# lecture 17 Confidence-Intervals-for-Means-1.pdf - Lecture...

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Lecture 17: Estimating population means, Sect. 9.2Review of Section 9.1: Confidence interval for proportionsAssumptions:The confidence interval applies for a large random sample. Typically,largemeansnˆp(1-ˆp)10 and less than 5% of whole population (n0.05N).ˆp-E < p <ˆp+Ewith margin of errorE=z/2sˆp(1-ˆp)nNote:Key components of the confidence interval:Thepoint estimateˆpof the unknown parameterp.Thecritical valuez/2that gives the number of standard deviations to include 1-of the possibleestimates.Thestandard errorse=qˆp(1-ˆp)nthat is the estimate of the standard deviation of the samplingdistribution. It represents the average error.Themargin of errorE= critical value·standard errorExample:In a random survey of 1002 people, 701 said that they voted in a recent presidential election.Voting records show that 61% of eligible voters actually did vote.