This paper provides four well-known statistical inferences for the principal parameters regarding the two-parameter Weibull distribution including its hazard, quantile, and survival function based on an adaptive progressive type-II censoring plan. The statistical inferences involve the likelihood and approximate likelihood methods, the Bayesian approach, the bootstrap procedure, and a new conditional technique. To construct Bayesian point estimators and credible intervals, Markov chain Monte Carlo, Metropolis-Hastings, and Gibbs sampling algorithms were used. The Bayesian estimators are developed under conjugate and non-conjugate priors and in the presence of symmetric and asymmetric loss functions. In addition, a conditional estimation technique with interesting distributional characteristics has been introduced. The aforementioned methods are compared extensively through a series of simulations. The results of comparative study showed the superiority of the conditional approach over the other ones. Finally, the developed methods are applied to analyze well-known wind speed data.