Confidence interval for a bounded distributionGiven 1000 observations that come from a distribution that is bounded between 0 and 1. How do you calculate correct 95% Confidence intervals for the MEAN when dealing with a bounded distribution?R codeset.seed(10)data =runif(1000, min = 0, max = 1)mean(data)mean(data)+1.96*sd(data)/sqrt(length(data)) #usual CIsmean(data)-1.96*sd(data)/sqrt(length(data)) #usual CIsAre there any references on how to calculate 95% CIs for bounded distributions?

Question

detegerex · Accepted Answer

Step 1You are using a Central Limit Theorem approximation for the distribution of the mean, justified by a finite variance of the original distribution (which is       1    12   in this case) and a large sample size (which is 1000 here)So unless your original random variable has particularly extreme features (it does not in this case), you do not need to worry much about whether the original random variable has bounded or unbounded supportStep 2Your example code gives a sample mean of about 0.505 and a confidence interval of about [0.487,0.523], which contains the true population mean of 0.5. Using different seeds and your 1.96 multiple, you would expect about 95% of examples of confidence intervals to contain the true population mean. I think that for example seeds of 28, 44, 100, 140, 141, 147, 153, 154, or 160 would not

Given 1000 observations that come from a distribution that is bounded between 0 and 1. How do you calculate correct 95% Confidence intervals for the MEAN when dealing with a bounded distribution?

Answered question

Answer & Explanation

New Questions in College Statistics