The Elsmar Cove Forum Confidence Interval - Definition of Confidence Interval
 Forum User Name Keep Me Logged In Password
 Register Photo Albums Blogs FAQ Social Groups Calendar Search Today's Posts Mark Forums Read

 Elsmar Cove Forum Sidebar @import url(http://www.google.com/cse/api/branding.css); Custom Search Monitor the Elsmar Forum Monitor New Forum Posts Follow Marc & Elsmar Elsmar Cove Groups Sponsor Links Donate and \$ Contributor Forum Access Sponsored Links Courtesy Quick Links Links that Elsmar Cove visitors will find useful in your quest for knowledge: Howard'sInternational Quality Services Atul'sSymphony Technologies Marcelo Antunes'SQR Consulting Bob Doering'sCorrect SPC - Precision Machining NIST's Engineering Statistics Handbook IRCA - International Register of Certified Auditors SAE - Society of Automotive Engineers Quality Digest Portal IEST - Institute of Environmental Sciences and Technology ASQ - American Society for Quality
#1
27th June 2009, 09:54 AM
 Yew Jin Involved - Posts   Registration Date: Aug 2006 Location: Penang, Malaysia Posts: 193 Thanks Given to Others: 23 Thanked 58 Times in 37 Posts Karma Power: 48 Karma: 761
Confidence Interval - Definition of Confidence Interval

Based on the the NIST engineering statistics handbook stated that "As a technical note, a 95% confidence interval does not mean that there is a 95% probability that the interval contains the true mean. The interval computed from a given sample either contains the true mean or it does not."

1. Why the confidence interval under a specific % does not contain the true mean by using the sample from the population?

2. Why the 95% of confidence interval is used commonly? Is the 5% of the risk stated in any standard to be used?

A confidence limits will be calculated from a sample of n1 size. However, with replicate on this, second sample of n2 size will be drawn from the same population and another confidence limits will be calculated. (n1 and n2 can be same or different in this case).

1. To get the narrower confidence limits, the overlap of the above 2 confidence limits should be considered.So that it will be more precise to estimate the true mean of population. How many time of samples should we considered in this case to estimate the true mean?
__________________
____________________________________________
failing to plan is planning to fail ~ Joseph Juran

#2
27th June 2009, 10:17 AM
 harry Super Moderator   Registration Date: Sep 2005 Location: Johore/Malaysia Posts: 5,958 Thanks Given to Others: 1,409 Thanked 2,752 Times in 1,912 Posts Blog Entries: 2 Karma Power: 662 Karma: 17700
Re: Definition of confidence interval

Welcome back Yew Jin. You had been missing for a while.

I'll leave it to the experts to help you but in the mean time, you may want to have a look at
 Thanks to harry for your informative Post and/or Attachment!
#3
27th June 2009, 11:37 PM
 Steve Prevette Deming Disciple   Registration Date: Feb 2004 Location: Aiken, SC Posts: 1,999 Thanks Given to Others: 145 Thanked 1,057 Times in 559 Posts Karma Power: 259 Karma: 11204
Re: Confidence Interval - Definition of Confidence Interval

Quote:
 In Reply to Parent Post by Yew Jin Based on the the NIST engineering statistics handbook stated that "As a technical note, a 95% confidence interval does not mean that there is a 95% probability that the interval contains the true mean. The interval computed from a given sample either contains the true mean or it does not." 1. Why the confidence interval under a specific % does not contain the true mean by using the sample from the population? A: We do NOT KNOW what the "true mean" is! All we have is a sample result. The sample result (and its confidence interval) MAY OR MAY NOT encompass the "true mean". The confidence interval expresses the probability that a true mean from outside the confidence interval could have given this result. 2. Why the 95% of confidence interval is used commonly? Is the 5% of the risk stated in any standard to be used? A. Rather arbitrary, but most folks won't accept much less than 90% confidence. Realize that if I make 10 estimates of confidence intervals at 90% confidence, I will on the average be wrong once (1 out of 10) A confidence limits will be calculated from a sample of n1 size. However, with replicate on this, second sample of n2 size will be drawn from the same population and another confidence limits will be calculated. (n1 and n2 can be same or different in this case). 1. To get the narrower confidence limits, the overlap of the above 2 confidence limits should be considered.So that it will be more precise to estimate the true mean of population. How many time of samples should we considered in this case to estimate the true mean?
A. Huh? I assume you mean that you will pool n1 and n2 and calculate a confidence interval?
__________________
Steve Prevette
"A Passionate Statistician", ASQ CQE, ASQ Fellow
 Thanks to Steve Prevette for your informative Post and/or Attachment!
#4
28th June 2009, 07:57 AM
 Yew Jin Involved - Posts   Registration Date: Aug 2006 Location: Penang, Malaysia Posts: 193 Thanks Given to Others: 23 Thanked 58 Times in 37 Posts Karma Power: 48 Karma: 761
Re: Confidence Interval - Definition of Confidence Interval

Thanks Harry and Steve, actually these 2 days, I was referring back to the Statistics Inference material in my last master degree stated that:

The probability that random interval covers the unknown true mean is 0.95 (if 95% confidence interval was chosen). If the samples of size n were repeatedly drawn from the normal population and the random interval were computed for each sample, then the relative frequency of those intervals containing the true unknown mean would approach 95%.

From here I understand that, if the population is in normal distribution, the 95% of the confidence interval will always cover the unknown true mean. (this is support by the 68, 95 and 99.7 rules). If the population is not in the normal distribution, based on the Central Limit Theorem, each sample was drawn with large sample size will be in the normal distribution. With this, the true mean of the population may not be covered in the 95% of the confidence interval.
__________________
____________________________________________
failing to plan is planning to fail ~ Joseph Juran
#5
29th June 2009, 08:53 AM
 CertifiedDataJunkie Registered Visitor   Registration Date: Jun 2006 Location: Nunya bizness Posts: 79 Thanks Given to Others: 11 Thanked 26 Times in 19 Posts Karma Power: 37 Karma: 553
Re: Confidence Interval - Definition of Confidence Interval

As much as I had wanted to reply to the original post, I must admit that I wanted to see Steve Prevette's response first!

 The Elsmar Cove Forum Confidence Interval - Definition of Confidence Interval

 Bookmarks

 Visitors Currently Viewing this Thread: 1 (0 Registered Visitors (Members) and 1 Unregistered Guest Visitors)

 Forum Posting Settings You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules

 Similar Discussion Threads Discussion Thread Title Thread Starter Forum Replies Last Post or Poll Vote convivial Reliability Analysis - Predictions, Testing and Standards 3 22nd June 2010 01:29 PM paizlea Inspection, Prints (Drawings), Testing, Sampling and Related Topics 6 29th July 2009 04:11 PM tahashamim SPC Monitoring and Statistical Analysis Techniques 1 2nd October 2008 03:52 PM khoshruba Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1 11th June 2008 12:16 PM BRDHard Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1 4th March 2007 07:57 AM

The time now is 05:11 PM. All times are GMT -4.