Advances and Applications in Statistics
Volume 25, Issue 1, Pages 47 - 61
(November 2011)
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CONFIDENCE INTERVALS FOR THE RATIO OF NORMAL MEANS WITH A KNOWN COEFFICIENT OF VARIATION
Suparat Niwitpong, Sanoe Koonprasert and Sa-aat Niwitpong
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Abstract: In this paper, we propose two new confidence intervals for the ratio of normal population means with a known coefficient of variation. This situation occurs in environment and agriculture experiments where the scientist needs to know the coefficient of variation of the control group (treatment) when compared with another treatment whose a coefficient of variation is unknown. This problem is analogous to Maity and Sherman [6] who suggested the new test statistics t-test for the difference means with a known variance, and Niwitpong [7] who constructed the confidence interval for the difference between normal means with a known variance. We propose two new confidence intervals for the ratio of normal means with a known coefficient of variation. One of our confidence intervals constructed from the pivotal statistic Z, where Zfollows a standard normal distribution, another confidence interval is constructed based on the generalized confidence interval (Weerahandi [8]). The performance of the proposed methods is assessed through Monte Carlo simulation studies. Coverage probabilities and expected lengths of these confidence intervals are used to assess these confidence intervals. |
Keywords and phrases: coefficient of variation. |
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