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In the paper, the relative potency of two drugs using confidence intervals for the ratio of two means of normal distributions with unknown coefficients of variation is considered. The new confidence intervals were constructed using the large sample approach, the method of variance estimates recovery (MOVER) approach, and then compared with the existing approach: the generalized confidence interval (GCI) approach of Lee and Lin [1]. A simulation study showed that the large sample approach can be used to estimate the confidence interval for the ratio of normal means with unknown coefficients of variation when the value of σY /σX is small otherwise the GCI approach is recommended when the value of σY/σX is large. Applications to drug testing and carboxyhemoglobin test are included.

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