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Is the population normally, or approximately normally, distributed?Cannot use the normal distribution or the t-distribution. YesIs g305known?NoUse the normal distribution withIf g305is unknown, use sinstead./2g305nxzα±YesNoUse the normal distribution with/2g305nxzα±YesUse the t-distribution with and n– 1 degrees of freedom./2,n-1nsxtα±g21g19g27Things you should knowg137How to construct a confidence interval for the meannstxnFor HW and Examsg21g19g28g21g20g19
Stat 104: Quantitative Methods for EconomistsClass 21: More Confidence Interval Topicsg21g20g20g38g82g81g73g76g71g72g81g70g72g44g81g87g72g85g89g68g79g73g82g85g68g51g85g82g83g82g85g87g76g82g81g132The Gallup Poll periodically asks a random sample of U.S. adults whether they think economic conditions are getting better, getting worse, or staying about the same. g132When they polled 2976 respondents March 2010, only 1012 thought economic conditions in the United States getting better—a sample proportion 1012/2976=34%. How wrong is this guess?in were of (proportion,π, is unknown)g51g82g83g88g79g68g87g76g82g81g53g68g81g71g82g80 g54g68g80g83g79g72proportion SampleI am 95% confident that πis between .19 & .49ˆ.34p=g21g20g22g51g82g76g81g87g40g86g87g76g80g68g87g72g73g82g85g51g82g83g88g79g68g87g76g82g81πPoint Estimate for g132The proportion of successes in a sample. g132Denoted by g137g137read as “phat”number of successes in sampleˆsample sizexpn==Estimate Population Parameter…with Sample Statistic Proportion: πˆg21g20g23F o rZNPZPZPZg53g72g89g76g72g90g178g86g87g68g81g71g68g85g71g76g93g68g87g76g82g81g85g88g79g7295% of the area is between –1.96 and 1.96g21g20g24We construct the interval estimate using the CLT.πp~(,)~(0,1)IfXN Mean VariancethenXMeanZNVariance-=-≤≤=-≤≤=-≤≤=~( 0 , 1 ) ,(11 )0 . 6 8(1 . 9 61 . 9 6 )0 . 9 5(33 )0 . 9 9 7-3-2-10123Recall that the CLT says that (for large n)Then by the Standardization Rule:ˆ~(0,1)(1) /pNnπππ--(1)ˆ ~,pNnπππ-g167g183g168g184g169g185g21g20g25