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Stat 321 – Day 24Lab 6 commentsPopulation size correction factorSlide 4Example 3: Estimating s2HW 7 CommentsLast Time – Point EstimatorsLab 8 PreviewStat 321 – Day 24Point Estimation (cont.)Lab 6 commentsParameterPopulationSampleProbabilityStatisticsxx xxxx xx x x x xxx x xx xx x x xxxx xx xxxx x xx xxxxx xxA statistic is an unbiased estimator for a parameter if its sampling distribution centers at the parameter value1. 2. Mean of empirical sampling distribution)(XE1. Humans not very good at selecting “random” samplesGettysburg, Literary Digest2. Sample size affects variability, not biasLarger probability of being close to 3. Population size doesn’t really matter!“bias” = systematic tendency to error in same directionNotes:- Sampling distribution vs. sample- Shape vs. spreadWith 664 randomly selected people, would have been within 5%Population size correction factorIf you do have a finite population, can apply a correction factor to the standard deviationBinomialHypergeometricN=303,572,923; n = 650 (+ 5%)N=303,572,923; n = 1500 (+ 2.5%))1()(,)( pnpXVnpXE NMnMnNnNXVNMnXE 11)(,)(Lab 6 commentsParameterPopulationSampleProbabilityStatisticsxx xxxx xx x x x xxx x xx xx x x xxxx xx xxxx x xx xxxxx xxA statistic is an unbiased estimator for a parameter if its sampling distribution centers at the parameter value1. 2. Mean of empirical sampling distribution)(XE ˆˆ?1)(θˆ211nXXniiMean = 71412Unbiased!Example 3: Estimating 2S2 is an unbiased estimator for 2 (p. 233)Although S is a biased estimator for     1)()(1)()(11)(1)()(1)()θˆE(212212212211nXEXVnXEXVnXEnXEnXnEXEnXXEiiniiiinininiiiiHW 7 CommentsMake sure you show lots details in deriving expected values and variancesInterpreting interval (# 3) vs. level (lab 7)Make sure have something random before making probability statementsSample size calculationsAlways round up to integer valueE(Y) = P(430.5 << 446.1) = .95? 1)//(2/2/nzXnzXPLast Time – Point EstimatorsFor parameters other than a mean or a proportion, need to think about best choice of estimatorMathematical formula for what you will do with your sample data to calculate an estimate of the parameter for a particular sampleGood properties to have:Unbiased: Sampling distribution of estimator centers at parameter, E(estimator) = Small variance/high precisionLab 8 PreviewDuring World War II, wanted to estimate the number of German tanksTurns out, the Mark V tanks were produced with sequential serial numbers, 1,…, NCan we use the numbers from n captured tanks to estimate N?Example: 170, 101, 5, 202, 43With one partner, suggest 3 estimators for NE.g., mean(Xi)Turn in with


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Cal Poly STAT 321 - Point Estimation (cont.)

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