In censored type II sampling, the total number, n, of individuals may be unknown. If the parent distribution is the one parameter exponential distribution, Blumenthal and Marcus (1975) estimated n using Bayesian and non-Bayesian approaches under the assumption that n treated as an integer value. In the present work we shall extend their results to the case where the underlying life time distribution is Weibull probability density function under the assumption that n will be treated as an continuous variable**. The extension will include the non-Bayesian and Bayesian estimators of the parameters and the unknown sample size n. A numerical investigation will be present for some difficult formulas using random numbers and computer facilities. A numerical comparison between Bayesian and non-Bayesian results will be made under the above two restrictions.