Approximate confidence interval for the reciprocal of a normal mean with a known coefficient of variation

An approximate confidence interval for the reciprocal of a normal population mean with a known coefficient of variation is proposed. This has applications in the area of nuclear physics, agriculture and economic when the researcher knows the coefficient of variation. The proposed confidence interval is based on the approximate expectation and variance of the estimator by Taylor series expansion. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence interval with the existing confidence interval. Simulation results show that the proposed confidence interval performs as well as the existing one in terms of coverage probability. However, the approximate confidence interval is very easy to calculate compared with the exact confidence interval.