9.28 Recitation.pdf - SAMPLING Concepts you need to know ● Population ● Population parameter(true value but unknown ● Sample ● Sample statistic

9.28 Recitation.pdf - SAMPLING Concepts you need to know...

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SAMPLING Concepts you need to know Population Population parameter (true value; but unknown) Sample Sample statistic Estimate (statistical inference) What is Sampling? Population Parameter←→ Sample Statistic Random Sampling Error Examples Population: Consists of 16 points, 1,1,0,0,0,0,1,1,0,1,1,0,1,1,1,0 Sample: 0,1,0,1 = .5 Sample: 1,1,0,1 =.75 (far away from population parameter) We draw a sample from the population and calculate a sample statistic (statistical inference) Why Does Sampling Work? Intuitively, sampling is random, thus the sample should be representative of the population (like a miniature) Each individual has a probability of n/N of being drawn Mathematically, we have the law of large numbers: As the sample size n goes to infinity, the sample average will converge to the population mean One of the most power theorems in statistics (first proved by Jakob Bernoulli) Random Sampling Error Note that we’re interested in estimating a population parameter
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