My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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 t-distribution with n-p degrees of freedom?

Why do they use the t-distribution instead of the normal?

For example see Coefficient Confidence Intervals: Coefficient Standard Errors and Confidence Intervals - MATLAB & Simulink - MathWorks United Kingdom
calypso is offline  
 
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 t-distribution is more accurate.

If the underlying distribution were assumed to be normal, we can safely use the normal sampling theorem instead.
123qwerty is offline  
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 t-distribution?

Is it just that coefficient estimates are not normally distributed?
calypso is offline  
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:
Originally Posted by calypso View Post
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 t-distribution?

Is it just that coefficient estimates are not normally distributed?
Oh darn, sorry, I didn't see your link. I thought you were talking about means. Yeah ,you have to use t for that. My professor didn't prove this in class, so I'll have to leave it to more experienced members to answer the question of why.
123qwerty is offline  
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
confidence, intervals



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Confidence Intervals... Artus Advanced Statistics 0 November 14th, 2012 03:39 PM
Confidence Intervals for Differences help... twobeatsoff Advanced Statistics 2 September 12th, 2012 07:49 AM
Confidence intervals [stats] jackinda Algebra 1 December 4th, 2011 03:39 AM
Confidence Intervals Help please! mochisushi01 Advanced Statistics 1 April 13th, 2010 01:54 AM
Confidence Intervals symmetry Advanced Statistics 1 March 29th, 2007 09:59 PM





Copyright © 2017 My Math Forum. All rights reserved.