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notes515fall10chap7 - STAT 515 - Chapter 7: Confidence...

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STAT 515 -- Chapter 7: Confidence Intervals • With a point estimate, we used a single number to estimate a parameter. • We can also use a set of numbers to serve as “reasonable” estimates for the parameter. Example: Assume we have a sample of size 100 from a population with σ = 0.1. From CLT: Empirical Rule: If we take many samples, calculating X _ each time, then about 95% of the values of X _ will be between: Therefore: This interval is called an approximate 95% “confidence interval” for μ .
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Confidence Interval : An interval (along with a level of confidence) used to estimate a parameter. • Values in the interval are considered “reasonable” values for the parameter. Confidence level : The percentage of all CIs (if we took many samples, each time computing the CI) that contain the true parameter. Note : The endpoints of the CI are statistics , calculated from sample data. (The endpoints are random, not the parameter!) In general, if X _ is normally distributed, then in 100(1 – α )% of samples, the interval will contain μ . Note: z α /2 = the z-value with α /2 area to the right: 100(1 – α )% CI for μ : X _ ± z ( α /2 n / σ )
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Problem: We typically do not know the parameter σ . We must use its estimate s instead. Formula
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This note was uploaded on 12/14/2011 for the course STAT 515 taught by Professor Zhao during the Spring '10 term at South Carolina.

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notes515fall10chap7 - STAT 515 - Chapter 7: Confidence...

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