Confidence Interval - Definition of Confidence Interval

[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?

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?

[harry]

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 confidence interval

[Steve Prevette]

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?

[Yew Jin]

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.

[CertifiedDataJunkie]

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!