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1STAT 2000Chapter 7CfidI tlConfidence IntervalsAgresti-FranklinIdentify ObjectiveQuestion(s) about a populationDesign StudyandCollect DataSelect a sample from a populationMake Inferences The Process of a Statistical StudyDescribe DataOrganize and present sampledataabout a populationMake predictions and drawconclusionsPrinciples of ProbabilityAs we begin to talk about Inference, let’s look back at what we have done before, and why.•Gathering Data – Statistical inference methods assume that data was collected with some type of randomization.•Sampling Distributions – Probability calculationsSampling Distributions Probability calculations used in inference refer to sampling distributions.Two types of Inference•Estimation – Chapter 7•Hypothesis Testing – Chapters 8-9A point estimateof a population parameter is an estimate given by a single value.Sample Statistics are point estimates of Population Parameters.SamplePopulation StatisticParameterMeanμStandard DeviationsσProportionpxˆpAn interval estimateof a population parameter is given by two values between which we expect to have the population parameter.(Why would we want an interval estimate instead of a point estimate?)Our interval estimateis given by point estimate±margin of errorThe margin of erroris how much we expect to be *off*. SAMPLE: Interviews with 706 likely voters, conducted by telephone on July 9-11, 2004.MARGIN OF ERROR: ± 4% The point estimate of the proportion that would vote for Bush was 0.46.The interval estimate would be 0.46 ± 0.04, and we would write this as (0.42, 0.50).The lower limit is 0.42, and the upper limit is 0.50.
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