**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**33006

##### Confidence Intervals for the Normal Mean with Known Coefficient of Variation

**Authors:**
Suparat Niwitpong

**Abstract:**

In this paper we proposed two new confidence intervals for the normal population mean with known coefficient of variation. This situation occurs normally in environment and agriculture experiments where the scientist knows the coefficient of variation of their experiments. We propose two new confidence intervals for this problem based on the recent work of Searls [5] and the new method proposed in this paper for the first time. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. Monte Carlo simulation will be used to assess the performance of these intervals based on their expected lengths.

**Keywords:**
confidence interval,
coverage probability,
expected length,
known coefficient of variation.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1334868

**References:**

[1] K. Bhat and K. A. Rao, On Tests for a Normal Mean with Known Coefficient of Variation, International Statistical Review , 75 (2007), 170-182

[2] V. Brazauskas and J. Ghorai, Estimating the common parameter of normal models with known coefficients of variation: a sensitivity study of asymptotically efficient estimators, Journal of Statistical Computation and Simulation, 77( 2007), 663-681

[3] R. A. Khan, A Note on Estimating the Mean of a Normal Distribution with Known Coefficient of Variation, Journal of the American Statistical Association, 63(1968), 1039-1041.

[4] S. Niwitpong and S. Niwitpong, Confidence interval for the difference of two normal population means with a known ratio of variances, Applied Mathematical Sciences , 4 (2010), 347 - 359.

[5] D. T. Searls, A Note on the Use of an Approximately Known Coefficient of Variation, The American Statistician, 21(1967), 20-21.

[6] D. T. Searls, The Utilization of a Known Coefficient of Variation in the Estimation Procedure, Journal of the American Statistical Association, 59(1964), 1225-1226.

[7] R.E. Walpole, R. H. Myers, S.L. Myers, K. Ye., Probability & Statistics for Engineers & Scientists, Prentice Hall, New Jersey, 2002.