Some Bootstrap and Randomization Distributionsslope(thousandths)-60-40-200204060Dot Plotr-0.4-0.20.00.20.40.6Nullxbar98.298.398.498.598.698.798.898.999.0Diff-4-3-2-101234xbar26272829303132Dot PlotSlope :Restaurant tipsCorrelation: Malevolent uniformsMean :Body TemperaturesDiff means: Finger tapsMean : Atlanta commutesphat0.30.40.50.60.70.8Proportion : Owners/dogsAll bell-shaped distributions
Density CurveA density curve is a theoretical model to describe a variable’s distribution.Think of a density curve as an idealized histogram, where:(1) The total area under the curve is one.(2) The proportion of the population in any interval is the areaover that interval.
Density for Bootstrap Means for Atlanta CommutesWhat proportion are between 30 and 31?
Parameters of a NormalNotation: X~N(μ,σ) Two features distinguish one normal density from another:•The meanis its center of symmetry (μ). •The standard deviation controls its spread (σ).
Example: A PopulationHeight ~ N(173.25, 10.3)
Example: Bootstrap Distribution̅"’s for Atlanta commutes ≈ N( 29.11, 0.93)Original sampleBootstrap std. dev. (SE)