# 100% confidence interval [duplicate]

Is it possible to produce a 100% confidence interval for a sample mean?

Or does a 100% confidence interval imply that it is no longer a sample mean; that the population mean is already known?

• It sounds like you really want to ask about a $0\%$ confidence interval, not a $100\%$ interval. Regardless, whatever size you stipulate has nothing to do with whether you know the population mean.
– whuber
Commented Nov 8, 2015 at 23:31
• "Or does a 100% confidence interval imply that it is no longer a sample mean; that the population mean is already known?" Can you clarify what you mean by this? My first reading of this was the same as @whuber: that you are interpreting "100% confidence" to mean "I am completely sure the mean is $\mu$", which isn't what a "100% confidence interval" would usually mean. Without some clarification on this point, it isn't clear what kind of answer you are expecting. Commented Nov 8, 2015 at 23:34
• The answer to this question might help you: stats.stackexchange.com/questions/107655/…
– Ihab
Commented Nov 8, 2015 at 23:35
• I believe this is a duplicate; see.here 1 or here 2. Commented Nov 8, 2015 at 23:36
• If you had the entire population, you could have a 100% CI for the mean consisting of a single point, but then the usual models for the distribution (such as the normal) would not hold (they require an infinite population for the distributional model to apply). Commented Nov 8, 2015 at 23:42