# class-slides-02.pdf - Catolica-Lisbon School of Business...

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Catolica-Lisbon School of Business and Economics2 - Introduction to Sampling DistributionsStatistics II - Fall 2021Filipa ReisCLSBEStatistics II1/38
Agenda1.Population, sample, and random sampling2.Case Study: Defect SamplingStatistics II2/38
Population, Sample, and Random samplingPopulation, Sample, and Random samplingStatistics II3/38
Key conceptsApopulationis the complete set of all items (usually people, objects,transactions, or events) that we are interested in studying.Asampleis a subset of units of a population.Anexperimental (or observational) unitis an object (e.g. person, thing,transaction, event) about which we collect data.Avariableis a characteristic or property of an individual experimental (orobservational) unit in the population.Population, Sample, and Random samplingStatistics II4/38
PracticeMoodle Quiz (Lecture 2)Q.1; Q.2; Q3Population, Sample, and Random samplingStatistics II5/38
Inferential statisticsHow can we characterize a whole population using only a sample of data?Aparameteris a numerical descriptive measure of a population. Because itis based on the observations in the population, its value is almost alwaysunknown.We use the information from asamplestatistics to makeinferencesaboutthe parameters of apopulation.A samplestatisticis a numerical descriptive measure of a sample. It iscalculated from the observations in the sample.Population, Sample, and Random samplingStatistics II6/38
Population parameters and corresponding sample statisticsPopulation ParameterSample StatisticMeanμ¯xVarianceσ2s2Standard deviationσsBinomial proportionpˆpPopulation, Sample, and Random samplingStatistics II7/38
Probability distributionA probability distribution is atable, graph, or mathematical function thatprovides the probabilities of occurrence of the different possible outcomesin an experiment.1Discrete Probability Distributions (probability mass functions, PMF)Continuous Probability Distributions (probability density functions, PDF)Features of probability distributionsWe are usually interested in a few features of the distributions of random variables,these include:Measures ofcentral tendencyMeasures ofvariabilityorspread1Visit to access an interactive website for creating and visualizing probabilitydistributions.Population, Sample, and Random samplingStatistics II8/38
Why sample?Thus far, we have assumed that we knew the probability distributions of therandom variables we were dealing with.Using this knowledge, we computed means, variances, and probabilities.However, in most practical applications, we don’t have this information; thetrue(population) mean and standard deviation areunknownquantities thathave to beestimated.

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Term
Fall
Professor
Ilidio Vidigal
Tags
minor defects