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Unformatted text preview: Confidence Intervals for a Population Mean μ ; t distributions • t distributions • t confidence intervals for a population mean μ • Sample size required to estimate μ The Importance of the Central Limit Theorem ■ When we select simple random samples of size n, the sample means we find will vary from sample to sample. We can model the distribution of these sample means with a probability model that is , N n μ σ Since the sampling model for x is the normal model, when we standardize x we get the standard normal z n x z σ μ = n x SD σ = ) ( that Note If μ is unknown, we probably don’t know σ either. The sample standard deviation s provides an estimate of the population standard deviation σ For a sample of size n, the sample standard deviation s is: n − 1 is the “degrees of freedom.” The value s/√n is called the standard error of x , denoted SE(x). n x SD σ = ) ( ∑ = 2 ) ( 1 1 x x n s i n s x SE = ) ( Standardize using s for σ ■ Substitute s (sample standard deviation) for σ n x z μ = σ σ σσσσσ ssss σ s ss s n x z σ μ = Note quite correct Not knowing σ means using z is no longer correct tdistributions...
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This note was uploaded on 04/21/2009 for the course BUS 350 taught by Professor Reiland during the Spring '08 term at N.C. State.
 Spring '08
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