Sampling Distributions and Logic of Inference/Confidence IntervalsInferential statistics: drawing conclusions about characteristics of a population based on what we observe in a sampleoMake inference about population parameter using sample statisticSample statistic (´X¿: characteristic of the sample that we actually observe Population parameter (μχ¿:characteristic of the pop. that we are interested in knowingEstimating population parameters (2 options) 1.assume population mean equal to sample mean (μχ=´X)a.point estimateb.very likely to be wrong b/c sample statistic likely to miss true population by at least a little (chance sampling error)c.reality: (μχ≠´X)2.better option: create a confidence intervala.defined by the confidence leveli.certainty that the confidence level will contain the true population parameterb.advantage: less likely to be wrong and can quantify riskof being wrongsampling distribution = theoretical probability distribution of all possible sample values for the statistic in which we are interested (key for inferential statistics)central limit theorem: if the size of our random sampleis large enough, we can assume that the sampling distribution isonormally distributedopop. mean approx. equal to sample meanostandard error (σ´x¿: standard deviation in distribution (all possible sample means) calculating confidence intervalsodecide on confidence level and corresponding z-scoreostandard error
