How Large Does n Have to be for Z and t Intervals?

Students invariably ask the question How large does n have to be for Z and t intervals to give appropriate coverage probabilities? In this article we review the role of p fi 1 (X)= p n, where p fi 1 (X) is the skewness coefficient of the random sample, in the answer to this question. We also comment on the opposite effect that p fi 1 (X) has on the behavior of t intervals compared to Z intervals. Finally, we suggest a simple exercise for determining rules of thumb for n that result in appropriate confidence interval coverage. KEY WORDS: Confidence interval; Convergence to normality; Central Limit Theorem; Edgeworth expansion; Kurtosis; Skewness; t statistic. Institute of Statistics Mimeo Series #2506 February 1998 Dennis D. Boos is Professor and Jacqueline M. Hughes-Oliver is Assistant Professor, Department of Statistics, North Carolina State University, Raleigh, NC 27695--8203. Email addresses are: boos@unity.ncsu.edu, hughesol@unity.ncsu.edu 1. INTRODUCTION In many cour...