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May 28th, 2016, 09:11 AM  #1 
Senior Member Joined: Feb 2015 From: london Posts: 121 Thanks: 0  Confidence intervals
In lots of examples when calculating confidence intervals they use the tdistribution with np degrees of freedom? Why do they use the tdistribution instead of the normal? For example see Coefficient Confidence Intervals: Coefficient Standard Errors and Confidence Intervals  MATLAB & Simulink  MathWorks United Kingdom 
May 28th, 2016, 10:21 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
The Central Limit Theorem states that the distribution of the sample mean tends to the normal distribution as the sample size tends to infinity. When the sample size is small (typically <30) and the underlying distribution is normal, the distribution sample mean hasn't converged close enough to the normal distribution, so Student's tdistribution is more accurate. If the underlying distribution were assumed to be normal, we can safely use the normal sampling theorem instead. 
May 28th, 2016, 10:28 AM  #3 
Senior Member Joined: Feb 2015 From: london Posts: 121 Thanks: 0 
Thanks for the reply. I am seeing examples in past papers where sample size is 100+ and they are still using t distribution for confidence interval. The question I was looking at were calculating the confidence interval intervals for coefficient estimates. And when I looked this up on the MathWork link posted above, they also suggest using the tdistribution? Is it just that coefficient estimates are not normally distributed? 
May 28th, 2016, 10:36 AM  #4  
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  Quote:
 

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