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标题：A Note on Confidence Interval for the Power of the One Sample <svg style="vertical-align:-0.162pt;width:7.1374998px;" id="M1" height="13.0375" version="1.1" viewBox="0 0 7.1374998 13.0375" width="7.1374998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.0375)"> <g transform="translate(72,-61.57)"> <text transform="matrix(1,0,0,-1,-71.95,61.78)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝑡</tspan> </text> </g> </g> </svg> Test
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作者：A. Wong
期刊名称：Journal of Probability and Statistics
印刷版ISSN：1687-952X
电子版ISSN：1687-9538
出版年度：2010
卷号：2010
DOI：10.1155/2010/139856
出版社：Hindawi Publishing Corporation
摘要：In introductory statistics texts, the power of the test of a one-sample mean when the variance is known is widely discussed. However, when the variance is unknown, the power of the Student's 𝑡-test is seldom mentioned. In this note, a general methodology for obtaining inference concerning a scalar parameter of interest of any exponential family model is proposed. The method is then applied to the one-sample mean problem with unknown variance to obtain a (1−𝛾)100% confidence interval for the power of the Student's 𝑡-test that detects the difference (𝜇−𝜇0). The calculations require only the density and the cumulative distribution functions of the standard normal distribution. In addition, the methodology presented can also be applied to determine the required sample size when the effect size and the power of a size 𝛼 test of mean are given.