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Statistics 6.3

Statistics 6.3 - 6-3 Estimating a Population Mean Known In...

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6-3 Estimating a Population Mean: σ Known In this case, we wish to estimate the population mean, μ . Assumptions 1. The sample is a simple random sample. 2. The value of the population standard deviation, σ , is known. 3. Either or both of these conditions are satisfied: The population is normally distributed or n > 30. The sample mean, x , is the best estimate for the population mean, μ . Question: How good is the best estimate? The confidence interval gives us a range of values instead of a single value. The difference between the sample mean and the population mean is called the error. Margin of Error for the Mean: σ Known / 2 E z n α σ = Confidence Interval Estimate of the Population Mean (with σ Known) / 2 , where x E x E E z n α μ σ < < + = Example For the sample of body temperatures from Data Set 4 in the textbook, we have n = 106 and x = F. Assume that the sample is a simple random sample and that

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