If I have the distribution of data from small sample size (e.g. N=250, 1000), and would like to estimate the distribution (e.g. sigma) of data on large population (e.g. N=1 million)? What is the confidence level / error on the prediction ?
(Assume the distribution is Normal distribution or same shape for small/large population)
To obtain confidence intervals for the standard deviation in JMP you can use the distribution platform. Here are steps to obtain those confidence limits:
From an open table:
1. Analyze > Distribution
2. Cast your variable of interest to the Y role and click OK
3. From the Red Triangle next to your variable name, select Confidence Interval
4. Select your desired level of confidence
The resulting table will display the confidence limits for both the mean and the standard deviation (as shown in the screenshot below). With sample sizes you described your intervals will probably be quite narrow. The size of the population from which the sample was drawn is irrelevant in this approach, and unless the sample size is some sizable proportion of the population size (e.g. 0.50 of the population) there are no "corrections" to this confidence interval necessary.