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

Dennis D. Boos and Jacqueline M. Hughes-Oliver
The American Statistician
Vol. 54, No. 2 (May, 2000), pp. 121-128
DOI: 10.2307/2686030
Stable URL: http://www.jstor.org/stable/2686030
Page Count: 8
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## Abstract

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 $\sqrt{\beta_1}$(X)/$\sqrt n$, where $\sqrt{\beta_1}$(X) is the skewness coefficient of the random sample, in the answer to this question. We also comment on the opposite effect that $\sqrt{\beta_1}$(X) has on the behavior of t intervals compared to Z intervals, and we suggest simple exercises for deriving rules of thumb for n that result in appropriate confidence interval coverage. Our presentation follows the format of lesson plans for three course levels: introductory, intermediate, and advance. These lesson plans are sequentially developed, meaning that the lesson plan for an intermediate level course includes all activities from the lesson plan for an introductory course, but with additional explanations and/or activities.

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