(Received December 19, 1988; revised November 10, 1989)
Abstract. The normal approximation of the confidence level of the standard confidence intervals leaves an error of the order O(1/n) (and not only O(n-1/2)). We use the first order term in the error to obtain simple lower bounds for the sample size.
Key words and phrases: Confidence interval, normal approximation, Edgeworth expansion, bounds for the sample size.