Model misspecification is common in practice specially when the sampling mechanism is not known. A sized-biased sample arises in case where the probability of a unit of the population to be chosen in a sample is proportional to some nonnegative weight function w(x) of its size x. In this chapter, we study the model misspecification results when a sized-biased sample from the Weibull distribution is treated as a random one as well as when a random sample is treated as biased. Special attention is paid on the misspecification effects on the parameter estimation and on some of the most important characteristics of the distribution, such as the mean, the median, and the variance. It is proven that when we treat a biased sample as a random one, the parameters are overestimated and in the opposite case are underestimated. Simulation results verify the theoretical findings for small as well as for large samples.