Stat 321 – Day 24 Point Estimation (cont.)

Lab 6 comments Parameter  Population Sample Probability Statistics A statistic is an unbiased estimator for a parameter if its sampling distribution centers at the parameter value Mean of empirical sampling distribution 1. Humans not very good at selecting “random” samples Gettysburg, Literary Digest 2. Sample size affects variability, not bias Larger probability of being close to  3. Population size doesn’t really matter! “bias” = systematic tendency to error in same direction Notes: - Sampling distribution vs. sample - Shape vs. spread With 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%)

Lab 6 comments Parameter  Population Sample Probability Statistics A statistic is an unbiased estimator for a parameter if its sampling distribution centers at the parameter value Mean of empirical sampling distribution   ? Mean = Unbiased!

Example 3: Estimating  2 S 2 is an unbiased estimator for  2 (p. 233)  Although S is a biased estimator for 

HW 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 value E(Y) = P(430.5 <  < 446.1) =.95?

Last 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 precision

Lab 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(X i )  Turn in with names…