# Confidence Interval for the Ratio of Bivariate Normal Means with a Known Coefficient of Variation

## Keywords:

Interval estimation, Central tendency, Standardized measure of dispersion, Coverage probability, Expected length## Abstract

An approximate confidence interval for the ratio of bivariate normal means with a known coefficient of variation is proposed in this paper. This application has the area of bioassay and bioequivalence when a scientist knows the coefficient of variation of a control group. The proposed confidence interval is based on the approximated expectation and variance of the estimator by the Taylor series expansion. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence interval with the existing confidence interval. The results showed that the simulation is considered confidence interval and the estimated coverage

probabilities close to the nominal confidence level for large sample sizes. The estimated coverage probabilities of the existing confidence interval are over estimated for all situations. In addition, the expected lengths of the proposed confidence interval are shorter than those of the existing confidence interval in all circumstances. When the sample size increases, the expected length become shorter. Therefore, our confidence interval presented in this paper performs well in terms of estimated coverage probability and the expected length in considering the simulation results. A comparison of the confidence intervals is also illustrated using an empirical application

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*Suan Sunandha Science and Technology Journal*,

*4*(1), 1–13. Retrieved from https://li02.tci-thaijo.org/index.php/ssstj/article/view/293