Suppose I have a normally distributed random variable with unknown mean μ and known standard deviation σ. Based on n samples of the RV, I'd like to compute an estimate of μ and a confidence interval at confidence level P%.(adsbygoogle = window.adsbygoogle || []).push({});

The usual way of doing this would be to use the standard error in the mean: if my sample mean is ##\bar{X}## and P is the total Gaussian probability between standard scores -Z and Z, then a confidence interval ##(\bar{X}- Z\sigma/\sqrt{n}, \bar{X}+ Z\sigma/\sqrt{n})## does the job. That is, if I repeat this sampling process many times then I can expect about P% of these confidence intervals to cover μ.

Am I "allowed" to choose a different procedure for constructing confidence intervals? Suppose my chosen confidence level is 30% and ##\sigma/\sqrt{n} = 1##. There is 30% (or close enough) probability that a given trial will yield a sample mean between ##\mu## and ##\mu + 0.85##, which I computed with the Gaussian CDF. Thus, the interval ##(\bar{X} - 0.85, \bar{X})## will cover μ about 30% of the times I do this n-sample experiment. So, it satisfies the requirement to be a 30% confidence interval.

Is there anything I'm missing about the definition of a confidence interval that doesn't allow me to do this construction? Obviously, the symmetric version based on the the standard error in the mean has nicer properties and does a better job of capturing the reliability of the estimator. If I don't care about that, though, am I free to make this slightly perverse construction instead?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Non-standard choices for confidence intervals

**Physics Forums | Science Articles, Homework Help, Discussion**