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Various methods based on Student t variates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariate t distribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass. Since such distributions involve many nuisance parameters, an impossible number of tables would be necessary in order to make exact confidence intervals. In the virtual absence of tables, approximations and bounds become important. In this paper, an attempt has been made to investigate the adequacy of certain suggested approximations [2], [5], [8] by computing the exact distributions for some particular cases. These exact distributions have been compared with approximations. This paper is concerned with two-sided confidence intervals, rather than one-sided intervals. [ABSTRACT FROM AUTHOR]

In the estimation of error rates for populations, whose error rate is quite small, the usual assumption of normality can lead to erroneous results. The confidence interval that is actually calculated for any given probability will have too low a lower bound, and not a high enough upper bound. Thus, the user may be misled into too optimistic a view of the population being sampled. This article discusses the nature of the problem and provides graphs from which the more accurate interval can be read. The final section of the paper deals with the related problem of confidence intervals when the observed error rate is zero. Tables are provided which facilitates the developing of confidence statements for such samples. [ABSTRACT FROM AUTHOR]

It is desired to set confidence limits for the probability of successful operation at least until time x[sub 0] of a series system of k dissimilar components. The components follow exponential failure laws, and data are available on failure times of components of each type. Exact confidence limits for k=2 have previously been given by Lentner and Buehler. The present paper deals with a large-sample approximation to the exact solution for arbitrary k. [ABSTRACT FROM AUTHOR]

The determination of sample size to meet certain probability requirements is a problem which often faces an experimenter when obtaining a confidence interval or testing a hypothesis. This paper includes some new graphs useful in selecting sample size and gives a reference to a new textbook which includes a number of other similar type graphs. The method of construction is explained in detail and examples are included. [ABSTRACT FROM AUTHOR]

When data are transformed to satisfy a spherical normal linear model, the mean θ of a variate in the original scale is a function of the mean μ and variance σ² of a normal variate. We consider several approximate confidence interval methods for θ, including a new method based on exact confidence intervals for linear functions of μ and σ² Monte Carlo estimates of coverage probabilities demonstrate the suitability of the new method for applications involving a wide range of data transformations, parameter values and sample sizes. [ABSTRACT FROM AUTHOR]