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Topic 6 Overview - wiki

# Topic 6 Overview - wiki - Confidence Intervals(Chapter 7...

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Confidence Intervals (Chapter 7) Confidence interval might not even contain μ 3 Cases for Confidence Intervals with mean (μ) of population: 1. When population distribution is Normal and σ is known 2. When we have a large sample (pop. distribution may not be normal and σ may not be known) 3. When we have a small sample from a normal distribution and σ is unknown Confidence Interval: A range of values ( l , u ) such that we are x % sure that the mean μ of a population lies within that range. Note: confidence intervals can be random, but μ is fixed: it never changes. Therefore, our confidence interval might not even contain μ. Case 1: Normal Population Distribution Given a sample X 1 to X n of size n from a normal distribution with (unknown) mean μ and (known) standard deviation σ, a x % Confidence Interval for μ is: Where n is the sample size and z α / 2 is a value such that the area underneath the Z-curve from − z α / 2 to z α / 2 is x : In α notation : α = 1 − x . For example, 95% confidence interval will have z α / 2

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