Statistics Notes 2 - Sampling Point Estimation and Interval...

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Statistics for Business Control and Regression Analysis – Fall 2008 1 Sampling, Point Estimation Sampling, Point Estimation and Interval Estimation and Interval Estimation
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Statistics for Business Control and Regression Analysis – Fall 2008 2 Sampling Sampling Q: What is the average income of all Stern students? Finding the exact answer (examining everybody ) is difficult Solution: examine a sample of students, and compute their average income Q: Will we get a precise answer for the original question? A: No!
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Statistics for Business Control and Regression Analysis – Fall 2008 3 Sampling Variability Sampling Variability Terminology All Stern students are the population Average income among all students, µ, is a parameter Students we examine are the sample Average income found in sample, , is an estimate Estimates are subject to randomness – different samples will give different estimates Estimators are Random Variables! x
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Statistics for Business Control and Regression Analysis – Fall 2008 4 Sampling Variability Sampling Variability The sad facts: estimates are (almost) never exactly correct, and information is always lost in estimation Excellent demonstration: http://www.ruf.rice.edu/%7Elane/stat_sim/sampling_dist/index.html Statistical theory helps us to Understand how an estimate fluctuates around the true value of a parameter Control the probability of errors Determine the sample size Draw valid conclusions from samples on populations
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Statistics for Business Control and Regression Analysis – Fall 2008 5 Statistics and Sampling Distribution Statistics and Sampling Distribution is a statistic – it’s a number we compute from the sample results Other statistics: sample range, sample SD, etc. Different statistics may serve as estimators of different parameters describing the population A statistic is a RV, and its distribution is called the sampling distribution The sampling distribution has its own mean, variance, and shape, which are almost always different from those of the population x
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Statistics for Business Control and Regression Analysis – Fall 2008 6 Random Sample Random Sample A random sample of size n from a finite population of size M is a sample chosen so that each of the possible samples is equally likely Sample is “without replacement” When population is infinite, a random sample is n independent observations from the population In our course: all populations are infinite, or M is sufficiently large so we can neglect finite population effects n M
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7 Biased Samples Biased Samples A biased sample is a sample which is not random, and is thus not representative Biased samples may lead to wrong conclusions When sampling Stern students, will it be OK to take our class as a sample? to email a randomly selected group of students, and
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Statistics Notes 2 - Sampling Point Estimation and Interval...

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