# Chapter 5.2.pdf - Confidence Intervals and P-values using...

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Confidence Intervals and P-values using Normal DistributionsSection 5.2
Central Limit TheoremFor random samples with a sufficiently large sample size, the distribution of sample statistic for a mean or a proportion is normally distributed
slope(thousandths)-60-40-200204060Dot Plotr-0.6-0.4-0.20.00.20.40.6Nullxbar98.298.398.498.598.698.798.898.999.0Dot PlotDiff-4-3-2-101234xbar26272829303132Dot PlotSlope :Restaurant tipsCorrelation: Malevolent uniformsMean :Body TemperaturesDiff means: Finger tapsMean : Atlanta commutesphat0.30.40.50.60.70.8Proportion : Owners/dogsBootstrap and Randomization Distributions
Central Limit TheoremThe central limit theorem holds for ANY original distribution, although “sufficiently large sample size” variesThe more skewed the original distribution is, the larger n has to be for the CLT to workFor quantitative variables that are not very skewed, n ≥ 30 is usually sufficient For categorical variables, counts of at least 10 within each category is usually sufficient
Hearing LossIn a random sample of 1771 Americans aged 12 to 19, 19.5% had some hearing loss (this is a dramatic increase from a decade ago!)