Chapter 5.1.pdf - Normal Distribution Section 5.1 Some Bootstrap and Randomization Distributions Correlation Malevolent uniforms Dot Plot Measures from

# Chapter 5.1.pdf - Normal Distribution Section 5.1 Some...

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Normal Distribution Section 5.1
Some Bootstrap and Randomization Distributions slope ( thousandths ) -60 -40 -20 0 20 40 60 Dot Plot r -0.4 -0.2 0.0 0.2 0.4 0.6 Nullxbar 98.2 98.3 98.4 98.5 98.6 98.7 98.8 98.9 99.0 Diff -4 -3 -2 -1 0 1 2 3 4 xbar 26 27 28 29 30 31 32 Dot Plot Slope :Restaurant tips Correlation: Malevolent uniforms Mean :Body Temperatures Diff means: Finger taps Mean : Atlanta commutes phat 0.3 0.4 0.5 0.6 0.7 0.8 Proportion : Owners/dogs All 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 Commutes What proportion are between 30 and 31?
Parameters of a Normal Notation: X~N(μ,σ) Two features distinguish one normal density from another: The mean is its center of symmetry (μ). The standard deviation controls its spread (σ).
μ σ µ+σ σ µ - σ µ - µ+2σ N(µ,σ)
Example: A Population Height ~ N(173.25, 10.3)
Example: Bootstrap Distribution ̅" ’s for Atlanta commutes ≈ N( 29.11, 0.93) Original sample Bootstrap std. dev. (SE)
Ex: Randomization Distribution ! " ’s for dog/owners matches ≈ N( 0.5, .10) H 0 Randomization std. dev. (SE)