Why not sample mean plus or minus two standard deviations ?
The sample mean plus or minus a multiple of the standard deviation would work except for one (two?) things: the sample mean (standard deviation) is not equal to the population mean (standard deviation). Suppose the population standard deviation were known. The population mean plus or minus two SDs contains 95% of the population. But now slide the interval to the right, say, mimicking what happens when it is centered around the sample mean. The interval now includes more of the right tail of the population, but it loses a lot more from the left tail. That is, the sample mean plus or minus two SDs will contain less than 95% of the population. Prediction Intervals Prediction Intervals are used to estimate the value of the next observation. They are like confidence intervals in that they are a way of generating intervals with the desired property. That is, 95% of 95% prediction intervals will contain the next observation. However, they are not probability statements because they are made a
