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Activity Number:
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283
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Type:
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Contributed
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Date/Time:
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Tuesday, August 4, 2009 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistical Education
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| Abstract - #304538 |
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Title:
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Classroom Simulation: Investigation of the Asymptotic Distribution of the Sample Median
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Author(s):
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Vadim Y. Bichutskiy*+ and Joshua Kerr and Bruce E. Trumbo
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Companies:
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California State University, East Bay and California State University, East Bay and California State University, East Bay
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Address:
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3375 Homestead Road #11, Santa Clara, CA, 95051,
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Keywords:
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Central Limit Theorem (CLT) ; sample median ; rate of convergence ; asymptotic normal distribution ; computer simulation ; R statistical software
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Abstract:
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The computer revolution has transformed statistical practice, requiring students of statistics to be skilled in computation. Here, we illustrate computation for statistical instruction by using simulations in R to investigate the asymptotic distribution of the sample median. We study the effect of the shape of the parent population on the rate of convergence and the properties of asymptotic confidence intervals for the population median. Further, a practical method for obtaining a confidence interval for the population median based on density estimation is explored. This paper provides an example of the interplay between theory and computation in statistical research. Results show that if the parent population is symmetric unimodal, then the sample median is approximately normal for n > 20 and confidence intervals have approximately nominal coverage probabilities for n > 30.
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