2
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© 2008 by Harvey A. Singer 6 Why Interval Estimation? As a best guess, the sample statistic is taken as an estimate of the corresponding population parameter. The statistic is the best single-number representation of the corresponding population parameter. The statistic is referred to as a point estimate of the parameter. In particular, x estimates μ . However, because of the accidents of sampling, the estimate will usually be off from the true but unknown parameter value. It is an accident who or what got sampled and who or what didn’t. The sample may or may not be representative of the population. The calculated x may or may not be representative of the sample. Therefore, x will usually not be the value of μ but will be “off” by some amount more or less of μ . The amount by which x is off form μ , x μ , is called the “sampling error.”
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© 2008 by Harvey A. Singer 7 Why Interval Estimation? Therefore, bracket a range around the statistic (as the point estimate) that is likely to contain the true value of the parameter. Bracket x by an interval wide enough so as to be likely to capture μ . The interval is based on the “margin of error.” The width of the interval is based on the likelihood or probability of the capture. The more likely the capture, the wider the interval.
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This note was uploaded on 01/26/2011 for the course OM 210 taught by Professor Singer during the Fall '08 term at George Mason.

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2.1 Interval Estimation - sigma known - Dr. Harvey A....

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