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What is the shortest confidence interval?
the one with k=0.5 is the shortest. Now, I feel I understand this problem conceptually pretty well. For the normal distribution, and really any distribution that is symmetric about the mean and is strictly decreasing away from the mean, the further away you go from the mean the less area there is under the curve.
What is expected length of confidence interval?
The expected length of a confidence interval is shown to equal the integral over false values of the probability each false value is included. Thus two desiderata for choosing among confidence procedures lead to the same measure of desirability.
What does the length of a confidence interval mean?
length of the interval is a measure of the “average extent” of the false values. included. There is another approach to the problem. A natural measure of the extent. to which the confidence interval procedure includes a particular false value is.
How to calculate the confidence interval in Excel?
Then, to construct the confidence interval, we need to calculate the standard error by plugging in sample counterparts of each of the terms in the variance above: This will require you to estimate the density of X, but this should be pretty straightforward. Alternatively, you could bootstrap the CI pretty easily too.
Which is an example of a reduced confidence level?
Another alternative may be to use a reduced confidence level. Let’s work through an example (also provided by Hahn & Meeker). They supply an ordered set of n = 100 “measurements of a compound from a chemical process” and ask for a 100(1 − α) = 95% confidence interval for the q = 0.90 percentile.
Why is the preceding interval a conservative interval?
The preceding interval is conservative because the actual confidence level, given by the left-hand side of Equation (1), is greater than the specified value 1 − α. It is sometimes impossible to construct a distribution-free statistical interval that has at least the desired confidence level.
What is the interval between the 85th and 97th largest?
The 85th largest is 24.33 and the 97th largest is 33.24. The interval therefore is [24.33, 33.24]. Let’s re-interpret that. This procedure was supposed to have at least a 95% chance of covering the 90th percentile.