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lecture21_2slides - Statistics 528 Lecture 21 Statistical...

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Statistics 528 - Lecture 21 1 Statistics 528 - Lecture 21 Prof. Kate Calder 1 Statistical Inference Idea: Estimate parameters of the population distribution using data. How: Use the sampling distribution of sample statistics and methods based on “what would happen if we used this inference procedure many times.” 1. Confidence Intervals 2. Hypothesis Tests Note: Be sure that you understand the meaning of these procedure in addition to being able to use them. Statistics 528 - Lecture 21 Prof. Kate Calder 2 Confidence Intervals Idea: We use a sample statistic to estimate a population parameter (e.g. use to estimate ° ). A confidence interval tells us how confident we are in our estimate. A confidence interval will have the form: estimate +/- margin of error **The smaller the margin or error, the higher our confidence in our estimate. x
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Statistics 528 - Lecture 21 2 Statistics 528 - Lecture 21 Prof. Kate Calder 3 Example: Assume that the sampling distribution of is N( ° , 4.5). lies within +/- 9 of ° in 95% of all samples, so ° also lines within +/- 9 of in those samples. x x x Statistics 528 - Lecture 21 Prof. Kate Calder 4 => In 95% of samples, - 9 < ° < + 9. We say that ( - 9, + 9) is a 95% confidence interval for ° . Requirements of a Confidence Interval for an Unknown Parameter: 1. an interval of the form (a, b), where a and b are numbers computed from the data 2. a confidence level that give the probability that the interval covers the parameter. Usually, confidence levels are 90% or 95%. x x x x
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Statistics 528 - Lecture 21 3 Statistics 528 - Lecture 21 Prof. Kate Calder 5 Definition of a Confidence Interval: A level C confidence interval for a parameter is an interval computed from sample data by a method that has probability C of producing an interval containing the true value of the parameter.
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