# Chapter 5 8 70 introduction to clt simulation small

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Chapter 58 / 70
Introduction to C.L.T.Simulation: Small Sample vs. Large SampleThe distribution of all sample proportions from samples of size 3has mean40%.Thissampling distributionhas a standard deviation about21.08%.Consider a population of 1,000,000 people of which 40% aremale. Randomly selectn=300of them.If we look at all possible samples, then the distribution of thesample proportions would haveMean = 40%Standard Error2.108%Chapter 59 / 70
Variability in estimates1Introduction to C.L.T.2Variability in estimatesApplication exerciseSampling distributions - via CLT3Confidence intervals4Hypothesis testing5Examining the Central Limit Theorem6Inference for other estimatorsChapter 5
Variability in estimatesChapter 510 / 70
Chapter 511 / 70
Variability in estimatesParameter estimationWe are often interested inpopulation parameters.Since complete populations are difficult (or impossible) to collectdata on, we usesample statisticsaspoint estimatesfor theunknown population parameters of interest.Sample statistics vary from sample to sample.Quantifying how sample statistics vary provides a way toestimate themargin of errorassociated with our point estimate.But before we get to quantifying the variability among samples,let’s try to understand how and why point estimates vary fromsample to sample.Suppose we randomly sample 1,000 adults from each state in the US.Would you expect the sample means of their heights to be the same,somewhat different, or very different?Chapter 512 / 70
Variability in estimatesParameter estimationWe are often interested inpopulation parameters.Since complete populations are difficult (or impossible) to collectdata on, we usesample statisticsaspoint estimatesfor theunknown population parameters of interest.Sample statistics vary from sample to sample.Quantifying how sample statistics vary provides a way toestimate themargin of errorassociated with our point estimate.But before we get to quantifying the variability among samples,let’s try to understand how and why point estimates vary fromsample to sample.
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