0
$\begingroup$

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?

$\endgroup$
5
  • $\begingroup$ 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. $\endgroup$
    – whuber
    Commented Nov 8, 2015 at 23:31
  • $\begingroup$ "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. $\endgroup$
    – Silverfish
    Commented Nov 8, 2015 at 23:34
  • $\begingroup$ The answer to this question might help you: stats.stackexchange.com/questions/107655/… $\endgroup$
    – Ihab
    Commented Nov 8, 2015 at 23:35
  • $\begingroup$ I believe this is a duplicate; see.here 1 or here 2. $\endgroup$
    – Glen_b
    Commented Nov 8, 2015 at 23:36
  • $\begingroup$ 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). $\endgroup$
    – Glen_b
    Commented Nov 8, 2015 at 23:42

1 Answer 1

1
$\begingroup$

If you are some parametric test, that assumes normal distribution, then your 100% confidence interval will be from -infinity to + infinity. If you are using permutation test, then your confidence interval is bounded by number of samples

$\endgroup$
2
  • $\begingroup$ In the case of the permutation test it will generally then not be a 100% confidence interval. $\endgroup$
    – whuber
    Commented Nov 8, 2015 at 23:31
  • $\begingroup$ yes, that's what I meant. Your maximum confidence is dependent on number of samples you are permuting, p value cannot be 0 $\endgroup$
    – rep_ho
    Commented Nov 9, 2015 at 0:25

Not the answer you're looking for? Browse other questions tagged or ask your own question.