Statistics 6.4 - 6-4 Estimating a Population Mean: Not...

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6-4 Estimating a Population Mean: σ Not Known In this case, we also wish to estimate the population mean, μ . Assumptions 1. The sample is a simple random sample. 2. 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, . 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. Because of unreliability of results of smaller samples, instead of the standard normal distribution, we use a distribution with larger values, called the Student t Distribution (or t Distribution). Student t Distribution If the distribution of a population is essentially normal (approximately bell shaped), then the distribution of / x t sn = is essentially a Student t Distribution. Definition The number of degrees of freedom for a collection of sample data is the number of
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This note was uploaded on 04/08/2008 for the course MAT 143 taught by Professor Stone during the Spring '07 term at North Shore Community College.

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Statistics 6.4 - 6-4 Estimating a Population Mean: Not...

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