The Annals of Mathematical Statistics

On the Cost of not Knowing the Variance when Making a Fixed-Width Confidence Interval for the Mean

Gordon Simons

Full-text: Open access

Abstract

It is shown that the mean of a normal distribution with unknown variance $\sigma^2$ may be estimated to lie within an interval of given fixed width at a prescribed confidence level using a procedure which overcomes ignorance about $\sigma^2$ with no more than a finite number of observations. That is, the expected sample size exceeds the (fixed) sample size one would use if $\sigma^2$ were known by a finite amount, the difference depending on the confidence level $\alpha$ but not depending on the values of the mean $\mu$, the variance $\sigma^2$ and the interval width $2d$. A number of unpublished results on the moments of the sample size are presented. Some do not depend on an assumption of normality.

Article information

Source
Ann. Math. Statist., Volume 39, Number 6 (1968), 1946-1952.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177698024

Digital Object Identifier
doi:10.1214/aoms/1177698024

Mathematical Reviews number (MathSciNet)
MR239699

Zentralblatt MATH identifier
0187.15805

JSTOR
links.jstor.org

Citation

Simons, Gordon. On the Cost of not Knowing the Variance when Making a Fixed-Width Confidence Interval for the Mean. Ann. Math. Statist. 39 (1968), no. 6, 1946--1952. doi:10.1214/aoms/1177698024. https://projecteuclid.org/euclid.aoms/1177698024


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