Sec5-12 - STAT 101 Dr Kari Lock Morgan Normal Distribution C hapte r 5 Normal distribution Central limit theorem Normal distribution for confidence

Sec5-12 - STAT 101 Dr Kari Lock Morgan Normal Distribution...

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Statistics: Unlocking the Power of Data Lock 5 Normal Distribution STAT 101 Dr. Kari Lock Morgan 10/18/12 Chapter 5 Normal distribution Central limit theorem Normal distribution for confidence intervals Normal distribution for p-values Standard normal
Statistics: Unlocking the Power of Data Lock 5 Project 1 Due Tuesday 5 pages, double spaced, including figures Hypotheses should not change based on data This is a research paper – there should be text and complete sentences.
Statistics: Unlocking the Power of Data Lock 5 slope ( thousandths ) -60 -40 -20 0 20 40 60 Dot Plot r -0.6 -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! Bootstrap and Randomization Distributions
Statistics: Unlocking the Power of Data Lock 5 The symmetric, bell-shaped curve we have seen for almost all of our bootstrap and randomization distributions is called a normal distribution Normal Distribution -3 -2 -1 0 1 2 3
Statistics: Unlocking the Power of Data Lock 5 Central Limit Theorem! For a sufficiently large sample size , the distribution of sample statistics for a mean or a proportion is normal
Statistics: Unlocking the Power of Data Lock 5 Central Limit Theorem The central limit theorem holds for ANY original distribution, although “sufficiently large sample size” varies The more skewed the original distribution is (the farther from normal), the larger the sample size has to be for the CLT to work
Statistics: Unlocking the Power of Data Lock 5 Central Limit Theorem For distributions of a quantitative variable that are not very skewed and without large outliers, n ≥ 30 is usually sufficient to use the CLT For distributions of a categorical variable, counts of at least 10 within each category is usually sufficient to use the CLT
Statistics: Unlocking the Power of Data Lock 5 The normal distribution is fully characterized by it’s mean and standard deviation Normal Distribution mean,standard deviation N
Statistics: Unlocking the Power of Data Lock 5 Normal Distribution 0.523,0.048 N

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