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Unformatted text preview: Stat 104: Quantitative Methods for Economists Class 21: Confidence Intervals Two Samples 1 Midterm Exam: October 18 s 7pm at nightlocations to be announced s Open book/Open notes s Topics Include b Mean and Variance of Data, Correlation, Covariance, Regression b Basic probability, 2x2 tables, conditional, indep. b Random Variables, means, variance, sums b Binomial and Normal Distributions b CI for means and proportions (all 95%) 2 Confidence Interval for the Confidence Coefficient s Recall that if we have two random variables X and Y, a measure of association is given by the correlation coefficient defined by ρ = Corr X Y ( , ) s Using data, we may obtain an estimate of ρ which we call r. A 95% confidence interval is given by 3 r r n ± 196 1 2 2 . Example: Haircut and TV Watching s What is the correlation between how much one spends on a haircut and the hours of tv they watch in a week ? s From class data, Correlation of haircut and tv = 0.182 4 2 2 1 1 ( .182) 1.96 .182 1.96 2 80 2 ( .4,.036) r r n  ± =  ± =  Interpretation of the Confidence Interval ? Summary so Far μ α X X z s n ± /2 Truth Truth Guess Guess Confidence Interval Confidence Interval 5 ρ α α p p p z p p n r r z r n ± ± / / ɵ ɵ ɵ ( ɵ ) 2 2 2 1 1 2 The Confidence Interval Recipe s By now, you should realize that all confidence intervals have the same form: point timate confidence efficien standard deviation f point e imate F G I J ± F G I J * F G I J s Remember this formula. It says how to create a confidence interval for everything we will be doing. All you need is a point estimate and a measure of how variable the estimate is (and this info usually comes from the CLT). 6 estimate coefficient of point estimate H K H K H K Comparison of Two Proportions s Very often we are interested in comparing two proportions: b The difference in unemployment rates between Republicans and Democrats b The difference in percentage if households that plan to buy a car during the next year in northeastern states versus southeastern states. 7 Two Sample Test s We have two independent samples from populations of interest....
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.
 Fall '11
 MichaelParzen
 Correlation, Covariance, Variance

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