On the Estimation of Central Intervals which Contain Assigned Proportions of a Normal Univariate Population

Abstract

For samples of any given size $N \geq 2$ from a normal population, Wilks [1] has shown how to choose the parameter $\lambda_p$ so that the expected coverage of the interval $\bar x \pm \lambda_ps$ will be $1 - p$. The present paper treats the choice of the minimal sample size $N$ necessary to effect a certain type of statistical control on the fluctuation of that coverage about its expected value; a brief table of such minimal sample sizes is given.