Generalized inferences on the common mean of several normal populations |
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| Institution: | 1. National Taichung Institute of Technology, 129 Sanmin Road, Sec. 3, Taichung 404, Taiwan;2. Institute of Statistics and Graduate Institute of Finance, National Chiao Tung University, Hsinchu 300, Taiwan;1. Department of Statistics and Biostatistics, Rutgers University, Piscataway, NJ 08854, USA;2. Department of Biostatistics, Yale University, School of Public Health, New Haven, CT 06511, USA;3. Independent Consultant, Sudbury, MA 01776, USA;1. Department of Chemistry, Periyar University, Salem 636 011, India;2. Centre for Advanced Studies in Crystallography and Biophysics, University of Madras, Guindy Campus, Chennai 600 025, India;3. Department of Chemistry, Karunya University, Karunya Nagar, Coimbatore 641 114, India;4. Department of Chemistry, Howard University, 525 College Street NW, Washington, DC 20059, USA;5. Department of Microbiology, Periyar University, Salem 636 011, India;1. AGH University of Science and Technology, Faculty of Energy and Fuels, Department of Hydrogen Energy, al. A. Mickiewicza 30, 30-059 Krakow, Poland;2. Shibaura Institute of Technology, Department of Engineering Science and Mechanics, 3-7-5 Toyosu, Koto-ku, 135-8548 Tokyo, Japan;3. Northern Illinois University, Department of Physics, DeKalb, 60115 IL, USA;1. School of Economics & Wang Yanan Institute for Studies in Economics, Xiamen University, China;2. Department of Biostatistics, Yale University, New Haven, CT 06520, USA;3. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China |
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| Abstract: | The hypothesis testing and interval estimation are considered for the common mean of several normal populations when the variances are unknown and possibly unequal. A new generalized pivotal is proposed based on the best linear unbiased estimator of the common mean and the generalized inference. An exact confidence interval for the common mean is also derived. The generalized confidence interval is illustrated with two numerical examples. The merits of the proposed method are numerically compared with those of the existing methods with respect to their expected lengths, coverage probabilities and powers under different scenarios. |
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