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CI_mu_sp08

# CI_mu_sp08 - Confidence Intervals for a Population Mean t...

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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

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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

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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 σ σσ σ σ ssss σ s ss s n x z σ μ - = Note quite correct Not knowing σ means using z is no longer correct

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