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Unformatted text preview: Ch. 19 - Statistical Inference Defn: Estimation is the assignment of value(s) to a population parameter based on a value of the corresponding sample statistic. An estimator is a rule used to calculate an estimate. An estimate is a specific value of an estimator. Note: in this chapter, always assuming an SRS. - Notation: - Let be a generic parameter. - Let be an estimator a statistic calculated from a random sample - Consequently, is an r.v. with mean E ( ) = and std. dev. Defn: A point estimate is a single number that is our best guess for the parameter. like a statistic , but more precise towards parameter estimation. An interval estimate is an interval of numbers within which the parameter value is believed to fall. Generic large sample confidence intervals : Defn: A confidence interval (CI) for a parameter is an interval estimate of plausible values for . With a chosen degree of confidence, the CIs construction is such that the value of is captured between the statistics L and U , the lower and upper endpoints of the interval, respectively. The confidence level of a CI estimate is the success rate of the method used to construct the interval (as opposed to confidence in any particular interval). The generic notation is 100(1 )%. Typical values are 90%, 95%, and 99%. e.g. Using 95% and the upcoming method to construct a CI, the method is successful 95% of the time. That is, if this method was used to generate an interval estimate over and over again with different samples, in the long run, 95% of the resulting...
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This note was uploaded on 07/31/2011 for the course STAT 141 taught by Professor Paulcartledge during the Winter '10 term at University of Alberta.
- Winter '10