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The Confidence Interval is a particular type of measurement that estimates a population's parameter. Usually, a confidence interval correlates with a percentage. The certain percentage represents how many of the same type of sample will include the true mean. Therefore, we would be a certain percent confident that the interval contains the true mean.
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Does the population mean have to fall within the confidence interval?
No. For instance, when you calculate a 95% confidence interval for a parameter this should be taken to mean that, if you were to repeat the entire procedure of sampling from the population and calculating the confidence interval many times then the collection of confidence intervals would include the given parameter 95% of the time. And sometimes the confidence intervals would not include the given parameter.
If the standard deviation is doubled what will be the effect on the confidence interval?
The confidence intervals will increase. How much it will increase depends on whether the underlying probability model is additive or multiplicative.
When comparing the 95 percent confidence and prediction intervals for a given regression analysis what is the relation between confidence and prediction interval?
Confidence interval considers the entire data series to fix the band width with mean and standard deviation considers the present data where as prediction interval is for independent value and for future values.
When the sample size is large valid confidence intervals can be established for the population mean irrespective of the shape of the underlying distribution?
Yes, but that begs the question: how large should the sample size be?
What does the term subnomial mean?
I found the word in "Better binomial confidence intervals" (J.F.Reed, J Mod App Stat MethJ. From the context, I think it is a typo or Freudian slip, as the apparent meaning was suboptimal. The comment refers to a graph showing that a Wald-estimate 95% confidence interval actually covers between 80 and 97% over most of the domain.
