BOUNDS FOR THE SAMPLE SIZE TO JUSTIFY NORMAL APPROXIMATION OF THE CONFIDENCE LEVEL

THOMAS HÖGLUND

Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden

(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.